diff --git a/README.md b/README.md index b0314243..aeca5d4c 100644 --- a/README.md +++ b/README.md @@ -1,8 +1,8 @@ -# dotSCAD 1.3 +# dotSCAD 2 (RC) -> Reduce the burden of 3D modeling in mathematics. Compatible with OpenSCAD 2015.03 or laters. +> **Reduce the burden of 3D modeling in mathematics. Based on OpenSCAD 2019.05.** -![dotSCAD](WhirlingTaiwan.JPG) +![dotSCAD](TaiwaneseBlackBear.JPG) [![license/LGPL](https://img.shields.io/badge/license-LGPL-blue.svg)](https://github.com/JustinSDK/lib-openscad/blob/master/LICENSE) @@ -16,6 +16,16 @@ Every module or function is located in the file which has the same name as the m line2d(p1 = [0, 0], p2 = [5, 0], width = 1); +Some module files are organized in a directory. For example, px_circle.scad exists in `pixel` directory. You have to prefix the directory name when including `px_circle`. + + include ; + points = px_circle(radius = 10); + for(pt = points) { + translate(pt) square(1); + } + +## Dependencies + Some modules depend on other modules. For example, the `polyline2d` module depends on the `line2d` module, so you also have to `include ;` besides `include ;`. include ; @@ -23,11 +33,11 @@ Some modules depend on other modules. For example, the `polyline2d` module depen polyline2d(points = [[1, 2], [-5, -4], [-5, 3], [5, 5]], width = 1); -If OpenSCAD generates "WARNING: Ignoring unknown xxx function" or "WARNING: Ignoring unknown xxx module" when using one module of dotSCAD. Just try to `include ;`. +If OpenSCAD generates "WARNING: Ignoring unknown xxx function" or "WARNING: Ignoring unknown xxx module" when using one module of dotSCAD. Just try to `include ;` or `include ` if xxx.scad exists in `dir` directory. Too many dependencies? Because OpenSCAD doesn't provide namespace management, I personally think that exposing dependencies is better than hiding them. In this way, users can have their own way to manage dependencies. How to categorize dependencies is up to you. For example, you can include your commonly-used modules and functions in "commonly_used.scad" and then `include ;` in the ".scad" file of your project. -If you really don't want to care about dependencies, `include ;` or `use ;` come to save you. +**If you really don't want to care about dependencies, `include ;` or `use ;` come to save you.** ## Documentation @@ -63,12 +73,9 @@ If you really don't want to care about dependencies, `include ;` o - Functon - [rotate_p](https://openhome.cc/eGossip/OpenSCAD/lib-rotate_p.html) - - [sub_str](https://openhome.cc/eGossip/OpenSCAD/lib-sub_str.html) - - [split_str](https://openhome.cc/eGossip/OpenSCAD/lib-split_str.html) - - [parse_number](https://openhome.cc/eGossip/OpenSCAD/lib-parse_number.html) - [cross_sections](https://openhome.cc/eGossip/OpenSCAD/lib-cross_sections.html) - [paths2sections](https://openhome.cc/eGossip/OpenSCAD/lib-paths2sections.html) - - [path_scaling_sections](https://openhome.cc/eGossip/OpenSCAD/lib-path_scaling_sections.html) + - [path_scaling_sections](https://openhome.cc/eGossip/OpenSCAD/lib2-path_scaling_sections.html) - [bijection_offset](https://openhome.cc/eGossip/OpenSCAD/lib-bijection_offset.html) - [in_polyline](https://openhome.cc/eGossip/OpenSCAD/lib-in_polyline.html) - [in_shape](https://openhome.cc/eGossip/OpenSCAD/lib-in_shape.html) @@ -117,19 +124,34 @@ If you really don't want to care about dependencies, `include ;` o - [archimedean_spiral_extrude](https://openhome.cc/eGossip/OpenSCAD/lib-archimedean_spiral_extrude.html) - [sphere_spiral_extrude](https://openhome.cc/eGossip/OpenSCAD/lib-sphere_spiral_extrude.html) +- Utilities + - [util/sub_str](https://openhome.cc/eGossip/OpenSCAD/lib2-sub_str.html) + - [util/split_str](https://openhome.cc/eGossip/OpenSCAD/lib2-split_str.html) + - [util/parse_number](https://openhome.cc/eGossip/OpenSCAD/lib2-parse_number.html) + - [util/reverse](https://openhome.cc/eGossip/OpenSCAD/lib2-reverse.html) + - [util/slice](https://openhome.cc/eGossip/OpenSCAD/lib2-slice.html) + - [util/sort](https://openhome.cc/eGossip/OpenSCAD/lib2-sort.html) + - Matrix - - [m_cumulate](https://openhome.cc/eGossip/OpenSCAD/lib-m_cumulate.html) - - [m_translation](https://openhome.cc/eGossip/OpenSCAD/lib-m_translation.html) - - [m_rotation](https://openhome.cc/eGossip/OpenSCAD/lib-m_rotation.html) - - [m_scaling](https://openhome.cc/eGossip/OpenSCAD/lib-m_scaling.html) - - [m_mirror](https://openhome.cc/eGossip/OpenSCAD/lib-m_mirror.html) - - [m_shearing](https://openhome.cc/eGossip/OpenSCAD/lib-m_shearing.html) + - [matrix/m_cumulate](https://openhome.cc/eGossip/OpenSCAD/lib2-m_cumulate.html) + - [matrix/m_translation](https://openhome.cc/eGossip/OpenSCAD/lib2-m_translation.html) + - [matrix/m_rotation](https://openhome.cc/eGossip/OpenSCAD/lib2-m_rotation.html) + - [matrix/m_scaling](https://openhome.cc/eGossip/OpenSCAD/lib2-m_scaling.html) + - [matrix/m_mirror](https://openhome.cc/eGossip/OpenSCAD/lib2-m_mirror.html) + - [matrix/m_shearing](https://openhome.cc/eGossip/OpenSCAD/lib2-m_shearing.html) -- Other - - [turtle2d](https://openhome.cc/eGossip/OpenSCAD/lib-turtle2d.html) - - [turtle3d](https://openhome.cc/eGossip/OpenSCAD/lib-turtle3d.html) - - [log](https://openhome.cc/eGossip/OpenSCAD/lib-log.html) +- Turtle + - [turtle/turtle2d](https://openhome.cc/eGossip/OpenSCAD/lib2-turtle2d.html) + - [turtle/turtle3d](https://openhome.cc/eGossip/OpenSCAD/lib2-turtle3d.html) +- Pixel + - [pixel/px_line](https://openhome.cc/eGossip/OpenSCAD/lib2-px_line.html) + - [pixel/px_polyline](https://openhome.cc/eGossip/OpenSCAD/lib2-px_polyline.html) + - [pixel/px_circle](https://openhome.cc/eGossip/OpenSCAD/lib2-px_circle.html) + - [pixel/px_cylinder](https://openhome.cc/eGossip/OpenSCAD/lib2-px_cylinder.html) + - [pixel/px_sphere](https://openhome.cc/eGossip/OpenSCAD/lib2-px_sphere.html) + - [pixel/px_polygon](https://openhome.cc/eGossip/OpenSCAD/lib2-px_polygon.html) + ## Bugs and Feedback For bugs, questions and discussions please use the [Github Issues](https://github.com/JustinSDK/dotSCAD/issues). diff --git a/RELEASE.md b/RELEASE.md index 16f2767f..313be215 100644 --- a/RELEASE.md +++ b/RELEASE.md @@ -1,5 +1,23 @@ > Version numbers are based on [Semantic Versioning](https://semver.org/). +# v2.0 +- Use new features of OpenSCAD-2019.05 to refactor internal implementation. +- Delete the `log` module which is never used. +- Directory changed. + - `m_cumulate`, `m_mirror`, `m_rotation`, `m_scaling`, `m_shearing` and `m_translation` are moved into the `matrix` directory. + - `turtle2d` and `turtle3d` are moved into the `turtle` directory. + - `parse_number`, `split_str` and `sub_str` are moved into the `util` directory. +- New modules and functions. + - [pixel/px_line](https://openhome.cc/eGossip/OpenSCAD/lib2-px_line.html) + - [pixel/px_polyline](https://openhome.cc/eGossip/OpenSCAD/lib2-px_polyline.html) + - [pixel/px_circle](https://openhome.cc/eGossip/OpenSCAD/lib2-px_circle.html) + - [pixel/px_cylinder](https://openhome.cc/eGossip/OpenSCAD/lib2-px_cylinder.html) + - [pixel/px_sphere](https://openhome.cc/eGossip/OpenSCAD/lib2-px_sphere.html) + - [pixel/px_polygon](https://openhome.cc/eGossip/OpenSCAD/lib2-px_polygon.html) + - [util/reverse](https://openhome.cc/eGossip/OpenSCAD/lib2-reverse.html) + - [util/slice](https://openhome.cc/eGossip/OpenSCAD/lib2-slice.html) + - [util/sort](https://openhome.cc/eGossip/OpenSCAD/lib2-sort.html) + # v1.3.3 - Bugfixes - `in_shape`: Wrong variable name. diff --git a/TaiwaneseBlackBear.JPG b/TaiwaneseBlackBear.JPG new file mode 100644 index 00000000..034759f2 Binary files /dev/null and b/TaiwaneseBlackBear.JPG differ diff --git a/all/dotSCAD.scad b/all/dotSCAD.scad index f26a1e46..939a7d0d 100644 --- a/all/dotSCAD.scad +++ b/all/dotSCAD.scad @@ -27,6 +27,7 @@ include ; include ; include ; include ; +<<<<<<< HEAD include ; include ; include ; @@ -37,6 +38,10 @@ include ; include ; include ; include ; +======= +include ; +include ; +>>>>>>> v2 include ; include ; include ; @@ -66,6 +71,7 @@ include ; include ; include ; include ; +<<<<<<< HEAD include ; include ; include ; @@ -76,4 +82,33 @@ include ; include ; include ; include ; -include ; \ No newline at end of file +include ; +======= +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +>>>>>>> v2 diff --git a/docs/images/lib2-px_circle-1.JPG b/docs/images/lib2-px_circle-1.JPG new file mode 100644 index 00000000..271049cc Binary files /dev/null and b/docs/images/lib2-px_circle-1.JPG differ diff --git a/docs/images/lib2-px_circle-2.JPG b/docs/images/lib2-px_circle-2.JPG new file mode 100644 index 00000000..9c0908ee Binary files /dev/null and b/docs/images/lib2-px_circle-2.JPG differ diff --git a/docs/images/lib2-px_cylinder-1.JPG b/docs/images/lib2-px_cylinder-1.JPG new file mode 100644 index 00000000..cc67dd68 Binary files /dev/null and b/docs/images/lib2-px_cylinder-1.JPG differ diff --git a/docs/images/lib2-px_cylinder-2.JPG b/docs/images/lib2-px_cylinder-2.JPG new file mode 100644 index 00000000..fcfd565c Binary files /dev/null and b/docs/images/lib2-px_cylinder-2.JPG differ diff --git a/docs/images/lib2-px_line-1.JPG b/docs/images/lib2-px_line-1.JPG new file mode 100644 index 00000000..e7fa7f50 Binary files /dev/null and b/docs/images/lib2-px_line-1.JPG differ diff --git a/docs/images/lib2-px_line-2.JPG b/docs/images/lib2-px_line-2.JPG new file mode 100644 index 00000000..dc99811c Binary files /dev/null and b/docs/images/lib2-px_line-2.JPG differ diff --git a/docs/images/lib2-px_polygon-1.JPG b/docs/images/lib2-px_polygon-1.JPG new file mode 100644 index 00000000..bc5928be Binary files /dev/null and b/docs/images/lib2-px_polygon-1.JPG differ diff --git a/docs/images/lib2-px_polyline-1.JPG b/docs/images/lib2-px_polyline-1.JPG new file mode 100644 index 00000000..cc2a2e85 Binary files /dev/null and b/docs/images/lib2-px_polyline-1.JPG differ diff --git a/docs/images/lib2-px_polyline-2.JPG b/docs/images/lib2-px_polyline-2.JPG new file mode 100644 index 00000000..302b2ed4 Binary files /dev/null and b/docs/images/lib2-px_polyline-2.JPG differ diff --git a/docs/images/lib2-px_sphere-1.JPG b/docs/images/lib2-px_sphere-1.JPG new file mode 100644 index 00000000..3d823a20 Binary files /dev/null and b/docs/images/lib2-px_sphere-1.JPG differ diff --git a/docs/lib-archimedean_spiral_extrude.md b/docs/lib-archimedean_spiral_extrude.md index 41e5e3b3..6929701d 100644 --- a/docs/lib-archimedean_spiral_extrude.md +++ b/docs/lib-archimedean_spiral_extrude.md @@ -4,8 +4,6 @@ Extrudes a 2D shape along the path of an archimedean spiral. When using this module, you should use points to represent the 2D shape. If your 2D shape is not solid, indexes of triangles are required. See [polysections](https://openhome.cc/eGossip/OpenSCAD/lib-polysections.html) for details. -Dependencies: `rotate_p`, `archimedean_spiral`, `cross_sections`, `polysections`. - ## Parameters - `shape_pts` : A list of points represent a shape. See the example below. diff --git a/docs/lib-bezier_smooth.md b/docs/lib-bezier_smooth.md index 4ab9057d..99daef6c 100644 --- a/docs/lib-bezier_smooth.md +++ b/docs/lib-bezier_smooth.md @@ -2,8 +2,6 @@ Given a path, the `bezier_smooth` function uses bazier curves to smooth all corners. You can use it to create smooth lines or rounded shapes. -Dependencies: the `bezier_curve` function. - ## Parameters - `path_pts` : A list of points represent the path. diff --git a/docs/lib-bezier_surface.md b/docs/lib-bezier_surface.md index 494dbce6..ad969885 100644 --- a/docs/lib-bezier_surface.md +++ b/docs/lib-bezier_surface.md @@ -2,8 +2,6 @@ Given a set of control points, the `bezier_surface` function returns points of the Bézier surface. Combined with the `function_grapher` module defined in my library, you can create a Bézier surface. -It depends on the `bezier_curve` function so remember to include bezier_curve.scad. - ## Parameters - `t_step` : The distance between two points of the Bézier path. diff --git a/docs/lib-cross_sections.md b/docs/lib-cross_sections.md index d04def35..c52d6266 100644 --- a/docs/lib-cross_sections.md +++ b/docs/lib-cross_sections.md @@ -2,8 +2,6 @@ Given a 2D shape, points and angles along the path, this function will return all cross-sections. Combined with the `polysections` module, you can create a specific path extrusion. -It depends on the `rotate_p` function. Remember to include "rotate_p.scad". - ## Parameters - `shape_pts`: A list of points represent a shape. See the example below. diff --git a/docs/lib-crystal_ball.md b/docs/lib-crystal_ball.md index c8c193c4..a5c7b076 100644 --- a/docs/lib-crystal_ball.md +++ b/docs/lib-crystal_ball.md @@ -4,8 +4,6 @@ Uses spherical coordinate system to create a crystal ball. ![Spherical coordinates (r, θ, φ) often used in mathematics](https://upload.wikimedia.org/wikipedia/commons/d/dc/3D_Spherical_2.svg) -Dependencies: `rotate_p`, `cross_sections`, `polysections`, `ring_extrude`, `shape_pie`. - ## Parameters - `radius` : The radial distance r. diff --git a/docs/lib-function_grapher.md b/docs/lib-function_grapher.md index a313adc6..ec8e8180 100644 --- a/docs/lib-function_grapher.md +++ b/docs/lib-function_grapher.md @@ -2,8 +2,6 @@ Given a set of points `[x, y, f(x, y)]` where `f(x, y)` is a mathematics function, the `function_grapher` module can create the graph of `f(x, y)`. -It depends on the `line3d`, `polyline3d`, `hull_polyline3d` modules so you have to include "line3d.scad", "polyline3d.scad" and "hull_polyline3d.scad". - ## Parameters - `points` : A set of points `[x, y, f(x, y)]`. See examples below. diff --git a/docs/lib-golden_spiral.md b/docs/lib-golden_spiral.md index 6968de9f..fbc22fae 100644 --- a/docs/lib-golden_spiral.md +++ b/docs/lib-golden_spiral.md @@ -4,8 +4,6 @@ Gets all points and angles on the path of a golden spiral based on Fibonacci num It returns a vector of `[[x, y], angle]`. -Because of depending on `circle_path` and `rotate_p`, remember to include "circle_path.scad" and "rotate_p.scad". - ## Parameters - `from` : The nth Fibonacci number you wanna start from. diff --git a/docs/lib-golden_spiral_extrude.md b/docs/lib-golden_spiral_extrude.md index 64bead22..b5c6b100 100644 --- a/docs/lib-golden_spiral_extrude.md +++ b/docs/lib-golden_spiral_extrude.md @@ -4,8 +4,6 @@ Extrudes a 2D shape along the path of a golden spiral. When using this module, you should use points to represent the 2D shape. If your 2D shape is not solid, indexes of triangles are required. See [polysections](https://openhome.cc/eGossip/OpenSCAD/lib-polysections.html) for details. -Dependencies: `circle_path`, `rotate_p`, `golden_spiral`, `cross_sections`, `polysections`. - ## Parameters - `shape_pts` : A list of points represent a shape. See the example below. diff --git a/docs/lib-helix_extrude.md b/docs/lib-helix_extrude.md index 7e0b2a89..3951a134 100644 --- a/docs/lib-helix_extrude.md +++ b/docs/lib-helix_extrude.md @@ -6,8 +6,6 @@ When using this module, you should use points to represent the 2D shape. If your Its `$fa`, `$fs` and `$fn` parameters are consistent with the `cylinder` module. -Dependencies: `helix`, `rotate_p`, `cross_sections`, `polysections`. - ## Parameters - `shape_pts` : A list of points represent a shape. See the example below. diff --git a/docs/lib-log.md b/docs/lib-log.md deleted file mode 100644 index d60249d7..00000000 --- a/docs/lib-log.md +++ /dev/null @@ -1,46 +0,0 @@ -# log - -A log module which supports simple level configurations and color titles. - -## Parameters - -- `$log_level` : The accepted values are `"OFF"` (-1), `"INFO"` (20), - `"WARNING"` (30), `"ERROR"` (40) or positive integers. The default value is `"INFO"`. -- `level` : The accepted values are `"OFF"` (-1), `"INFO"` (20), - `"WARNING"` (30), `"ERROR"` (40) or positive integers. If the value is greater or equal to `$log_level`, the `echo` message will display in the console. -- `level_color` : Controls the color of level title. It accepts the same values as the CSS `color` property. - -## Examples - - include ; - - log() - echo(" INFO message"); - - log("WARNING") - echo(" WARNING message"); - - log("ERROR") { - echo(" ERROR message 1"); - echo(" ERROR message 2"); - } - -![log](images/lib-log-1.JPG) - - include ; - - $log_level = "WARNING"; - - log() - echo(" INFO message"); - - log("WARNING", "purple") - echo(" WARNING message"); - - log("ERROR", "rgb(255, 100, 100)") { - echo(" ERROR message 1"); - echo(" ERROR message 2"); - } - -![log](images/lib-log-2.JPG) - diff --git a/docs/lib-parse_number.md b/docs/lib-parse_number.md deleted file mode 100644 index 4312a01d..00000000 --- a/docs/lib-parse_number.md +++ /dev/null @@ -1,16 +0,0 @@ -# parse_number - -Parses the string argument as an number. It depends on the `split_str` and the `sub_str` functions so remember to include split_str.scad and sub_str.scad. - -## Parameters - -- `t` : A string containing the number representation to be parsed. - -## Examples - - include ; - include ; - include ; - - echo(parse_number("10") + 1); // ECHO: 11 - echo(parse_number("-1.1") + 1); // ECHO: -0.1 diff --git a/docs/lib-path_extrude.md b/docs/lib-path_extrude.md index edd92bbc..c8425f9f 100644 --- a/docs/lib-path_extrude.md +++ b/docs/lib-path_extrude.md @@ -2,8 +2,6 @@ It extrudes a 2D shape along a path. This module is suitable for a path created by a continuous function. -It depends on the `rotate_p` function and the `polysections` module. Remember to include "rotate_p.scad" and "polysections.scad". - When using this module, you should use points to represent the 2D shape. If your 2D shape is not solid, indexes of triangles are required. See [polysections](https://openhome.cc/eGossip/OpenSCAD/lib-polysections.html) for details. ## Parameters diff --git a/docs/lib-polyline2d.md b/docs/lib-polyline2d.md index 98d4e560..b7674673 100644 --- a/docs/lib-polyline2d.md +++ b/docs/lib-polyline2d.md @@ -1,6 +1,6 @@ # polyline2d -Creates a polyline from a list of `x`, `y` coordinates. When the end points are `CAP_ROUND`, you can use `$fa`, `$fs` or `$fn` to controll the circle module used internally. It depends on the `line2d` module so you have to `include` line2d.scad. +Creates a polyline from a list of `x`, `y` coordinates. When the end points are `CAP_ROUND`, you can use `$fa`, `$fs` or `$fn` to controll the circle module used internally. ## Parameters diff --git a/docs/lib-polyline3d.md b/docs/lib-polyline3d.md index ef6f1614..ac123ffb 100644 --- a/docs/lib-polyline3d.md +++ b/docs/lib-polyline3d.md @@ -1,6 +1,6 @@ # polyline3d -Creates a polyline from a list of `[x, y, z]` coordinates. It depends on the `line3d` module so you have to `include` line3d.scad. +Creates a polyline from a list of `[x, y, z]` coordinates. ## Parameters diff --git a/docs/lib-ring_extrude.md b/docs/lib-ring_extrude.md index fe88e3c4..823f9dfc 100644 --- a/docs/lib-ring_extrude.md +++ b/docs/lib-ring_extrude.md @@ -4,8 +4,6 @@ Rotational extrusion spins a 2D shape around the Z-axis. It's similar to the bui Because we cannot retrieve the shape points of built-in 2D modules, it's necessary to provide `shapt_pts` and `triangles`. -This module depends on `rotate_p`, `cross_section` and `polysections`. Remember to include corresponding ".scad". - If your 2D shape is not solid, indexes of triangles are required. See [polysections](https://openhome.cc/eGossip/OpenSCAD/lib-polysections.html) for details. ## Parameters diff --git a/docs/lib-shape_glued2circles.md b/docs/lib-shape_glued2circles.md index e9894500..1568fb2b 100644 --- a/docs/lib-shape_glued2circles.md +++ b/docs/lib-shape_glued2circles.md @@ -2,8 +2,6 @@ Returns shape points of two glued circles. They can be used with xxx_extrude modules of dotSCAD. The shape points can be also used with the built-in polygon module. -Dependencies: `rotate_p`, `bezier_curve`, `shape_pie`. - ## Parameters - `radius` : The radius of two circles. diff --git a/docs/lib-shape_path_extend.md b/docs/lib-shape_path_extend.md index af34bbac..f9fc36b0 100644 --- a/docs/lib-shape_path_extend.md +++ b/docs/lib-shape_path_extend.md @@ -4,8 +4,6 @@ It extends a 2D stroke along a path to create a 2D shape. This module is suitabl When using this function, you should use points to represent the 2D stroke. -It depends on the `rotate_p` function. Remember to include "rotate_p.scad". - ## Parameters - `stroke_pts` : A list of points represent a stroke. See the example below. diff --git a/docs/lib-sphere_spiral.md b/docs/lib-sphere_spiral.md index 9b776716..2c6adde2 100644 --- a/docs/lib-sphere_spiral.md +++ b/docs/lib-sphere_spiral.md @@ -1,6 +1,6 @@ # sphere_spiral -Creates all points and angles on the path of a spiral around a sphere. It returns a vector of `[[x, y, z], [ax, ay, az]]`. `[x, y, z]` is actually obtained from rotating `[radius, 0, 0]` by `[ax, ay, az]`. It depends on the `rotate_p` function. Remember to include rotate_p.scad first. +Creates all points and angles on the path of a spiral around a sphere. It returns a vector of `[[x, y, z], [ax, ay, az]]`. `[x, y, z]` is actually obtained from rotating `[radius, 0, 0]` by `[ax, ay, az]`. ## Parameters diff --git a/docs/lib-sphere_spiral_extrude.md b/docs/lib-sphere_spiral_extrude.md index 44f5d17a..53ceea4b 100644 --- a/docs/lib-sphere_spiral_extrude.md +++ b/docs/lib-sphere_spiral_extrude.md @@ -4,8 +4,6 @@ Extrudes a 2D shape along the path of a sphere spiral. When using this module, you should use points to represent the 2D shape. If your 2D shape is not solid, indexes of triangles are required. See [polysections](https://openhome.cc/eGossip/OpenSCAD/lib-polysections.html) for details. -Dependencies: `rotate_p`, `sphere_spiral`, `cross_sections`, `polysections`. - ## Parameters - `shape_pts` : A list of points represent a shape. See the example below. diff --git a/docs/lib-m_cumulate.md b/docs/lib2-m_cumulate.md similarity index 72% rename from docs/lib-m_cumulate.md rename to docs/lib2-m_cumulate.md index ff1b604e..207cd103 100644 --- a/docs/lib-m_cumulate.md +++ b/docs/lib2-m_cumulate.md @@ -6,14 +6,16 @@ The power of using transformation matrice is that you can cumulate all transform ## Parameters +The dir changed since 2.0. + - `matrice` : A list of 4x4 transformation matrice. ## Examples - include ; - include ; - include ; - include + include ; + include ; + include ; + include m = m_cumulate([ m_translation([10, 20, 10]), m_scaling(2), m_rotation(60)] diff --git a/docs/lib2-m_mirror.md b/docs/lib2-m_mirror.md new file mode 100644 index 00000000..744649c0 --- /dev/null +++ b/docs/lib2-m_mirror.md @@ -0,0 +1,25 @@ +# m_mirror + +The dir changed since 2.0. + +Generate a 4x4 transformation matrix which can pass into `multmatrix` to mirror the child element on a plane through the origin. + +**Since:** 1.1 + +## Parameters + +- `v` : The normal vector of a plane intersecting the origin through which to mirror the object. + +## Examples + + include ; + + rotate([0, 0, 10]) + cube([3, 2, 1]); + + multmatrix(m_mirror([1, 1, 0])) + rotate([0, 0, 10]) + cube([3, 2, 1]); + +![m_mirror](images/lib-m_mirror-1.JPG) + diff --git a/docs/lib-m_rotation.md b/docs/lib2-m_rotation.md similarity index 94% rename from docs/lib-m_rotation.md rename to docs/lib2-m_rotation.md index 5fc24248..b546dd98 100644 --- a/docs/lib-m_rotation.md +++ b/docs/lib2-m_rotation.md @@ -1,5 +1,7 @@ # m_rotation +The dir changed since 2.0. + Generate a 4x4 transformation matrix which can pass into `multmatrix` to rotate the child element about the axis of the coordinate system or around an arbitrary axis. **Since:** 1.1 @@ -11,7 +13,7 @@ Generate a 4x4 transformation matrix which can pass into `multmatrix` to rotate ## Examples - include ; + include ; point = [20, 0, 0]; a = [0, -45, 45]; diff --git a/docs/lib-m_scaling.md b/docs/lib2-m_scaling.md similarity index 85% rename from docs/lib-m_scaling.md rename to docs/lib2-m_scaling.md index ad695763..f4c13ce3 100644 --- a/docs/lib-m_scaling.md +++ b/docs/lib2-m_scaling.md @@ -1,5 +1,7 @@ # m_scaling +The dir changed since 2.0. + Generate a 4x4 transformation matrix which can pass into `multmatrix` to scale its child elements using the specified vector. **Since:** 1.1 @@ -10,7 +12,7 @@ Generate a 4x4 transformation matrix which can pass into `multmatrix` to scale i ## Examples - include ; + include ; cube(10); translate([15, 0, 0]) diff --git a/docs/lib-m_shearing.md b/docs/lib2-m_shearing.md similarity index 95% rename from docs/lib-m_shearing.md rename to docs/lib2-m_shearing.md index 6f3a6868..de7e07d2 100644 --- a/docs/lib-m_shearing.md +++ b/docs/lib2-m_shearing.md @@ -1,5 +1,7 @@ # m_shearing +The dir changed since 2.0. + Generate a 4x4 transformation matrix which can pass into `multmatrix` to shear all child elements along the X-axis, Y-axis, or Z-axis in 3D. **Since:** 1.1 @@ -12,7 +14,7 @@ Generate a 4x4 transformation matrix which can pass into `multmatrix` to shear a ## Examples - include ; + include ; color("red") { multmatrix(m_shearing(sx = [1, 0])) diff --git a/docs/lib-m_translation.md b/docs/lib2-m_translation.md similarity index 85% rename from docs/lib-m_translation.md rename to docs/lib2-m_translation.md index e8bed044..9efd52f0 100644 --- a/docs/lib-m_translation.md +++ b/docs/lib2-m_translation.md @@ -1,5 +1,7 @@ # m_translation +The dir changed since 2.0. + Generate a 4x4 transformation matrix which can pass into `multmatrix` to translates (moves) its child elements along the specified vector. **Since:** 1.1 @@ -10,7 +12,7 @@ Generate a 4x4 transformation matrix which can pass into `multmatrix` to transla ## Examples - include ; + include ; cube(2, center = true); multmatrix(m_translation([5, 0, 0])) diff --git a/docs/lib2-parse_number.md b/docs/lib2-parse_number.md new file mode 100644 index 00000000..95a0c861 --- /dev/null +++ b/docs/lib2-parse_number.md @@ -0,0 +1,18 @@ +# parse_number + +The dir changed since 2.0. + +Parses the string argument as an number. + +## Parameters + +- `t` : A string containing the number representation to be parsed. + +## Examples + + include ; + include ; + include ; + + echo(parse_number("10") + 1); // ECHO: 11 + echo(parse_number("-1.1") + 1); // ECHO: -0.1 diff --git a/docs/lib-path_scaling_sections.md b/docs/lib2-path_scaling_sections.md similarity index 96% rename from docs/lib-path_scaling_sections.md rename to docs/lib2-path_scaling_sections.md index e8392b3e..ce393a37 100644 --- a/docs/lib-path_scaling_sections.md +++ b/docs/lib2-path_scaling_sections.md @@ -18,7 +18,6 @@ You can use any point as the first point of the edge path. Just remember that yo include ; include ; include ; - include ; include ; taiwan = shape_taiwan(100); @@ -42,7 +41,6 @@ You can use any point as the first point of the edge path. Just remember that yo include ; include ; include ; - include ; include ; include ; @@ -67,7 +65,6 @@ You can use any point as the first point of the edge path. Just remember that yo include ; include ; - include ; include ; include ; include ; @@ -105,7 +102,6 @@ You can use any point as the first point of the edge path. Just remember that yo include ; include ; include ; - include ; include ; include ; diff --git a/docs/lib2-px_circle.md b/docs/lib2-px_circle.md new file mode 100644 index 00000000..18d5e16b --- /dev/null +++ b/docs/lib2-px_circle.md @@ -0,0 +1,32 @@ +# px_circle + +Returns points that can be used to draw a pixel-style circle. + +**Since:** 2.0 + +## Parameters + +- `radius` : The circle radius. The value must be an integer. +- `filled` : Default to `false`. Set it `true` if you want a filled circle. + +## Examples + + include ; + + for(pt = px_circle(10)) { + translate(pt) + square(1, center = true); + } + +![px_circle](images/lib2-px_circle-1.JPG) + + include ; + + for(pt = px_circle(10, filled = true)) { + translate(pt) + linear_extrude(1, scale = 0.5) + square(1, center = true); + } + +![px_circle](images/lib2-px_circle-2.JPG) + diff --git a/docs/lib2-px_cylinder.md b/docs/lib2-px_cylinder.md new file mode 100644 index 00000000..dd26b81f --- /dev/null +++ b/docs/lib2-px_cylinder.md @@ -0,0 +1,33 @@ +# px_cylinder + +Returns points that can be used to draw a pixel-style cylinder. + +**Since:** 2.0 + +## Parameters + +- `radius` : The radius of the cylinder. It also accepts a vector `[r1, r2]`. `r1` is the bottom radius and `r2` is the top radius of a cone. Values must be an integer. +- `h` : The height of the cylinder or cone. +- `filled` : Default to `false`. Set it `true` if you want a filled cylinder. +- `thickness`: Default to 1. The thickness when `filled` is `false`. The value must be an integer. + +## Examples + + include ; + + for(pt = px_cylinder([10, 15], 10)) { + translate(pt) + cube(1, center = true); + } + +![px_cylinder](images/lib2-px_cylinder-1.JPG) + + include ; + + for(pt = px_cylinder([20, 15], h = 10, thickness = 3)) { + translate(pt) + cube(1, center = true); + } + +![px_cylinder](images/lib2-px_cylinder-2.JPG) + diff --git a/docs/lib2-px_line.md b/docs/lib2-px_line.md new file mode 100644 index 00000000..284b9ca7 --- /dev/null +++ b/docs/lib2-px_line.md @@ -0,0 +1,31 @@ +# px_line + +Given two points. `px_line` returns points that can be used to draw a pixel-style line. + +**Since:** 2.0 + +## Parameters + +- `p1` : The start point `[x, y]` or `[x, y, z]`. x, y, z must be integer. +- `p2` : The end point `[x, y]` or `[x, y, z]`. x, y, z must be integer. + +## Examples + + include ; + + for(pt = px_line([-10, 0], [20, 50])) { + translate(pt) + square(1, center = true); + } + +![px_line](images/lib2-px_line-1.JPG) + + include ; + + for(pt = px_line([-10, 0, -10], [20, 50, 10])) { + translate(pt) + cube(1, center = true); + } + +![px_line](images/lib2-px_line-2.JPG) + diff --git a/docs/lib2-px_polygon.md b/docs/lib2-px_polygon.md new file mode 100644 index 00000000..1e326d91 --- /dev/null +++ b/docs/lib2-px_polygon.md @@ -0,0 +1,39 @@ +# px_polygon + +Returns points that can be used to draw a pixel-style polygon. + +**Since:** 2.0 + +## Parameters + +- `points` : A list of points. Each point can be `[x, y]`. x, y must be integer. +- `filled` : Default to `false`. Set it `true` if you want a filled polygon. + +## Examples + + include ; + include ; + include ; + include ; + include ; + + pentagram = [ + for(pt = shape_pentagram(15)) + [round(pt[0]), round(pt[1])] + ]; + + for(pt = px_polygon(pentagram)) { + translate(pt) + linear_extrude(1, scale = 0.5) + square(1, center = true); + } + + translate([30, 0]) + for(pt = px_polygon(pentagram, filled = true)) { + translate(pt) + linear_extrude(1, scale = 0.5) + square(1, center = true); + } + +![px_polygon](images/lib2-px_polygon-1.JPG) + diff --git a/docs/lib2-px_polyline.md b/docs/lib2-px_polyline.md new file mode 100644 index 00000000..220be428 --- /dev/null +++ b/docs/lib2-px_polyline.md @@ -0,0 +1,55 @@ +# px_polyline + +Given a list of points. `px_polyline` returns points that can be used to draw a pixel-style polyline. + +**Since:** 2.0 + +## Parameters + +- `points` : A list of points. Each point can be `[x, y]` or `[x, y, z]`. x, y, z must be integer. + +## Examples + + include ; + include ; + include ; + + pentagram = [ + for(pt = shape_pentagram(15)) + [round(pt[0]), round(pt[1])] + ]; + + for(pt = px_polyline(concat(pentagram, [pentagram[0]]))) { + translate(pt) + linear_extrude(1, scale = 0.5) + square(1, center = true); + } + +![px_polyline](images/lib2-px_polyline-1.JPG) + + include ; + include ; + include ; + include ; + + points_angles = sphere_spiral( + radius = 20, + za_step = 5 + ); + + points = [ + for(pa = points_angles) + let(pt = pa[0]) + [round(pt[0]), round(pt[1]), round(pt[2])] + ]; + + for(a = [0:30:330]) { + rotate(a) + for(pt = px_polyline(points)) { + translate(pt) + cube(1, center = true); + } + } + +![px_polyline](images/lib2-px_polyline-2.JPG) + diff --git a/docs/lib2-px_sphere.md b/docs/lib2-px_sphere.md new file mode 100644 index 00000000..5dcec60c --- /dev/null +++ b/docs/lib2-px_sphere.md @@ -0,0 +1,22 @@ +# px_sphere + +Returns points that can be used to draw a pixel-style sphere. + +**Since:** 2.0 + +## Parameters + +- `radius` : The radius of the sphere. The value must be an integer. +- `filled` : Default to `false`. Set it `true` if you want a filled sphere. +- `thickness`: Default to 1. The thickness when `filled` is `false`. The value must be an integer. + +## Examples + + include ; + + for(pt = px_sphere(10)) { + translate(pt) + cube(1, center = true); + } + +![px_sphere](images/lib2-px_sphere-1.JPG) diff --git a/docs/lib2-reverse.md b/docs/lib2-reverse.md new file mode 100644 index 00000000..fc8c7696 --- /dev/null +++ b/docs/lib2-reverse.md @@ -0,0 +1,16 @@ +# reverse + +Reverse a list. + +**Since: **: 2.0 + +## Parameters + +- `lt` : The list to be reversed. + +## Examples + + include ; + + echo(reverse([1, 2, 3])); // ECHO: [3, 2, 1] + diff --git a/docs/lib2-slice.md b/docs/lib2-slice.md new file mode 100644 index 00000000..6e656f45 --- /dev/null +++ b/docs/lib2-slice.md @@ -0,0 +1,18 @@ +# slice + +Returns a list selected from `begin` to `end`, or to the `end` of the list (`end` not included). + +**Since:** 2.0 + +## Parameters + +- `lt` : The original list. +- `begin` : The beginning index, inclusive. +- `end` : The ending index, exclusive. If it's omitted, the list begins with the character at the specified `begin` and extends to the end of the original list. + +## Examples + + include ; + + echo(slice([for(c = "helloworld") c], 0, 5)); // ECHO: ["h", "e", "l", "l", "o"] + echo(slice([for(c = "helloworld") c], 5)); // ECHO: ["w", "o", "r", "l", "d"] diff --git a/docs/lib2-sort.md b/docs/lib2-sort.md new file mode 100644 index 00000000..5d674771 --- /dev/null +++ b/docs/lib2-sort.md @@ -0,0 +1,32 @@ +# sort + +Sorts the elements of a list in ascending order. The list is a list-of-list construct, such as `[[a0, a1, a2...], [b0, b1, b2,...], [c0, c1, c2,...],...]`. When sorting, the function looks only at one index position of each sublist. + +**Since:** 2.0 + +## Parameters + +- `lt` : The original list. +- `by` : Can be `"x"`、`"y"`、`"z"`, or `"idx"` (Default). +- `idx` : When `by` is `"idx"`, the value of `idx` is used. The Default value is 0. + +## Examples + + include ; + + assert( + [[2, 0, 0], [5, 0, 0], [7, 0, 0], [9, 0, 0], [10, 0, 0]] == + sort([[10, 0, 0], [5, 0, 0], [7, 0, 0], [2, 0, 0], [9, 0, 0]]) + ); + + assert( + [[2, 0, 0], [5, 0, 0], [7, 0, 0], [9, 0, 0], [10, 0, 0]] == + sort([[10, 0, 0], [5, 0, 0], [7, 0, 0], [2, 0, 0], [9, 0, 0]], by = "x") + ); + + assert( + [[0, 2, 0], [0, 5, 0], [0, 7, 0], [0, 9, 0], [0, 10, 0]] == + sort([[0, 10, 0], [0, 5, 0], [0, 7, 0], [0, 2, 0], [0, 9, 0]], by = "idx", idx = 1) + ); + + diff --git a/docs/lib-split_str.md b/docs/lib2-split_str.md similarity index 63% rename from docs/lib-split_str.md rename to docs/lib2-split_str.md index fcbba9ef..d1d12636 100644 --- a/docs/lib-split_str.md +++ b/docs/lib2-split_str.md @@ -1,6 +1,8 @@ # split_str -Splits the given string around matches of the given delimiting character. It depeneds on the `sub_str` function so remember to `include `. +The dir changed since 2.0. + +Splits the given string around matches of the given delimiting character. ## Parameters @@ -9,8 +11,8 @@ Splits the given string around matches of the given delimiting character. It dep ## Examples - include ; - include ; + include ; + include ; echo(split_str("hello,world", ",")); // ECHO: ["hello", "world"] diff --git a/docs/lib-sub_str.md b/docs/lib2-sub_str.md similarity index 70% rename from docs/lib-sub_str.md rename to docs/lib2-sub_str.md index 2d565eae..a3d01e6a 100644 --- a/docs/lib-sub_str.md +++ b/docs/lib2-sub_str.md @@ -1,6 +1,8 @@ # sub_str -Returns a new string that is a substring of the given string. +The dir changed since 2.0. + +Returns the part of the string from `begin` to `end`, or to the `end` of the string (`end` not included). ## Parameters @@ -10,7 +12,7 @@ Returns a new string that is a substring of the given string. ## Examples - include ; + include ; echo(sub_str("helloworld", 0, 5)); // ECHO: "hello" echo(sub_str("helloworld", 5)); // ECHO: "world" diff --git a/docs/lib-turtle2d.md b/docs/lib2-turtle2d.md similarity index 97% rename from docs/lib-turtle2d.md rename to docs/lib2-turtle2d.md index 90112e45..71c844c1 100644 --- a/docs/lib-turtle2d.md +++ b/docs/lib2-turtle2d.md @@ -1,5 +1,7 @@ # turtle2d +The dir changed since 2.0. + An OpenSCAD implementation of Turtle Graphics. It moves on the xy plane. You can get the cooridinate `[x, y]` or `angle` of its current position. ## Parameters @@ -16,7 +18,7 @@ An OpenSCAD implementation of Turtle Graphics. It moves on the xy plane. You can ## Examples include ; - include ; + include ; module turtle_spiral(t_before, times, side_leng, angle, width) { $fn = 24; @@ -47,7 +49,7 @@ An OpenSCAD implementation of Turtle Graphics. It moves on the xy plane. You can ![turtle2d](images/lib-turtle2d-1.JPG) include ; - include ; + include ; module turtle_spiral(t_before, side_leng, d_step, min_leng, angle, width) { $fn = 24; diff --git a/docs/lib-turtle3d.md b/docs/lib2-turtle3d.md similarity index 97% rename from docs/lib-turtle3d.md rename to docs/lib2-turtle3d.md index 32028c54..dbe41c60 100644 --- a/docs/lib-turtle3d.md +++ b/docs/lib2-turtle3d.md @@ -1,11 +1,11 @@ # turtle3d +The dir changed since 2.0. + An OpenSCAD implementation of 3D Turtle Graphics. When using the function, imagine that you are sitting on the turtle. You move or turn the turtle from the your viewpoint, not the viewpoint of OpenSCAD coordinates. For more details, please see [3D turtle graphics](https://openhome.cc/eGossip/OpenSCAD/3DTurtleGraphics.html). - - ## Parameters - `cmd` : A string command. Different commands use different numbers of arguments. @@ -17,7 +17,7 @@ For more details, please see [3D turtle graphics](https://openhome.cc/eGossip/Op ## Examples - include ; + include ; include ; leng = 10; @@ -47,7 +47,7 @@ For more details, please see [3D turtle graphics](https://openhome.cc/eGossip/Op ![turtle3d](images/lib-turtle3d-1.JPG) - include ; + include ; include ; module tree(t, leng, leng_scale1, leng_scale2, leng_limit, diff --git a/examples/TaiwaneseBlackBear.scad b/examples/TaiwaneseBlackBear.scad new file mode 100644 index 00000000..8e30937a --- /dev/null +++ b/examples/TaiwaneseBlackBear.scad @@ -0,0 +1,47 @@ +include ; +include ; +include ; +include ; +include ; +include ; +include ; + +module blocks(points) { + for(pt = points) { + translate(pt) + cube(1, center = true); + } +} + +// Well, quick and dirty!! +color("MediumSeaGreen") + translate([3, -5, -27]) + for(pt = px_polygon([for(p = shape_taiwan(92, distance = 1)) [round(p[0]), round(p[1])]], filled = true)) { + translate(pt) + linear_extrude(1, scale = 0.5) + square(1, center = true); + } + +color(c = [0.3, 0.3, 0.3]) { + blocks(px_sphere(10)); + translate([7, 0, 9]) blocks(px_sphere(3)); + translate([-7, 0, 9]) blocks(px_sphere(3)); + translate([0, 0, -13]) blocks(px_sphere(12)); + translate([6, 0, -26]) blocks(px_cylinder([3, 4], 6)); + translate([-6, 0, -26]) blocks(px_cylinder([3, 4], 6)) + translate([10, 0, -13]) cube([6, 5, 10], center = true); + translate([-10, 0, -13]) cube([6, 5, 10], center = true); +} +color("white") { + translate([3, -7, 2]) blocks(px_sphere(2)); + translate([-3, -7, 2]) blocks(px_sphere(2)); + translate([0, -7, 0]) blocks(px_sphere(3)); + translate([0, -9, -4]) blocks(px_sphere(1)); + blocks(px_polyline([[0, -12, -10], [5, -9, -7], [8, -6, -6]])); + blocks(px_polyline([[0, -12, -10], [5, -9, -8], [8, -6, -7]])); + blocks(px_polyline([[0, -12, -10], [5, -9, -9], [8, -6, -8]])); + blocks(px_polyline([[0, -12, -10], [5, -9, -9], [8, -6, -8]])); + blocks(px_polyline([[0, -12, -10], [-5, -9, -7], [-8, -6, -6]])); + blocks(px_polyline([[0, -12, -10], [-5, -9, -8], [-8, -6, -7]])); + blocks(px_polyline([[0, -12, -10], [-5, -9, -9], [-8, -6, -8]])); +} \ No newline at end of file diff --git a/examples/dancing_taiwan.scad b/examples/dancing_taiwan.scad new file mode 100644 index 00000000..9d803909 --- /dev/null +++ b/examples/dancing_taiwan.scad @@ -0,0 +1,69 @@ +include ; +include ; +include ; +include ; +include ; +include ; +include ; + +x1 = 4; // [-20:4] +x2 = 3; // [-20:4] +x3 = 4; // [-20:4] +y1 = 20; +y2 = 40; +y3 = 90; +twist = -90; +t_step = 0.1; + +module dancing_formosan(x1, x2, x3, y1, y2, y3, twist, t_step) { + + function cal_sections(shapt_pts, edge_path, twist) = + let( + sects = path_scaling_sections(shapt_pts, edge_path), + leng = len(sects), + twist_step = twist / leng + ) + [ + for(i = [0:leng - 1]) + [ + for(p = sects[i]) + rotate_p(p, twist_step * i) + ] + ]; + + taiwan = shape_taiwan(100, 0.6); + fst_pt = [13, 0, 0]; + + edge_path = bezier_curve(t_step, [ + fst_pt, + fst_pt + [0, 0, 10], + fst_pt + [x1, 0, y1], + fst_pt + [x2, 0, 35], + fst_pt + [x3, 0, y2], + fst_pt + [0, 0, 55], + fst_pt + [0, 0, y3] + ]); + + + offseted = bijection_offset(taiwan, -2); + + edge_path2 = [for(p = edge_path) p + [-2, 0, 0]]; + taiwan2 = trim_shape(offseted, 1, len(offseted) - 4); + + sections = cal_sections(taiwan, edge_path, twist); + sections2 = cal_sections(taiwan2, edge_path2, twist); + + difference() { + polysections(sections); + polysections(sections2); + } + + translate([0, 0, -2]) + linear_extrude(2) + rotate(twist - twist / len(sections)) + polygon(taiwan); + +} + +dancing_formosan(x1, x2, x3, y1, y2, y3, twist, t_step); + diff --git a/examples/klein_bottle.scad b/examples/klein_bottle.scad new file mode 100644 index 00000000..31d2cfaf --- /dev/null +++ b/examples/klein_bottle.scad @@ -0,0 +1,126 @@ +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; + +radius1 = 10; +radius2 = 20; +bottom_height = 60; +thickness = 1.5; +t_step = 0.025; +fn = 24; +cut = false; // [true,false] + +module klein_bottle(radius1, radius2, bottom_height, thickness, t_step, fn) { + $fn = fn; + + module bottom() { + rotate(180) rotate_extrude() { + + + translate([radius1 + radius2, 0, 0]) + polyline2d( + arc_path(radius = radius2, angle = [180, 360]) + ,thickness + ); + + polyline2d( + bezier_curve(t_step, [ + [radius1 + radius2 * 2, 0, 0], + [radius1 + radius2 * 2, bottom_height * 0.25, 0], + [radius1 + radius2 * 0.5, bottom_height * 0.5, 0], + [radius1, bottom_height * 0.75, 0], + [radius1, bottom_height, 0] + ]), + thickness + ); + } + } + + module tube() { + + mid_pts = [ + [0, 0, bottom_height + radius1], + [0, 0, bottom_height + radius1 * 2], + [0, radius1, bottom_height + radius1 * 3], + [0, radius1 * 2, bottom_height + radius1 * 3], + [0, radius1 * 3, bottom_height + radius1 * 3], + [0, radius1 * 4, bottom_height + radius1 * 2], + [0, radius1 * 4, bottom_height + radius1], + [0, radius1 * 4, bottom_height], + [0, radius1 * 3, bottom_height - radius1], + [0, radius1 * 2, bottom_height - radius1 * 2], + [0, radius1, bottom_height + thickness / 2 - radius1 * 3], + [0, 0, bottom_height - radius1 * 4], + [0, 0, bottom_height - radius1 * 5] + ]; + + tube_path = bezier_curve( + t_step, + concat( + concat([[0, 0, bottom_height]], mid_pts), + [[0, 0, 0]] + ) + ); + + tube_path2 = bezier_curve( + t_step, + concat( + concat([[0, 0, bottom_height - thickness]], mid_pts), + [[0, 0, -thickness] ] + ) + ); + + difference() { + union() { + bottom(); + + path_extrude( + circle_path(radius1 + thickness / 2), + tube_path + ); + } + + path_extrude( + circle_path(radius1 - thickness / 2), + tube_path2 + ); + } + + } + + tube(); +} + +module cutted_klein_bottle(radius1, radius2, bottom_height, thickness, t_step, fn) { + difference() { + union() { + translate([radius2 + thickness, 0, 0]) + rotate([0, 90, 0]) klein_bottle(radius1, radius2, bottom_height, thickness, t_step, fn); + translate([-radius2 - thickness, 0, 0]) + rotate([0, -90, 0]) klein_bottle(radius1, radius2, bottom_height, thickness, t_step, fn); + + + } + + h = (radius1 + radius2) * 2; + w = 2 * h; + l = bottom_height * 4; + translate([0, 0, h / 2]) + cube([l, w, h], center = true); + } +} + +if(cut) { + cutted_klein_bottle(radius1, radius2, bottom_height, thickness, t_step, fn); +} else { + klein_bottle(radius1, radius2, bottom_height, thickness, t_step, fn); +} + + + + diff --git a/examples/knot.scad b/examples/knot.scad new file mode 100644 index 00000000..ac0dd9ab --- /dev/null +++ b/examples/knot.scad @@ -0,0 +1,21 @@ +include ; +include ; +include ; +include ; +include ; + +p = 2; +q = 3; +phi_step = 0.05; +star_radius = 0.5; + +pts = torus_knot(p, q, phi_step); + +shape_pentagram_pts = shape_pentagram(star_radius); + +path_extrude( + shape_pentagram_pts, + concat(pts, [pts[0]]), + closed = true, + method = "EULER_ANGLE" +); diff --git a/examples/pixel_vase.scad b/examples/pixel_vase.scad new file mode 100644 index 00000000..5457ff55 --- /dev/null +++ b/examples/pixel_vase.scad @@ -0,0 +1,44 @@ +include ; +include ; +include ; +include ; + +x1 = 5; +x2 = 20; +x3 = 8; +thickness = 1; + +module pixel_vase(x1, x2, x3, thickness) { + p0 = [x1, 0, 0]; + p1 = [10, 0, 4]; + p2 = [x2, 0, 8]; + p3 = [3, 0, 20]; + p4 = [x3, 0, 30]; + + rounded_points = [for(pt = bezier_curve(0.1, + [p0, p1, p2, p3, p4] + )) [round(pt[0]), round(pt[1]), round(pt[2])]]; + + px_path = px_polyline(rounded_points); + leng = len(px_path); + + for(p = px_cylinder(px_path[0][0], 1, true)) { + linear_extrude(1) union() { + translate([p[0], p[1]]) + square(1.1, center = true); + } + } + + for(i = [0:leng - 1]) { + r = px_path[i][0]; + for(p = px_cylinder(r, 1, thickness = thickness)) { + translate([0, 0, i]) + linear_extrude(1) union() { + translate([p[0], p[1]]) + square(1.1, center = true); + } + } + } +} + +pixel_vase(x1, x2, x3, thickness); \ No newline at end of file diff --git a/examples/stereographic_projection.scad b/examples/stereographic_projection.scad new file mode 100644 index 00000000..c10b6e11 --- /dev/null +++ b/examples/stereographic_projection.scad @@ -0,0 +1,25 @@ +include ; + +rows = 8; +line_width = 15; +block_width = 50; + +module grid(rows, block_width, line_width) { + half_side_length = (block_width * rows + line_width) / 2; + + translate([-half_side_length, -half_side_length]) + for(i = [0:rows]) { + translate([0, i * block_width, 0]) + square([block_width * rows, line_width]); + + translate([i * block_width, 0, 0]) + square([line_width, block_width * rows + line_width]); + } +} + +stereographic_extrude(block_width * rows + line_width, $fn = 48) + grid(rows, block_width, line_width); + +if($preview) { + color("black") grid(rows, block_width, line_width); + } \ No newline at end of file diff --git a/examples/superformula_vase.scad b/examples/superformula_vase.scad new file mode 100644 index 00000000..bd97032c --- /dev/null +++ b/examples/superformula_vase.scad @@ -0,0 +1,72 @@ +include ; +include ; +include ; +include ; +include ; +include ; +include ; + +/* [Superformula] */ +phi_step = 0.025; +m = 8; +n = 5; +n3 = 8; + +/* [Offset] */ +d = 0.1; + +/* [Curve] */ +r1 = 1; +r2 = 2; +h1 = 5; +h2 = 8; +t_step = 0.025; +twist = 90; + +module superformula_vase(phi_step, m, n, n3, d, r1, r2, h1, h2, t_step, twist) { + + function cal_sections(shapt_pts, edge_path, twist) = + let( + sects = path_scaling_sections(shapt_pts, edge_path), + leng = len(sects), + twist_step = twist / leng + ) + [ + for(i = [0:leng - 1]) + [ + for(p = sects[i]) + rotate_p(p, twist_step * i) + ] + ]; + + superformula = shape_superformula(phi_step, m, m, n, n, n3); + + edge_path = bezier_curve(t_step, [ + [1, 0, 0], + [4, 0, 3], + [2, 0, 4], + [r1, 0, h1], + [1, 0, 6], + [r2, 0, h2], + ]); + + offseted = bijection_offset(superformula, d); + + edge_path2 = [for(p = edge_path) p + [d, 0, 0]]; + superformula2 = trim_shape(offseted, 3, len(offseted) - 1, epsilon = 0.0001); + + sections = cal_sections(superformula, edge_path, twist); + outer_sections = cal_sections(superformula2, edge_path2, twist); + + difference() { + polysections(outer_sections); + polysections(sections); + } + + linear_extrude(d) + rotate(twist - twist / len(sections)) + polygon(superformula2); +} + +superformula_vase(phi_step, m, n, n3, d, r1, r2, h1, h2, t_step, twist); + \ No newline at end of file diff --git a/examples/text_sphere.scad b/examples/text_sphere.scad new file mode 100644 index 00000000..fb15340c --- /dev/null +++ b/examples/text_sphere.scad @@ -0,0 +1,58 @@ +include ; +include ; +include ; +include ; +include ; + +tx = "3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989"; +font_name = "Liberation Sans:style=Bold Italic"; +thickness = 2; + +module text_sphere(tx, font_name, thickness) { + $fn = 24; + radius = 40; + za_step = 360 / $fn; + z_circles = 48; + begin_angle = 720; + end_angle = 630; + + half_thickness = thickness / 2; + + points_angles = sphere_spiral( + radius = radius, + za_step = za_step, + z_circles = z_circles, + begin_angle = begin_angle, + end_angle = end_angle + ); + + rotate(-180 / $fn) sphere_spiral_extrude( + [ + [thickness, half_thickness], + [-half_thickness, half_thickness], + [-half_thickness, -half_thickness], + [thickness, -half_thickness] + ], + radius = radius, + za_step = za_step, + z_circles = z_circles, + begin_angle = begin_angle, + end_angle = end_angle + ); + + + for(i = [0:len(points_angles) - 1]) { + pa = points_angles[i]; + translate(pa[0]) rotate(pa[1] + [0, 8, 0]) + rotate([90, 0, 90]) + linear_extrude(half_thickness) + translate([0, -10, 0]) + text(tx[i], font = font_name, halign = "center"); + } + + translate([0, 0, -radius]) + linear_extrude(thickness * 2.5) + circle(radius / 2); +} + + text_sphere(tx, font_name, thickness); \ No newline at end of file diff --git a/examples/text_tower.scad b/examples/text_tower.scad new file mode 100644 index 00000000..5067a068 --- /dev/null +++ b/examples/text_tower.scad @@ -0,0 +1,61 @@ +include ; +include ; +include ; +include ; +include ; + +tx = "3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989"; +font_name = "Liberation Sans:style=Bold Italic"; +radius = 60; +height = 150; +thickness = 2; + +module text_tower(tx, font_name, radius, height, thickness) { + + font_size = 2 * PI * radius / $fn; + angle_step = 360 / $fn; + half_angle_step = angle_step / 2; + half_thickness = thickness / 2; + + module body() { + points = helix( + radius = radius, + levels = height / font_size, + level_dist = font_size, + vt_dir = "SPI_DOWN" + ); + for(i = [0:len(points) - 1]) { + translate(points[i]) + rotate([90, 0, 90 + angle_step * i]) + linear_extrude(thickness, center = true) + text( + tx[i], + font = font_name, + size = font_size, + halign = "center" + ); + } + + rotate(-half_angle_step) + helix_extrude( + [ + [thickness, half_thickness], + [-thickness, half_thickness], + [-thickness, -half_thickness], + [thickness, -half_thickness] + ], + radius = radius, + levels = height / font_size + 1, + level_dist = font_size, + vt_dir = "SPI_DOWN" + ); + } + + translate([0, 0, -font_size - half_thickness]) + body(); + rotate(-half_angle_step) + translate([0, 0, -font_size - thickness]) + cylinder(h = font_size, r = radius + thickness); +} + +text_tower(tx, font_name, radius, height, thickness, $fn = 24); \ No newline at end of file diff --git a/examples/tree.scad b/examples/tree.scad new file mode 100644 index 00000000..edecb013 --- /dev/null +++ b/examples/tree.scad @@ -0,0 +1,38 @@ +include ; +include ; + +module tree(t, leng, leng_scale1, leng_scale2, leng_limit, + angleZ, angleX, width) { + if(leng > leng_limit) { + t2 = turtle3d("xu_move", t, leng); + + line3d( + turtle3d("pt", t), turtle3d("pt", t2), + width); + + tree( + turtle3d("zu_turn", t2, angleZ), + leng * leng_scale1, leng_scale1, leng_scale2, leng_limit, + angleZ, angleX, + width); + + tree( + turtle3d("xu_turn", t2, angleX), + leng * leng_scale2, leng_scale1, leng_scale2, leng_limit, + angleZ, angleX, + width); + } +} + +leng = 100; +leng_limit = 1; +leng_scale1 = 0.4; +leng_scale2 = 0.9; +angleZ = 60; +angleX = 135; +width = 2; + +t = turtle3d("create"); + +tree(t, leng, leng_scale1, leng_scale2, leng_limit, + angleZ, angleX, width); \ No newline at end of file diff --git a/examples/voronoi_bracelet.scad b/examples/voronoi_bracelet.scad new file mode 100644 index 00000000..9db5647c --- /dev/null +++ b/examples/voronoi_bracelet.scad @@ -0,0 +1,40 @@ +include ; +include ; +include ; + +r = 35; +height = 35; +thickness = 2.5; +n = 25; +frags = 24; +offset_r = 0.5; +region_type = "square"; // [square, circle] + +module voronoi_bracelet(r, height, thickness, n, frags, offset_r, region_type) { + $fn = 12; + + x = 2 * PI * r - thickness; + y = height; + + xs = rands(0, x, n); + ys = rands(0, y, n); + + points = [for(i = [0: len(xs) - 1]) [xs[i], ys[i]]]; + + bend_extrude( + size = [x, y], + thickness = thickness, + angle = 360 * (1 - thickness / (2 * PI * r)), + frags = frags + ) + { + difference() { + square([x, y]); + voronoi2d(points, spacing = thickness, r = offset_r, region_type = region_type); + } + hollow_out(thickness * 1.5) + square([x, y]); + } +} + +voronoi_bracelet(r, height, thickness, n, frags, offset_r, region_type); diff --git a/examples/voronoi_vase.scad b/examples/voronoi_vase.scad new file mode 100644 index 00000000..860486b1 --- /dev/null +++ b/examples/voronoi_vase.scad @@ -0,0 +1,69 @@ +include ; +include ; +include ; +include ; + +r = 13; +h = 60; +thickness = 2; +num_of_pts = 16; +fn = 6; +profile_step = 0.1; + +module voronoi_vase(r, h, thickness, num_of_pts, fn, profile_step) { + + profile = bezier_curve(profile_step, [ + [r, 0, 0], + [r, 0, h / 6], + [r + 10, 0, h / 4], + [r + 18, 0, h * 0.4], + [r + 10, 0, h / 2], + [r, 0, h * 2 / 3], + [r + 2, 0, h] + ]); + + + a_step = 360 / fn; + sections = [ + for(pt = profile) [ + for(i = [0:fn - 1]) + let(r = pt[0], z = pt[2], a = a_step * i) + [r * cos(a), r * sin(a), z] + ] + ]; + + pts = [for(sect = sections) each sect]; + indices = rands(0, len(pts) - 1, num_of_pts - 4); + + last_section_i = len(sections) - 1; + half_fn = fn * 0.5; + + + + sxy = (r * 0.95 - thickness * 0.5) / r; + + difference() { + scale([0.95, 0.95, 1]) + polysections(sections); + scale([0.85, 0.85, 1]) + polysections(sections); + intersection() { + polysections(sections); + render() + voronoi3d(concat([for(i = indices) pts[i]], [sections[0][0], sections[0][half_fn], sections[last_section_i][0], sections[last_section_i][half_fn]])); + } + } + + linear_extrude(thickness) + polygon([for(pt = sections[0]) [pt[0], pt[1]]]); + + translate([0, 0, h]) + linear_extrude(thickness) + hollow_out(thickness) + polygon([for(pt = sections[last_section_i]) [pt[0], pt[1]]]); + + + +} +voronoi_vase(r, h, thickness, num_of_pts, fn, profile_step); + \ No newline at end of file diff --git a/src/__private__/__angy_angz.scad b/src/__comm__/__angy_angz.scad similarity index 75% rename from src/__private__/__angy_angz.scad rename to src/__comm__/__angy_angz.scad index cbc605bf..480b758e 100644 --- a/src/__private__/__angy_angz.scad +++ b/src/__comm__/__angy_angz.scad @@ -3,6 +3,6 @@ function __angy_angz(p1, p2) = dx = p2[0] - p1[0], dy = p2[1] - p1[1], dz = p2[2] - p1[2], - ya = atan2(dz, sqrt(pow(dx, 2) + pow(dy, 2))), + ya = atan2(dz, sqrt(dx * dx + dy * dy)), za = atan2(dy, dx) ) [ya, za]; \ No newline at end of file diff --git a/src/__private__/__edge_r.scad b/src/__comm__/__edge_r.scad similarity index 100% rename from src/__private__/__edge_r.scad rename to src/__comm__/__edge_r.scad diff --git a/src/__private__/__frags.scad b/src/__comm__/__frags.scad similarity index 55% rename from src/__private__/__frags.scad rename to src/__comm__/__frags.scad index 395b8845..9b929dc6 100644 --- a/src/__private__/__frags.scad +++ b/src/__comm__/__frags.scad @@ -1,3 +1,3 @@ function __frags(radius) = $fn > 0 ? ($fn >= 3 ? $fn : 3) : - max(min(360 / $fa, radius * 6.28318 / $fs), 5); \ No newline at end of file + max(min(360 / $fa, radius * PI * 2 / $fs), 5); \ No newline at end of file diff --git a/src/__private__/__half_trapezium.scad b/src/__comm__/__half_trapezium.scad similarity index 98% rename from src/__private__/__half_trapezium.scad rename to src/__comm__/__half_trapezium.scad index e08b9ca8..0a6db4f8 100644 --- a/src/__private__/__half_trapezium.scad +++ b/src/__comm__/__half_trapezium.scad @@ -44,7 +44,7 @@ function __br_corner(frags, b_ang, l1, l2, h, round_r) = function __half_trapezium(length, h, round_r) = let( - is_flt = __is_float(length), + is_flt = is_num(length), l1 = is_flt ? length : length[0], l2 = is_flt ? length : length[1], frags = __frags(round_r), diff --git a/src/__private__/__in_line.scad b/src/__comm__/__in_line.scad similarity index 100% rename from src/__private__/__in_line.scad rename to src/__comm__/__in_line.scad diff --git a/src/__private__/__line_intersection.scad b/src/__comm__/__line_intersection.scad similarity index 100% rename from src/__private__/__line_intersection.scad rename to src/__comm__/__line_intersection.scad diff --git a/src/__comm__/__lines_from.scad b/src/__comm__/__lines_from.scad new file mode 100644 index 00000000..59720652 --- /dev/null +++ b/src/__comm__/__lines_from.scad @@ -0,0 +1,10 @@ +function __lines_from(pts, closed = false) = + let( + leng = len(pts), + endi = leng - 1 + ) + concat( + [for(i = 0; i < endi; i = i + 1) [pts[i], pts[i + 1]]], + closed ? [[pts[len(pts) - 1], pts[0]]] : [] + ); + \ No newline at end of file diff --git a/src/__private__/__nearest_multiple_of_4.scad b/src/__comm__/__nearest_multiple_of_4.scad similarity index 100% rename from src/__private__/__nearest_multiple_of_4.scad rename to src/__comm__/__nearest_multiple_of_4.scad diff --git a/src/__private__/__pie_for_rounding.scad b/src/__comm__/__pie_for_rounding.scad similarity index 87% rename from src/__private__/__pie_for_rounding.scad rename to src/__comm__/__pie_for_rounding.scad index 5ea0f6c8..c67024b6 100644 --- a/src/__private__/__pie_for_rounding.scad +++ b/src/__comm__/__pie_for_rounding.scad @@ -5,7 +5,7 @@ function __pie_for_rounding(r, begin_a, end_a, frags) = is_integer = frags % 1 == 0 ) r < 0.00005 ? [[0, 0]] : concat([ - for(ang = [begin_a:step_a:end_a]) + for(ang = begin_a; ang <= end_a; ang = ang + step_a) [ r * cos(ang), r * sin(ang) diff --git a/src/__private__/__polytransversals.scad b/src/__comm__/__polytransversals.scad similarity index 81% rename from src/__private__/__polytransversals.scad rename to src/__comm__/__polytransversals.scad index 6fcb8647..3239f88a 100644 --- a/src/__private__/__polytransversals.scad +++ b/src/__comm__/__polytransversals.scad @@ -3,12 +3,12 @@ function __polytransversals(transversals) = leng_trs = len(transversals), leng_tr = len(transversals[0]), lefts = [ - for(i = [1:leng_trs - 2]) + for(i = 1; i < leng_trs - 1; i = i + 1) let(tr = transversals[leng_trs - i]) tr[0] ], rights = [ - for(i = [1:leng_trs - 2]) + for(i = 1; i < leng_trs - 1; i = i + 1) let(tr = transversals[i]) tr[leng_tr - 1] ] diff --git a/src/__private__/__ra_to_xy.scad b/src/__comm__/__ra_to_xy.scad similarity index 100% rename from src/__private__/__ra_to_xy.scad rename to src/__comm__/__ra_to_xy.scad diff --git a/src/__private__/__shape_arc.scad b/src/__comm__/__shape_arc.scad similarity index 86% rename from src/__private__/__shape_arc.scad rename to src/__comm__/__shape_arc.scad index 37911574..0eb84476 100644 --- a/src/__private__/__shape_arc.scad +++ b/src/__comm__/__shape_arc.scad @@ -6,7 +6,7 @@ function __shape_arc(radius, angle, width, width_mode = "LINE_CROSS") = frags = __frags(radius), a_step = 360 / frags, half_a_step = a_step / 2, - angles = __is_float(angle) ? [0, angle] : angle, + angles = is_num(angle) ? [0, angle] : angle, m = floor(angles[0] / a_step) + 1, n = floor(angles[1] / a_step), r_outer = radius + w_offset[0], @@ -15,14 +15,13 @@ function __shape_arc(radius, angle, width, width_mode = "LINE_CROSS") = // outer arc path [__ra_to_xy(__edge_r_begin(r_outer, angles[0], a_step, m), angles[0])], m > n ? [] : [ - for(i = [m:n]) - __ra_to_xy(r_outer, a_step * i) + for(i = m; i <= n; i = i + 1) __ra_to_xy(r_outer, a_step * i) ], angles[1] == a_step * n ? [] : [__ra_to_xy(__edge_r_end(r_outer, angles[1], a_step, n), angles[1])], // inner arc path angles[1] == a_step * n ? [] : [__ra_to_xy(__edge_r_end(r_inner, angles[1], a_step, n), angles[1])], m > n ? [] : [ - for(i = [m:n]) + for(i = m; i <= n; i = i + 1) let(idx = (n + (m - i))) __ra_to_xy(r_inner, a_step * idx) diff --git a/src/__private__/__shape_pie.scad b/src/__comm__/__shape_pie.scad similarity index 87% rename from src/__private__/__shape_pie.scad rename to src/__comm__/__shape_pie.scad index db5e5504..967b3168 100644 --- a/src/__private__/__shape_pie.scad +++ b/src/__comm__/__shape_pie.scad @@ -3,7 +3,7 @@ function __shape_pie(radius, angle) = frags = __frags(radius), a_step = 360 / frags, leng = radius * cos(a_step / 2), - angles = __is_float(angle) ? [0:angle] : angle, + angles = is_num(angle) ? [0:angle] : angle, m = floor(angles[0] / a_step) + 1, n = floor(angles[1] / a_step), edge_r_begin = leng / cos((m - 0.5) * a_step - angles[0]), @@ -11,7 +11,7 @@ function __shape_pie(radius, angle) = shape_pts = concat( [[0, 0], __ra_to_xy(edge_r_begin, angles[0])], m > n ? [] : [ - for(i = [m:n]) + for(i = m; i <= n; i = i + 1) let(a = a_step * i) __ra_to_xy(radius, a) ], diff --git a/src/__private__/__to2d.scad b/src/__comm__/__to2d.scad similarity index 100% rename from src/__private__/__to2d.scad rename to src/__comm__/__to2d.scad diff --git a/src/__private__/__to3d.scad b/src/__comm__/__to3d.scad similarity index 100% rename from src/__private__/__to3d.scad rename to src/__comm__/__to3d.scad diff --git a/src/__private__/__to_ang_vect.scad b/src/__comm__/__to_ang_vect.scad similarity index 64% rename from src/__private__/__to_ang_vect.scad rename to src/__comm__/__to_ang_vect.scad index e393ed64..2ce95b6a 100644 --- a/src/__private__/__to_ang_vect.scad +++ b/src/__comm__/__to_ang_vect.scad @@ -4,4 +4,4 @@ function __to_3_elems_ang_vect(a) = leng == 2 ? [a[0], a[1], 0] : [a[0], 0, 0] ); -function __to_ang_vect(a) = __is_float(a) ? [0, 0, a] : __to_3_elems_ang_vect(a); \ No newline at end of file +function __to_ang_vect(a) = is_num(a) ? [0, 0, a] : __to_3_elems_ang_vect(a); \ No newline at end of file diff --git a/src/__comm__/__to_degree.scad b/src/__comm__/__to_degree.scad new file mode 100644 index 00000000..963506f5 --- /dev/null +++ b/src/__comm__/__to_degree.scad @@ -0,0 +1 @@ +function __to_degree(phi) = 180 / PI * phi; \ No newline at end of file diff --git a/src/__private__/__trapezium.scad b/src/__comm__/__trapezium.scad similarity index 89% rename from src/__private__/__trapezium.scad rename to src/__comm__/__trapezium.scad index 3dddac87..5715ff5e 100644 --- a/src/__private__/__trapezium.scad +++ b/src/__comm__/__trapezium.scad @@ -3,7 +3,7 @@ function __trapezium(length, h, round_r) = r_half_trapezium = __half_trapezium(length / 2, h, round_r), to = len(r_half_trapezium) - 1, l_half_trapezium = [ - for(i = [0:to]) + for(i = 0; i <= to; i = i + 1) let(pt = r_half_trapezium[to - i]) [-pt[0], pt[1]] ] diff --git a/src/__private__/__is_float.scad b/src/__private__/__is_float.scad deleted file mode 100644 index f5889769..00000000 --- a/src/__private__/__is_float.scad +++ /dev/null @@ -1 +0,0 @@ -function __is_float(value) = value + 0 != undef; \ No newline at end of file diff --git a/src/__private__/__is_vector.scad b/src/__private__/__is_vector.scad deleted file mode 100644 index a4e9d880..00000000 --- a/src/__private__/__is_vector.scad +++ /dev/null @@ -1 +0,0 @@ -function __is_vector(value) = !(value >= "") && len(value) != undef; \ No newline at end of file diff --git a/src/__private__/__lines_from.scad b/src/__private__/__lines_from.scad deleted file mode 100644 index 47fd8754..00000000 --- a/src/__private__/__lines_from.scad +++ /dev/null @@ -1,7 +0,0 @@ -function __lines_from(pts, closed = false) = - let(leng = len(pts)) - concat( - [for(i = [0:leng - 2]) [pts[i], pts[i + 1]]], - closed ? [[pts[len(pts) - 1], pts[0]]] : [] - ); - \ No newline at end of file diff --git a/src/__private__/__reverse.scad b/src/__private__/__reverse.scad deleted file mode 100644 index 62048e03..00000000 --- a/src/__private__/__reverse.scad +++ /dev/null @@ -1,6 +0,0 @@ -function __reverse(vt) = - let(leng = len(vt)) - [ - for(i = [0:leng - 1]) - vt[leng - 1 - i] - ]; \ No newline at end of file diff --git a/src/__private__/__to_degree.scad b/src/__private__/__to_degree.scad deleted file mode 100644 index 21797396..00000000 --- a/src/__private__/__to_degree.scad +++ /dev/null @@ -1 +0,0 @@ -function __to_degree(phi) = 180 / 3.14159 * phi; \ No newline at end of file diff --git a/src/all/dotSCAD.scad b/src/all/dotSCAD.scad new file mode 100644 index 00000000..efe889ca --- /dev/null +++ b/src/all/dotSCAD.scad @@ -0,0 +1,87 @@ +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; +include ; \ No newline at end of file diff --git a/src/along_with.scad b/src/along_with.scad index bd915359..54b742da 100644 --- a/src/along_with.scad +++ b/src/along_with.scad @@ -8,35 +8,25 @@ * **/ -include <__private__/__angy_angz.scad>; -include <__private__/__is_float.scad>; -include <__private__/__to3d.scad>; - -// Becuase of improving the performance, this module requires m_rotation.scad which doesn't require in dotSCAD 1.0. -// For backward compatibility, I directly include m_rotation here. -include ; +include <__comm__/__angy_angz.scad>; +include <__comm__/__to3d.scad>; +include ; module along_with(points, angles, twist = 0, scale = 1.0, method = "AXIS_ANGLE") { leng_points = len(points); leng_points_minus_one = leng_points - 1; twist_step_a = twist / leng_points; - angles_defined = angles != undef; + angles_defined = !is_undef(angles); - scale_step_vt = __is_float(scale) ? - scale_step() : + scale_step_vt = is_num(scale) ? + let(s = (scale - 1) / leng_points_minus_one) [s, s, s] : [ (scale[0] - 1) / leng_points_minus_one, (scale[1] - 1) / leng_points_minus_one, - scale[2] == undef ? 0 : (scale[2] - 1) / leng_points_minus_one + is_undef(scale[2]) ? 0 : (scale[2] - 1) / leng_points_minus_one ]; - - function scale_step() = - let(s = (scale - 1) / leng_points_minus_one) - [s, s, s]; - - /* Sadly, children(n) cannot be used with inner modules so I have to do things in the first level. Ugly!! @@ -53,16 +43,16 @@ module along_with(points, angles, twist = 0, scale = 1.0, method = "AXIS_ANGLE") ]; function axis_angle_local_ang_vects(j) = - j == 0 ? [] : axis_angle_local_ang_vects_sub(j); - - function axis_angle_local_ang_vects_sub(j) = - let( - vt0 = points[j] - points[j - 1], - vt1 = points[j + 1] - points[j], - a = acos((vt0 * vt1) / (norm(vt0) * norm(vt1))), - v = cross(vt0, vt1) - ) - concat([[a, v]], axis_angle_local_ang_vects(j - 1)); + [ + for(i = j; i > 0; i = i - 1) + let( + vt0 = points[i] - points[i - 1], + vt1 = points[i + 1] - points[i], + a = acos((vt0 * vt1) / (norm(vt0) * norm(vt1))), + v = cross(vt0, vt1) + ) + [a, v] + ]; function axis_angle_cumulated_rot_matrice(i, rot_matrice) = let( @@ -101,7 +91,6 @@ module along_with(points, angles, twist = 0, scale = 1.0, method = "AXIS_ANGLE") module axis_angle_align_with_pts_init(a, s) { angleyz = __angy_angz(__to3d(points[0]), __to3d(points[1])); - rotate([0, -angleyz[0], angleyz[1]]) rotate([90, 0, -90]) rotate(a) @@ -126,13 +115,8 @@ module along_with(points, angles, twist = 0, scale = 1.0, method = "AXIS_ANGLE") // >>> begin: modules and functions for "EULER-ANGLE" - function _euler_angle_path_angles(pts, end_i, i = 0) = - i == end_i ? - [] : - concat( - [__angy_angz(pts[i], pts[i + 1])], - _euler_angle_path_angles(pts, end_i, i + 1) - ); + function _euler_angle_path_angles(pts, end_i) = + [for(i = 0; i < end_i; i = i + 1) __angy_angz(pts[i], pts[i + 1])]; function euler_angle_path_angles(children) = let( @@ -171,7 +155,7 @@ module along_with(points, angles, twist = 0, scale = 1.0, method = "AXIS_ANGLE") else { cumu_rot_matrice = axis_angle_cumulated_rot_matrice(0, [ for(ang_vect = axis_angle_local_ang_vects(leng_points - 2)) - m_rotation(ang_vect[0], ang_vect[1]) + __m_rotation(ang_vect[0], ang_vect[1]) ]); translate(points[0]) @@ -195,16 +179,21 @@ module along_with(points, angles, twist = 0, scale = 1.0, method = "AXIS_ANGLE") } else if(method == "EULER_ANGLE") { angs = angles_defined ? angles : euler_angle_path_angles($children); - + if($children == 1) { for(i = [0:leng_points_minus_one]) { euler_angle_align(i, angs) children(0); } - } else { for(i = [0:min(leng_points, $children) - 1]) { euler_angle_align(i, angs) children(i); } - } + } + + test_along_with_angles(angs); } +} + +module test_along_with_angles(angles) { + } \ No newline at end of file diff --git a/src/arc.scad b/src/arc.scad index 61bc78e0..c4b152e2 100644 --- a/src/arc.scad +++ b/src/arc.scad @@ -8,11 +8,10 @@ * **/ -include <__private__/__frags.scad>; -include <__private__/__is_float.scad>; -include <__private__/__ra_to_xy.scad>; -include <__private__/__edge_r.scad>; -include <__private__/__shape_arc.scad>; +include <__comm__/__frags.scad>; +include <__comm__/__ra_to_xy.scad>; +include <__comm__/__edge_r.scad>; +include <__comm__/__shape_arc.scad>; module arc(radius, angle, width, width_mode = "LINE_CROSS") { polygon(__shape_arc(radius, angle, width, width_mode)); diff --git a/src/arc_path.scad b/src/arc_path.scad index ab4fedb5..f8bbc73d 100644 --- a/src/arc_path.scad +++ b/src/arc_path.scad @@ -8,21 +8,20 @@ * **/ -include <__private__/__frags.scad>; -include <__private__/__is_float.scad>; -include <__private__/__ra_to_xy.scad>; -include <__private__/__edge_r.scad>; +include <__comm__/__frags.scad>; +include <__comm__/__ra_to_xy.scad>; +include <__comm__/__edge_r.scad>; function arc_path(radius, angle) = let( frags = __frags(radius), a_step = 360 / frags, - angles = __is_float(angle) ? [0, angle] : angle, + angles = is_num(angle) ? [0, angle] : angle, m = floor(angles[0] / a_step) + 1, n = floor(angles[1] / a_step), points = concat([__ra_to_xy(__edge_r_begin(radius, angles[0], a_step, m), angles[0])], m > n ? [] : [ - for(i = [m:n]) + for(i = m; i <= n; i = i + 1) __ra_to_xy(radius, a_step * i) ], angles[1] == a_step * n ? [] : [__ra_to_xy(__edge_r_end(radius, angles[1], a_step, n), angles[1])]) diff --git a/src/archimedean_spiral.scad b/src/archimedean_spiral.scad index cef6dc0b..18ef215b 100644 --- a/src/archimedean_spiral.scad +++ b/src/archimedean_spiral.scad @@ -10,7 +10,7 @@ function _radian_step(b, theta, l) = let(r_square = pow(b * theta, 2)) - acos((2 * r_square - pow(l, 2)) / (2 * r_square)) / 180 * 3.14159; + acos((2 * r_square - pow(l, 2)) / (2 * r_square)) / 180 * PI; function _find_radians(b, point_distance, radians, n, count = 1) = let(pre_radians = radians[count - 1]) @@ -27,7 +27,7 @@ function _find_radians(b, point_distance, radians, n, count = 1) = ); function archimedean_spiral(arm_distance, init_angle, point_distance, num_of_points, rt_dir = "CT_CLK") = - let(b = arm_distance / 6.28318, init_radian = init_angle *3.14159 / 180) + let(b = arm_distance / (2 * PI), init_radian = init_angle * PI / 180) [ for(theta = _find_radians(b, point_distance, [init_radian], num_of_points)) let(r = b * theta, a = (rt_dir == "CT_CLK" ? 1 : -1) * theta * 57.2958) diff --git a/src/bezier_curve.scad b/src/bezier_curve.scad index 6ed7b901..820b54f0 100644 --- a/src/bezier_curve.scad +++ b/src/bezier_curve.scad @@ -8,7 +8,7 @@ * **/ -include <__private__/__to2d.scad>; +include <__comm__/__to2d.scad>; function _combi(n, k) = let( @@ -51,7 +51,7 @@ function _bezier_curve_point(t, points) = function bezier_curve(t_step, points) = let( pts = concat([ - for(t = [0: ceil(1 / t_step) - 1]) + for(t = 0; t < ceil(1 / t_step); t = t + 1) _bezier_curve_point(t * t_step, points) ], [_bezier_curve_point(1, points)]) ) diff --git a/src/bezier_smooth.scad b/src/bezier_smooth.scad index 06ad1c3b..1a95f06b 100644 --- a/src/bezier_smooth.scad +++ b/src/bezier_smooth.scad @@ -8,9 +8,9 @@ * **/ -include <__private__/__to3d.scad>; -include <__private__/__to2d.scad>; -include <__private__/__angy_angz.scad>; +include <__comm__/__to3d.scad>; +include <__comm__/__to2d.scad>; +include <__comm__/__angy_angz.scad>; function _corner_ctrl_pts(round_d, p1, p2, p3) = let( @@ -37,13 +37,13 @@ function _corner_ctrl_pts(round_d, p1, p2, p3) = function _bezier_corner(round_d, t_step, p1, p2, p3) = bezier_curve(t_step, _corner_ctrl_pts(round_d, p1, p2, p3)); -function _recursive_bezier_smooth(pts, round_d, t_step, leng, i = 0) = - i <= leng - 3 ? - concat( - _bezier_corner(round_d, t_step, pts[i], pts[i + 1], pts[i + 2]), - _recursive_bezier_smooth(pts, round_d, t_step, leng, i + 1) - ) - : []; +function _recursive_bezier_smooth(pts, round_d, t_step, leng) = + let(end_i = leng - 2) + [ + for(i = 0; i < end_i; i = i + 1) + each _bezier_corner(round_d, t_step, pts[i], pts[i + 1], pts[i + 2]) + ]; + function bezier_smooth(path_pts, round_d, t_step = 0.1, closed = false) = let( diff --git a/src/bezier_surface.scad b/src/bezier_surface.scad index ccc36177..e1889149 100644 --- a/src/bezier_surface.scad +++ b/src/bezier_surface.scad @@ -10,10 +10,10 @@ function bezier_surface(t_step, ctrl_pts) = let(pts = [ - for(i = [0:len(ctrl_pts) - 1]) + for(i = 0; i < len(ctrl_pts); i = i + 1) bezier_curve(t_step, ctrl_pts[i]) ]) - [for(x = [0:len(pts[0]) - 1]) + [for(x = 0; x < len(pts[0]); x = x + 1) bezier_curve(t_step, [for(y = [0:len(pts) - 1]) pts[y][x]] ) diff --git a/src/bijection_offset.scad b/src/bijection_offset.scad index d02291e7..fdb5cbd5 100644 --- a/src/bijection_offset.scad +++ b/src/bijection_offset.scad @@ -8,8 +8,8 @@ * **/ -include <__private__/__lines_from.scad>; -include <__private__/__line_intersection.scad>; +include <__comm__/__lines_from.scad>; +include <__comm__/__line_intersection.scad>; function _bijection_inward_edge_normal(edge) = let( @@ -51,7 +51,7 @@ function bijection_offset(pts, d, epsilon = 0.0001) = ) concat( [ - for(i = [0:leng - 2]) + for(i = 0; i < leng - 1; i = i + 1) let( this_edge = offset_es[i], next_edge = offset_es[i + 1], diff --git a/src/circle_path.scad b/src/circle_path.scad index b8e5f543..30a69081 100644 --- a/src/circle_path.scad +++ b/src/circle_path.scad @@ -8,15 +8,15 @@ * **/ -include <__private__/__frags.scad>; +include <__comm__/__frags.scad>; function circle_path(radius, n) = let( _frags = __frags(radius), step_a = 360 / _frags, - end_a = 360 - step_a * ((n == undef || n > _frags) ? 1 : _frags - n + 1) + end_a = 360 - step_a * ((is_undef(n) || n > _frags) ? 1 : _frags - n + 1) ) [ - for(a = [0 : step_a : end_a]) + for(a = 0; a <= end_a; a = a + step_a) [radius * cos(a), radius * sin(a)] ]; diff --git a/src/cross_sections.scad b/src/cross_sections.scad index 1eeb1563..063001d8 100644 --- a/src/cross_sections.scad +++ b/src/cross_sections.scad @@ -8,15 +8,14 @@ * **/ -include <__private__/__to3d.scad>; -include <__private__/__is_float.scad>; +include <__comm__/__to3d.scad>; function cross_sections(shape_pts, path_pts, angles, twist = 0, scale = 1.0) = let( len_path_pts_minus_one = len(path_pts) - 1, sh_pts = len(shape_pts[0]) == 3 ? shape_pts : [for(p = shape_pts) __to3d(p)], pth_pts = len(path_pts[0]) == 3 ? path_pts : [for(p = path_pts) __to3d(p)], - scale_step_vt = __is_float(scale) ? + scale_step_vt = is_num(scale) ? [(scale - 1) / len_path_pts_minus_one, (scale - 1) / len_path_pts_minus_one] : [(scale[0] - 1) / len_path_pts_minus_one, (scale[1] - 1) / len_path_pts_minus_one] , @@ -25,7 +24,7 @@ function cross_sections(shape_pts, path_pts, angles, twist = 0, scale = 1.0) = twist_step = twist / len_path_pts_minus_one ) [ - for(i = [0:len_path_pts_minus_one]) + for(i = 0; i <= len_path_pts_minus_one; i = i + 1) [ for(p = sh_pts) let(scaled_p = [p[0] * (1 + scale_step_x * i), p[1] * (1 + scale_step_y * i), p[2]]) diff --git a/src/crystal_ball.scad b/src/crystal_ball.scad index 696cd12e..9758adb5 100644 --- a/src/crystal_ball.scad +++ b/src/crystal_ball.scad @@ -8,11 +8,10 @@ * **/ -include <__private__/__nearest_multiple_of_4.scad>; -include <__private__/__is_float.scad>; +include <__comm__/__nearest_multiple_of_4.scad>; module crystal_ball(radius, theta = 360, phi = 180) { - phis = __is_float(phi) ? [0, phi] : phi; + phis = is_num(phi) ? [0, phi] : phi; frags = __frags(radius); @@ -22,13 +21,10 @@ module crystal_ball(radius, theta = 360, phi = 180) { $fn = __nearest_multiple_of_4(frags) ); - // _hole_r = 0.0005 for avoiding warnings when using 2015.03 - // I downloaded 2017.01.20 and found that the problem is solved. - _hole_r = version_num() >= 20170120 ? 0 : 0.0005; ring_extrude( shape_pts, angle = theta, - radius = _hole_r, + radius = 0, $fn = frags ); diff --git a/src/dotSCAD.scad b/src/dotSCAD.scad index ab148ad1..b17cb718 100644 --- a/src/dotSCAD.scad +++ b/src/dotSCAD.scad @@ -8,115 +8,282 @@ * @see https://github.com/JustinSDK/dotSCAD */ -function __polytransversals(transversals) = - let( - leng_trs = len(transversals), - leng_tr = len(transversals[0]), - lefts = [ - for(i = [1:leng_trs - 2]) - let(tr = transversals[leng_trs - i]) - tr[0] - ], - rights = [ - for(i = [1:leng_trs - 2]) - let(tr = transversals[i]) - tr[leng_tr - 1] - ] - ) concat( - transversals[0], - rights, - __reverse(transversals[leng_trs - 1]), - lefts - ); - /** -* m_translation.scad -* -* @copyright Justin Lin, 2019 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-m_translation.html -* -**/ - - -function _to_3_elems_translation_vect(v) = - let(leng = len(v)) - leng == 3 ? v : ( - leng == 2 ? [v[0], v[1], 0] : [v[0], 0, 0] - ); - -function _to_translation_vect(v) = __is_float(v) ? [v, 0, 0] : _to_3_elems_translation_vect(v); - -function m_translation(v) = - let(vt = _to_translation_vect(v)) - [ - [1, 0, 0, vt[0]], - [0, 1, 0, vt[1]], - [0, 0, 1, vt[2]], - [0, 0, 0, 1] - ]; - -function __angy_angz(p1, p2) = - let( - dx = p2[0] - p1[0], - dy = p2[1] - p1[1], - dz = p2[2] - p1[2], - ya = atan2(dz, sqrt(pow(dx, 2) + pow(dy, 2))), - za = atan2(dy, dx) - ) [ya, za]; - -/** -* cross_sections.scad +* rounded_cylinder.scad * * @copyright Justin Lin, 2017 * @license https://opensource.org/licenses/lgpl-3.0.html * -* @see https://openhome.cc/eGossip/OpenSCAD/lib-cross_sections.html +* @see https://openhome.cc/eGossip/OpenSCAD/lib-rounded_cylinder.html * **/ -function cross_sections(shape_pts, path_pts, angles, twist = 0, scale = 1.0) = - let( - len_path_pts_minus_one = len(path_pts) - 1, - sh_pts = len(shape_pts[0]) == 3 ? shape_pts : [for(p = shape_pts) __to3d(p)], - pth_pts = len(path_pts[0]) == 3 ? path_pts : [for(p = path_pts) __to3d(p)], - scale_step_vt = __is_float(scale) ? - [(scale - 1) / len_path_pts_minus_one, (scale - 1) / len_path_pts_minus_one] : - [(scale[0] - 1) / len_path_pts_minus_one, (scale[1] - 1) / len_path_pts_minus_one] - , - scale_step_x = scale_step_vt[0], - scale_step_y = scale_step_vt[1], - twist_step = twist / len_path_pts_minus_one - ) - [ - for(i = [0:len_path_pts_minus_one]) - [ - for(p = sh_pts) - let(scaled_p = [p[0] * (1 + scale_step_x * i), p[1] * (1 + scale_step_y * i), p[2]]) - rotate_p( - rotate_p(scaled_p, twist_step * i) - , angles[i] - ) + pth_pts[i] - ] - ]; +module rounded_cylinder(radius, h, round_r, convexity = 2, center = false) { + r_corners = __half_trapezium(radius, h, round_r); + + shape_pts = concat( + [[0, -h/2]], + r_corners, + [[0, h/2]] + ); + + center_pt = center ? [0, 0, 0] : [0, 0, h/2]; + + translate(center ? [0, 0, 0] : [0, 0, h/2]) + rotate(180) + rotate_extrude(convexity = convexity) + polygon(shape_pts); + + // hook for testing + test_center_half_trapezium(center_pt, shape_pts); +} + +// override it to test +module test_center_half_trapezium(center_pt, shape_pts) { + +} /** -* shear.scad +* rounded_extrude.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-rounded_extrude.html +* +**/ + + +module rounded_extrude(size, round_r, angle = 90, twist = 0, convexity = 10) { + + is_flt = is_num(size); + x = is_flt ? size : size[0]; + y = is_flt ? size : size[1]; + + q_corner_frags = __frags(round_r) / 4; + + step_a = angle / q_corner_frags; + twist_step = twist / q_corner_frags; + + module layers(pre_x, pre_y, pre_h = 0, i = 1) { + module one_layer(current_a) { + wx = pre_x; + wy = pre_y; + + h = (round_r - pre_h) - round_r * cos(current_a); + + d_leng = + round_r * (sin(current_a) - sin(step_a * (i - 1))); + + sx = (d_leng * 2 + wx) / wx; + sy = (d_leng * 2 + wy) / wy; + + translate([0, 0, pre_h]) + rotate(-twist_step * (i - 1)) + linear_extrude( + h, + slices = 1, + scale = [sx, sy], + convexity = convexity, + twist = twist_step + ) scale([wx / x, wy / y]) + children(); + + test_rounded_extrude_data(i, wx, wy, pre_h, sx, sy); + + layers(wx * sx, wy * sy, h + pre_h, i + 1) + children(); + + } + + if(i <= q_corner_frags) { + one_layer(i * step_a) + children(); + } else if(i - q_corner_frags < 1) { + one_layer(q_corner_frags * step_a) + children(); + } + } + + layers(x, y) + children(); +} + +module test_rounded_extrude_data(i, wx, wy, pre_h, sx, sy) { + +} + +/** +* hexagons.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-hexagons.html +* +**/ + +module hexagons(radius, spacing, levels) { + beginning_n = 2 * levels - 1; + offset_x = radius * cos(30); + offset_y = radius + radius * sin(30); + r_hexagon = radius - spacing / 2; + offset_step = 2 * offset_x; + center_offset = 2 * (offset_x - offset_x * levels); + + module hexagon() { + rotate(30) + circle(r_hexagon, $fn = 6); + } + + function hexagons_pts(hex_datum) = + let( + tx = hex_datum[0][0], + ty = hex_datum[0][1], + n = hex_datum[1], + offset_xs = [for(i = 0; i < n; i = i + 1) i * offset_step + center_offset] + ) + [ + for(x = offset_xs) [x + tx, ty] + ]; + + module line_hexagons(hex_datum) { + tx = hex_datum[0][0]; + ty = hex_datum[0][1]; + n = hex_datum[1]; + + offset_xs = [for(i = 0; i < n; i = i + 1) i * offset_step + center_offset]; + for(x = offset_xs) { + p = [x + tx, ty, 0]; + translate(p) + hexagon(); + } + } + + upper_hex_data = levels > 1 ? [ + for(i = [1:beginning_n - levels]) + let( + x = offset_x * i, + y = offset_y * i, + n = beginning_n - i + ) [[x, y], n] + ] : []; + + lower_hex_data = levels > 1 ? [ + for(hex_datum = upper_hex_data) + [[hex_datum[0][0], -hex_datum[0][1]], hex_datum[1]] + ] : []; + + total_hex_data = concat( + [ + [[0, 0], beginning_n] // first line + ], + upper_hex_data, + lower_hex_data + ); + + pts_all_lines = [ + for(hex_datum = total_hex_data) + hexagons_pts(hex_datum) + ]; + + for(pts_one_line = pts_all_lines) { + for(pt = pts_one_line) { + translate(pt) + hexagon(); + } + } + + test_each_hexagon(r_hexagon, pts_all_lines); +} + +// override it to test +module test_each_hexagon(hex_r, pts_all_lines) { + +} + +/** +* px_polyline.scad * * @copyright Justin Lin, 2019 * @license https://opensource.org/licenses/lgpl-3.0.html * -* @see https://openhome.cc/eGossip/OpenSCAD/lib-shear.html +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-px_polyline.html +* +**/ + + +function px_polyline(points) = + let( + is_2d = len(points[0]) == 2, + pts = is_2d ? [for(pt = points) __to3d(pt)] : points, + polyline = [for(line = __lines_from(pts)) each px_line(line[0], line[1])] + ) + is_2d ? [for(pt = polyline) __to2d(pt)] : polyline; + +function __to_3_elems_ang_vect(a) = + let(leng = len(a)) + leng == 3 ? a : ( + leng == 2 ? [a[0], a[1], 0] : [a[0], 0, 0] + ); + +function __to_ang_vect(a) = is_num(a) ? [0, 0, a] : __to_3_elems_ang_vect(a); + +/** +* px_polygon.scad +* +* @copyright Justin Lin, 2019 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-px_polygon.html +* +**/ + +function px_polygon(points, filled = false) = + filled ? + let( + xs = [for(pt = points) pt[0]], + ys = [for(pt = points) pt[1]], + max_x = max(xs), + min_x = min(xs), + max_y = max(ys), + min_y = min(ys) + ) + [ + for(y = min_y; y <= max_y; y = y + 1) + for(x = min_x; x <= max_x; x = x + 1) + let(pt = [x, y]) + if(in_shape(points, pt, true)) pt + ] + : + px_polyline( + concat(points, [points[len(points) - 1], points[0]]) + ); + + +function __reverse(vt) = [for(i = len(vt) - 1; i >= 0; i = i - 1) vt[i]]; + +/** +* m_cumulate.scad +* +* @copyright Justin Lin, 2019 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-m_cumulate.html * **/ +function _m_cumulate(matrice, i) = + i == len(matrice) - 2 ? + matrice[i] * matrice[i + 1] : + matrice[i] * _m_cumulate(matrice, i + 1); + +function m_cumulate(matrice) = + len(matrice) == 1 ? matrice[0] : _m_cumulate(matrice, 0); + -module shear(sx = [0, 0], sy = [0, 0], sz = [0, 0]) { - multmatrix(__m_shearing(sx, sy, sz)) children(); -} /** * bend.scad @@ -178,1968 +345,6 @@ module test_bend_tri_frag(points, angle) { } -/** -* helix.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-helix.html -* -**/ - - -function helix(radius, levels, level_dist, vt_dir = "SPI_DOWN", rt_dir = "CT_CLK") = - let( - is_flt = __is_float(radius), - r1 = is_flt ? radius : radius[0], - r2 = is_flt ? radius : radius[1], - init_r = vt_dir == "SPI_DOWN" ? r2 : r1, - _frags = __frags(init_r), - h = level_dist * levels, - vt_d = vt_dir == "SPI_DOWN" ? 1 : -1, - rt_d = rt_dir == "CT_CLK" ? 1 : -1, - r_diff = (r1 - r2) * vt_d, - h_step = level_dist / _frags * vt_d, - r_step = r_diff / (levels * _frags), - a_step = 360 / _frags * rt_d, - begin_r = vt_dir == "SPI_DOWN" ? r2 : r1, - begin_h = vt_dir == "SPI_DOWN" ? h : 0 - ) - [ - for(i = [0:_frags * levels]) - let(r = begin_r + r_step * i, a = a_step * i) - [r * cos(a), r * sin(a), begin_h - h_step * i] - ]; - -/** -* m_scaling.scad -* -* @copyright Justin Lin, 2019 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-m_scaling.html -* -**/ - - -function _to_3_elems_scaling_vect(s) = - let(leng = len(s)) - leng == 3 ? s : ( - leng == 2 ? [s[0], s[1], 1] : [s[0], 1, 1] - ); - -function _to_scaling_vect(s) = __is_float(s) ? [s, s, s] : _to_3_elems_scaling_vect(s); - -function m_scaling(s) = - let(v = _to_scaling_vect(s)) - [ - [v[0], 0, 0, 0], - [0, v[1], 0, 0], - [0, 0, v[2], 0], - [0, 0, 0, 1] - ]; - -/** -* bezier_curve.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-bezier_curve.html -* -**/ - - -function _combi(n, k) = - let( - bi_coef = [ - [1], // n = 0: for padding - [1,1], // n = 1: for Linear curves, how about drawing a line directly? - [1,2,1], // n = 2: for Quadratic curves - [1,3,3,1] // n = 3: for Cubic Bézier curves - ] - ) - n < len(bi_coef) ? bi_coef[n][k] : ( - k == 0 ? 1 : (_combi(n, k - 1) * (n - k + 1) / k) - ); - -function bezier_curve_coordinate(t, pn, n, i = 0) = - i == n + 1 ? 0 : - (_combi(n, i) * pn[i] * pow(1 - t, n - i) * pow(t, i) + - bezier_curve_coordinate(t, pn, n, i + 1)); - -function _bezier_curve_point(t, points) = - let(n = len(points) - 1) - [ - bezier_curve_coordinate( - t, - [for(p = points) p[0]], - n - ), - bezier_curve_coordinate( - t, - [for(p = points) p[1]], - n - ), - bezier_curve_coordinate( - t, - [for(p = points) p[2]], - n - ) - ]; - -function bezier_curve(t_step, points) = - let( - pts = concat([ - for(t = [0: ceil(1 / t_step) - 1]) - _bezier_curve_point(t * t_step, points) - ], [_bezier_curve_point(1, points)]) - ) - len(points[0]) == 3 ? pts : [for(pt = pts) __to2d(pt)]; - - -/** -* m_shearing.scad -* -* @copyright Justin Lin, 2019 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-m_shearing.html -* -**/ - - -function m_shearing(sx = [0, 0], sy = [0, 0], sz = [0, 0]) = __m_shearing(sx, sy, sz); - -/** -* trim_shape.scad -* -* @copyright Justin Lin, 2019 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-trim_shape.html -* -**/ - - -function _trim_shape_any_intersection_sub(lines, line, lines_leng, i, epsilon) = - let( - p = __line_intersection(lines[i], line, epsilon) - ) - (p != [] && __in_line(line, p, epsilon) && __in_line(lines[i], p, epsilon)) ? [i, p] : _trim_shape_any_intersection(lines, line, lines_leng, i + 1, epsilon); - -// return [idx, [x, y]] or [] -function _trim_shape_any_intersection(lines, line, lines_leng, i, epsilon) = - i == lines_leng ? [] : _trim_shape_any_intersection_sub(lines, line, lines_leng, i, epsilon); - -function _trim_sub(lines, leng, epsilon) = - let( - current_line = lines[0], - next_line = lines[1], - lines_from_next = [for(j = [1 : leng - 1]) lines[j]], - lines_from_next2 = [for(j = [2 : leng - 1]) lines[j]], - current_p = current_line[0], - leng_lines_from_next2 = len(lines_from_next2), - inter_p = _trim_shape_any_intersection(lines_from_next2, current_line, leng_lines_from_next2, 0, epsilon) - ) - // no intersecting pt, collect current_p and trim remain lines - inter_p == [] ? (concat([current_p], _trim_shape_trim_lines(lines_from_next, epsilon))) : ( - // collect current_p, intersecting pt and the last pt - (leng == 3 || (inter_p[0] == (leng_lines_from_next2 - 1))) ? [current_p, inter_p[1], lines[leng - 1]] : ( - // collect current_p, intersecting pt and trim remain lines - concat([current_p, inter_p[1]], - _trim_shape_trim_lines([for(i = [inter_p[0] + 1 : leng_lines_from_next2 - 1]) lines_from_next2[i]], epsilon) - ) - ) - ); - -function _trim_shape_trim_lines(lines, epsilon) = - let(leng = len(lines)) - leng > 2 ? _trim_sub(lines, leng, epsilon) : _trim_shape_collect_pts_from(lines, leng); - -function _trim_shape_collect_pts_from(lines, leng) = - concat([for(line = lines) line[0]], [lines[leng - 1][1]]); - -function trim_shape(shape_pts, from, to, epsilon = 0.0001) = - let( - pts = [for(i = [from:to]) shape_pts[i]], - trimmed = _trim_shape_trim_lines(__lines_from(pts), epsilon) - ) - len(shape_pts) == len(trimmed) ? trimmed : trim_shape(trimmed, 0, len(trimmed) - 1, epsilon); - - -/** -* parse_number.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib2-parse_number.html -* -**/ - -function _str_to_int(t) = - let( - dict = [["0", 0], ["1", 1], ["2", 2], ["3", 3], ["4", 4], ["5", 5], ["6", 6], ["7", 7], ["8", 8], ["9", 9]], - n = dict[search(t, dict)[0]][1] - ) n; - -function _parse_positive_int(t, value = 0, i = 0) = - i == len(t) ? value : _parse_positive_int(t, value * pow(10, i) + _str_to_int(t[i]), i + 1); - -function _parse_positive_decimal(t, value = 0, i = 0) = - i == len(t) ? value : _parse_positive_decimal(t, value + _str_to_int(t[i]) * pow(10, -(i + 1)), i + 1); - -function _parse_positive_number(t) = - len(search(".", t)) == 0 ? _parse_positive_int(t) : - _parse_positive_int(split_str(t, ".")[0]) + _parse_positive_decimal(split_str(t, ".")[1]); - -function parse_number(t) = - t[0] == "-" ? -_parse_positive_number(sub_str(t, 1, len(t))) : _parse_positive_number(t); - - - -/** -* polyline2d.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-polyline2d.html -* -**/ - -module polyline2d(points, width, startingStyle = "CAP_SQUARE", endingStyle = "CAP_SQUARE") { - leng_pts = len(points); - - module line_segment(index) { - styles = index == 1 ? [startingStyle, "CAP_ROUND"] : ( - index == leng_pts - 1 ? ["CAP_BUTT", endingStyle] : [ - "CAP_BUTT", "CAP_ROUND" - ] - ); - - p1 = points[index - 1]; - p2 = points[index]; - p1Style = styles[0]; - p2Style = styles[1]; - - line2d(points[index - 1], points[index], width, - p1Style = p1Style, p2Style = p2Style); - - // hook for testing - test_line_segment(index, p1, p2, width, p1Style, p2Style); - } - - module polyline2d_inner(index) { - if(index < leng_pts) { - line_segment(index); - polyline2d_inner(index + 1); - } - } - - polyline2d_inner(1); -} - -// override it to test -module test_line_segment(index, point1, point2, width, p1Style, p2Style) { - -} - -/** -* midpt_smooth.scad -* -* @copyright Justin Lin, 2019 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-midpt_smooth.html -* -**/ - -function _midpt_smooth_sub(points, iend, i, closed = false) = - i == iend ? ( - closed ? [(points[i] + points[0]) / 2] - : [] - ) : concat([(points[i] + points[i + 1]) / 2], _midpt_smooth_sub(points, iend, i + 1, closed)); - -function midpt_smooth(points, n, closed = false) = - let( - smoothed = _midpt_smooth_sub(points, len(points) - 1, 0, closed) - ) - n == 1 ? smoothed : midpt_smooth(smoothed, n - 1, closed); - -function __frags(radius) = $fn > 0 ? - ($fn >= 3 ? $fn : 3) : - max(min(360 / $fa, radius * 6.28318 / $fs), 5); - -/** -* turtle2d.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-turtle2d.html -* -**/ - -function _turtle2d_turtle(x, y, angle) = [[x, y], angle]; - -function _turtle2d_set_point(turtle, point) = [point, _turtle2d_get_angle(turtle)]; - -function _turtle2d_set_x(turtle, x) = [[x, _turtle2d_get_y(turtle)], _turtle2d_get_angle(turtle)]; -function _turtle2d_set_y(turtle, y) = [[_turtle2d_get_x(turtle), y], _turtle2d_get_angle(turtle)]; -function _turtle2d_set_angle(turtle, angle) = [_turtle2d_get_pt(turtle), angle]; - -function _turtle2d_forward(turtle, leng) = - _turtle2d_turtle( - _turtle2d_get_x(turtle) + leng * cos(_turtle2d_get_angle(turtle)), - _turtle2d_get_y(turtle) + leng * sin(_turtle2d_get_angle(turtle)), - _turtle2d_get_angle(turtle) - ); - -function _turtle2d_turn(turtle, angle) = [_turtle2d_get_pt(turtle), _turtle2d_get_angle(turtle) + angle]; - -function _turtle2d_get_x(turtle) = turtle[0][0]; -function _turtle2d_get_y(turtle) = turtle[0][1]; -function _turtle2d_get_pt(turtle) = turtle[0]; -function _turtle2d_get_angle(turtle) = turtle[1]; - -function _turtle2d_three_args_command(cmd, arg1, arg2, arg3) = - cmd == "create" ? _turtle2d_turtle(arg1, arg2, arg3) : _turtle2d_two_args_command(cmd, arg1, arg2); - -function _turtle2d_two_args_command(cmd, arg1, arg2) = - arg2 == undef ? _turtle2d_one_arg_command(cmd, arg1) : ( - cmd == "pt" ? _turtle2d_set_point(arg1, arg2) : ( - cmd == "x" ? _turtle2d_set_x(arg1, arg2) : ( - cmd == "y" ? _turtle2d_set_y(arg1, arg2) : ( - cmd == "angle" ? _turtle2d_set_angle(arg1, arg2) : ( - cmd == "forward" ? _turtle2d_forward(arg1, arg2) : ( - cmd == "turn" ? _turtle2d_turn(arg1, arg2) : undef - ) - ) - ) - ) - ) - ); - -function _turtle2d_one_arg_command(cmd, arg) = - cmd == "x" ? _turtle2d_get_x(arg) : ( - cmd == "y" ? _turtle2d_get_y(arg) : ( - cmd == "angle" ? _turtle2d_get_angle(arg) : ( - cmd == "pt" ? _turtle2d_get_pt(arg) : undef - ) - ) - ); - -function turtle2d(cmd, arg1, arg2, arg3) = - _turtle2d_three_args_command(cmd, arg1, arg2, arg3); - - -/** -* shape_cyclicpolygon.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-shape_cyclicpolygon.html -* -**/ - - -function shape_cyclicpolygon(sides, circle_r, corner_r) = - let( - frag_a = 360 / sides, - corner_a = (180 - frag_a), - corner_circle_a = 180 - corner_a, - half_corner_circle_a = corner_circle_a / 2, - corner_circle_center = circle_r - corner_r / sin(corner_a / 2), - first_corner = [ - for( - pt = __pie_for_rounding( - corner_r, - -half_corner_circle_a, - half_corner_circle_a, - __frags(corner_r) * corner_circle_a / 360 - ) - ) - [pt[0] + corner_circle_center, pt[1]] - ] - - ) - concat( - first_corner, - [ - for(side = [1:sides - 1]) - for(pt = first_corner) - let( - a = frag_a * side, - x = pt[0], - y = pt[1], - sina = sin(a), - cosa = cos(a) - ) - [ - x * cosa - y * sina, - x * sina + y * cosa - ] - ] - ); - -/** -* path_extrude.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-path_extrude.html -* -**/ - - -// Becuase of improving the performance, this module requires m_rotation.scad which doesn't require in dotSCAD 1.0. -// For backward compatibility, I directly include m_rotation here. - -module path_extrude(shape_pts, path_pts, triangles = "SOLID", twist = 0, scale = 1.0, closed = false, method = "AXIS_ANGLE") { - sh_pts = len(shape_pts[0]) == 3 ? shape_pts : [for(p = shape_pts) __to3d(p)]; - pth_pts = len(path_pts[0]) == 3 ? path_pts : [for(p = path_pts) __to3d(p)]; - - len_path_pts = len(pth_pts); - len_path_pts_minus_one = len_path_pts - 1; - - - module axis_angle_path_extrude() { - twist_step_a = twist / len_path_pts; - - function scale_pts(pts, s) = [ - for(p = pts) [p[0] * s[0], p[1] * s[1], p[2] * s[2]] - ]; - - function translate_pts(pts, t) = [ - for(p = pts) [p[0] + t[0], p[1] + t[1], p[2] + t[2]] - ]; - - function rotate_pts(pts, a, v) = [for(p = pts) rotate_p(p, a, v)]; - - function scale_step() = - let(s = (scale - 1) / len_path_pts_minus_one) - [s, s, s]; - - scale_step_vt = __is_float(scale) ? - scale_step() : - [ - (scale[0] - 1) / len_path_pts_minus_one, - (scale[1] - 1) / len_path_pts_minus_one, - scale[2] == undef ? 0 : (scale[2] - 1) / len_path_pts_minus_one - ]; - - // get rotation matrice for sections - - function local_ang_vects(j) = - j == 0 ? [] : local_ang_vects_sub(j); - - function local_ang_vects_sub(j) = - let( - vt0 = pth_pts[j] - pth_pts[j - 1], - vt1 = pth_pts[j + 1] - pth_pts[j], - a = acos((vt0 * vt1) / (norm(vt0) * norm(vt1))), - v = cross(vt0, vt1) - ) - concat([[a, v]], local_ang_vects(j - 1)); - - rot_matrice = [ - for(ang_vect = local_ang_vects(len_path_pts - 2)) - m_rotation(ang_vect[0], ang_vect[1]) - ]; - - leng_rot_matrice = len(rot_matrice); - leng_rot_matrice_minus_one = leng_rot_matrice - 1; - leng_rot_matrice_minus_two= leng_rot_matrice - 2; - - identity_matrix = [ - [1, 0, 0, 0], - [0, 1, 0, 0], - [0, 0, 1, 0], - [0, 0, 0, 1] - ]; - - function cumulated_rot_matrice(i) = - leng_rot_matrice == 0 ? [identity_matrix] : ( - leng_rot_matrice == 1 ? [rot_matrice[0], identity_matrix] : - ( - i == leng_rot_matrice_minus_two ? - [ - rot_matrice[leng_rot_matrice_minus_one], - rot_matrice[leng_rot_matrice_minus_two] * rot_matrice[leng_rot_matrice_minus_one] - ] - : cumulated_rot_matrice_sub(i)) - ); - - function cumulated_rot_matrice_sub(i) = - let( - matrice = cumulated_rot_matrice(i + 1), - curr_matrix = rot_matrice[i], - prev_matrix = matrice[len(matrice) - 1] - ) - concat(matrice, [curr_matrix * prev_matrix]); - - cumu_rot_matrice = cumulated_rot_matrice(0); - - // get all sections - - function init_section(a, s) = - let(angleyz = __angy_angz(pth_pts[0], pth_pts[1])) - rotate_pts( - rotate_pts( - rotate_pts( - scale_pts(sh_pts, s), a - ), [90, 0, -90] - ), [0, -angleyz[0], angleyz[1]] - ); - - function local_rotate_section(j, init_a, init_s) = - j == 0 ? - init_section(init_a, init_s) : - local_rotate_section_sub(j, init_a, init_s); - - function local_rotate_section_sub(j, init_a, init_s) = - let( - vt0 = pth_pts[j] - pth_pts[j - 1], - vt1 = pth_pts[j + 1] - pth_pts[j], - ms = cumu_rot_matrice[j - 1] - ) - [ - for(p = init_section(init_a, init_s)) - [ - [ms[0][0], ms[0][1], ms[0][2]] * p, - [ms[1][0], ms[1][1], ms[1][2]] * p, - [ms[2][0], ms[2][1], ms[2][2]] * p - ] - ]; - - function sections() = - let( - fst_section = - translate_pts(local_rotate_section(0, 0, [1, 1, 1]), pth_pts[0]), - remain_sections = [ - for(i = [0:len_path_pts - 2]) - - translate_pts( - local_rotate_section(i, i * twist_step_a, [1, 1, 1] + scale_step_vt * i), - pth_pts[i + 1] - ) - - - ] - ) concat([fst_section], remain_sections); - - sects = sections(); - - function calculated_sections() = - closed && pth_pts[0] == pth_pts[len_path_pts_minus_one] ? - concat(sects, [sects[0]]) : // round-robin - sects; - - polysections( - calculated_sections(), - triangles = triangles - ); - - // hook for testing - test_path_extrude(sects); - } - - module euler_angle_path_extrude() { - scale_step_vt = __is_float(scale) ? - [(scale - 1) / len_path_pts_minus_one, (scale - 1) / len_path_pts_minus_one] : - [(scale[0] - 1) / len_path_pts_minus_one, (scale[1] - 1) / len_path_pts_minus_one]; - - scale_step_x = scale_step_vt[0]; - scale_step_y = scale_step_vt[1]; - twist_step = twist / len_path_pts_minus_one; - - function section(p1, p2, i) = - let( - length = norm(p1 - p2), - angy_angz = __angy_angz(p1, p2), - ay = -angy_angz[0], - az = angy_angz[1] - ) - [ - for(p = sh_pts) - let(scaled_p = [p[0] * (1 + scale_step_x * i), p[1] * (1 + scale_step_y * i), p[2]]) - rotate_p( - rotate_p( - rotate_p(scaled_p, twist_step * i), [90, 0, -90] - ) + [i == 0 ? 0 : length, 0, 0], - [0, ay, az] - ) + p1 - ]; - - function path_extrude_inner(index) = - index == len_path_pts ? [] : - concat( - [section(pth_pts[index - 1], pth_pts[index], index)], - path_extrude_inner(index + 1) - ); - - function calculated_sections() = - let(sections = path_extrude_inner(1)) - closed && pth_pts[0] == pth_pts[len_path_pts_minus_one] ? - concat(sections, [sections[0]]) : // round-robin - concat([section(pth_pts[0], pth_pts[1], 0)], sections); - - sections = calculated_sections(); - - polysections( - sections, - triangles = triangles - ); - - // hook for testing - test_path_extrude(sections); - } - - if(method == "AXIS_ANGLE") { - axis_angle_path_extrude(); - } - else if(method == "EULER_ANGLE") { - euler_angle_path_extrude(); - } -} - - -// override to test -module test_path_extrude(sections) { - -} - -/** -* bezier_surface.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-bezier_surface.html -* -**/ - -function bezier_surface(t_step, ctrl_pts) = - let(pts = [ - for(i = [0:len(ctrl_pts) - 1]) - bezier_curve(t_step, ctrl_pts[i]) - ]) - [for(x = [0:len(pts[0]) - 1]) - bezier_curve(t_step, - [for(y = [0:len(pts) - 1]) pts[y][x]] - ) - ]; - -/** -* torus_knot.scad -* -* @copyright Justin Lin, 2019 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-torus_knot.html -* -**/ - -function torus_knot(p, q, phi_step) = [ - for(phi = [0:phi_step:6.28318]) - let( - degree = phi * 180 / 3.14159, - r = cos(q * degree) + 2, - x = r * cos(p * degree), - y = r * sin(p * degree), - z = -sin(q * degree) - ) - [x, y, z] -]; - -/** -* rounded_square.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-rounded_square.html -* -**/ - - -module rounded_square(size, corner_r, center = false) { - is_flt = __is_float(size); - x = is_flt ? size : size[0]; - y = is_flt ? size : size[1]; - - position = center ? [0, 0] : [x / 2, y / 2]; - points = __trapezium( - length = x, - h = y, - round_r = corner_r - ); - - translate(position) - polygon(points); - - // hook for testing - test_rounded_square(position, points); -} - -// override it to test -module test_rounded_square(position, points) { -} - -/** -* m_mirror.scad -* -* @copyright Justin Lin, 2019 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-m_mirror.html -* -**/ - -function m_mirror(v) = - let( - nv = v / norm(v), - txx = -2* nv[0] * nv[0], - txy = -2* nv[0] * nv[1], - txz = -2* nv[0] * nv[2], - tyy = -2* nv[1] * nv[1], - tyz = -2* nv[1] * nv[2], - tzz = -2* nv[2] * nv[2] - ) - [ - [1 + txx, txy, txz, 0], - [txy, 1 + tyy, tyz, 0], - [txz, tyz, 1 + tzz, 0], - [0, 0, 0, 1] - ]; - -/** -* polyline3d.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-polyline3d.html -* -**/ - -module polyline3d(points, thickness, startingStyle = "CAP_CIRCLE", endingStyle = "CAP_CIRCLE") { - leng_pts = len(points); - - module line_segment(index) { - styles = index == 1 ? [startingStyle, "CAP_BUTT"] : ( - index == leng_pts - 1 ? ["CAP_SPHERE", endingStyle] : [ - "CAP_SPHERE", "CAP_BUTT" - ] - ); - - p1 = points[index - 1]; - p2 = points[index]; - p1Style = styles[0]; - p2Style = styles[1]; - - line3d(p1, p2, thickness, - p1Style = p1Style, p2Style = p2Style); - - // hook for testing - test_line3d_segment(index, p1, p2, thickness, p1Style, p2Style); - } - - module polyline3d_inner(index) { - if(index < leng_pts) { - line_segment(index); - polyline3d_inner(index + 1); - } - } - - polyline3d_inner(1); -} - -// override it to test -module test_line3d_segment(index, point1, point2, thickness, p1Style, p2Style) { - -} - -/** -* polysections.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-polysections.html -* -**/ - - -module polysections(sections, triangles = "SOLID") { - - function side_indexes(sects, begin_idx = 0) = - let( - leng_sects = len(sects), - leng_pts_sect = len(sects[0]) - ) - concat( - [ - for(j = [begin_idx:leng_pts_sect:begin_idx + (leng_sects - 2) * leng_pts_sect]) - for(i = [0:leng_pts_sect - 1]) - [ - j + i, - j + (i + 1) % leng_pts_sect, - j + (i + 1) % leng_pts_sect + leng_pts_sect - ] - ], - [ - for(j = [begin_idx:leng_pts_sect:begin_idx + (leng_sects - 2) * leng_pts_sect]) - for(i = [0:leng_pts_sect - 1]) - [ - j + i, - j + (i + 1) % leng_pts_sect + leng_pts_sect , - j + i + leng_pts_sect - ] - ] - ); - - function search_at(f_sect, p, leng_pts_sect, i = 0) = - i < leng_pts_sect ? - (p == f_sect[i] ? i : search_at(f_sect, p, leng_pts_sect, i + 1)) : -1; - - function the_same_after_twisting(f_sect, l_sect, leng_pts_sect) = - let( - found_at_i = search_at(f_sect, l_sect[0], leng_pts_sect) - ) - found_at_i <= 0 ? false : - l_sect == concat( - [for(i = [found_at_i:leng_pts_sect-1]) f_sect[i]], - [for(i = [0:found_at_i - 1]) f_sect[i]] - ); - - function to_v_pts(sects) = - [ - for(sect = sects) - for(pt = sect) - pt - ]; - - module solid_sections(sects) { - - leng_sects = len(sects); - leng_pts_sect = len(sects[0]); - first_sect = sects[0]; - last_sect = sects[leng_sects - 1]; - - v_pts = [ - for(sect = sects) - for(pt = sect) - pt - ]; - - function begin_end_the_same() = - first_sect == last_sect || - the_same_after_twisting(first_sect, last_sect, leng_pts_sect); - - if(begin_end_the_same()) { - f_idxes = side_indexes(sects); - - polyhedron( - v_pts, - f_idxes - ); - - // hook for testing - test_polysections_solid(v_pts, f_idxes); - } else { - first_idxes = [for(i = [0:leng_pts_sect - 1]) leng_pts_sect - 1 - i]; - last_idxes = [ - for(i = [0:leng_pts_sect - 1]) - i + leng_pts_sect * (leng_sects - 1) - ]; - - f_idxes = concat([first_idxes], side_indexes(sects), [last_idxes]); - - polyhedron( - v_pts, - f_idxes - ); - - // hook for testing - test_polysections_solid(v_pts, f_idxes); - } - } - - module hollow_sections(sects) { - leng_sects = len(sects); - leng_sect = len(sects[0]); - half_leng_sect = leng_sect / 2; - half_leng_v_pts = leng_sects * half_leng_sect; - - function strip_sects(begin_idx, end_idx) = - [ - for(i = [0:leng_sects - 1]) - [ - for(j = [begin_idx:end_idx]) - sects[i][j] - ] - ]; - - function first_idxes() = - [ - for(i = [0:half_leng_sect - 1]) - [ - i, - i + half_leng_v_pts, - (i + 1) % half_leng_sect + half_leng_v_pts, - (i + 1) % half_leng_sect - ] - ]; - - function last_idxes(begin_idx) = - [ - for(i = [0:half_leng_sect - 1]) - [ - begin_idx + i, - begin_idx + (i + 1) % half_leng_sect, - begin_idx + (i + 1) % half_leng_sect + half_leng_v_pts, - begin_idx + i + half_leng_v_pts - ] - ]; - - outer_sects = strip_sects(0, half_leng_sect - 1); - inner_sects = strip_sects(half_leng_sect, leng_sect - 1); - - outer_v_pts = to_v_pts(outer_sects); - inner_v_pts = to_v_pts(inner_sects); - - outer_idxes = side_indexes(outer_sects); - inner_idxes = [ - for(idxes = side_indexes(inner_sects, half_leng_v_pts)) - __reverse(idxes) - ]; - - first_outer_sect = outer_sects[0]; - last_outer_sect = outer_sects[leng_sects - 1]; - first_inner_sect = inner_sects[0]; - last_inner_sect = inner_sects[leng_sects - 1]; - - leng_pts_sect = len(first_outer_sect); - - function begin_end_the_same() = - (first_outer_sect == last_outer_sect && first_inner_sect == last_inner_sect) || - ( - the_same_after_twisting(first_outer_sect, last_outer_sect, leng_pts_sect) && - the_same_after_twisting(first_inner_sect, last_inner_sect, leng_pts_sect) - ); - - v_pts = concat(outer_v_pts, inner_v_pts); - - if(begin_end_the_same()) { - f_idxes = concat(outer_idxes, inner_idxes); - - polyhedron( - v_pts, - f_idxes - ); - - // hook for testing - test_polysections_solid(v_pts, f_idxes); - } else { - first_idxes = first_idxes(); - last_idxes = last_idxes(half_leng_v_pts - half_leng_sect); - - f_idxes = concat(first_idxes, outer_idxes, inner_idxes, last_idxes); - - polyhedron( - v_pts, - f_idxes - ); - - // hook for testing - test_polysections_solid(v_pts, f_idxes); - } - } - - module triangles_defined_sections() { - module tri_sections(tri1, tri2) { - hull() polyhedron( - points = concat(tri1, tri2), - faces = [ - [0, 1, 2], - [3, 5, 4], - [1, 3, 4], [2, 1, 4], [2, 3, 0], - [0, 3, 1], [2, 4, 5], [2, 5, 3] - ] - ); - } - - module two_sections(section1, section2) { - for(idx = triangles) { - tri_sections( - [ - section1[idx[0]], - section1[idx[1]], - section1[idx[2]] - ], - [ - section2[idx[0]], - section2[idx[1]], - section2[idx[2]] - ] - ); - } - } - - for(i = [0:len(sections) - 2]) { - two_sections( - sections[i], - sections[i + 1] - ); - } - } - - if(triangles == "SOLID") { - solid_sections(sections); - } else if(triangles == "HOLLOW") { - hollow_sections(sections); - } - else { - triangles_defined_sections(); - } -} - -// override it to test - -module test_polysections_solid(points, faces) { - -} - -/** -* shape_arc.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-shape_arc.html -* -**/ - - -function shape_arc(radius, angle, width, width_mode = "LINE_CROSS") = - __shape_arc(radius, angle, width, width_mode); - -/** -* starburst.scad -* -* @copyright Justin Lin, 2019 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-starburst.html -* -**/ - -module starburst(r1, r2, n, height) { - a = 180 / n; - - p0 = [0, 0, 0]; - p1 = [r2 * cos(a), r2 * sin(a), 0]; - p2 = [r1, 0, 0]; - p3 = [0, 0, height]; - - module half_burst() { - polyhedron(points = [p0, p1, p2, p3], - faces = [ - [0, 2, 1], - [0, 1, 3], - [0, 3, 2], - [2, 1, 3] - ] - ); - } - - module burst() { - hull() { - half_burst(); - mirror([0, 1,0]) half_burst(); - } - } - - union() { - for(i = [0 : n - 1]) { - rotate(2 * a * i) burst(); - } - } -} - -/** -* archimedean_spiral.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-archimedean_spiral.html -* -**/ - -function _radian_step(b, theta, l) = - let(r_square = pow(b * theta, 2)) - acos((2 * r_square - pow(l, 2)) / (2 * r_square)) / 180 * 3.14159; - -function _find_radians(b, point_distance, radians, n, count = 1) = - let(pre_radians = radians[count - 1]) - count == n ? radians : ( - _find_radians( - b, - point_distance, - concat( - radians, - [pre_radians + _radian_step(b, pre_radians, point_distance)] - ), - n, - count + 1) - ); - -function archimedean_spiral(arm_distance, init_angle, point_distance, num_of_points, rt_dir = "CT_CLK") = - let(b = arm_distance / 6.28318, init_radian = init_angle *3.14159 / 180) - [ - for(theta = _find_radians(b, point_distance, [init_radian], num_of_points)) - let(r = b * theta, a = (rt_dir == "CT_CLK" ? 1 : -1) * theta * 57.2958) - [[r * cos(a), r * sin(a)], a] - ]; - -/** -* helix_extrude.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-helix_extrude.html -* -**/ - - -module helix_extrude(shape_pts, radius, levels, level_dist, - vt_dir = "SPI_DOWN", rt_dir = "CT_CLK", - twist = 0, scale = 1.0, triangles = "SOLID") { - - function reverse(vt) = - let(leng = len(vt)) - [ - for(i = [0:leng - 1]) - vt[leng - 1 - i] - ]; - - is_flt = __is_float(radius); - r1 = is_flt ? radius : radius[0]; - r2 = is_flt ? radius : radius[1]; - - init_r = vt_dir == "SPI_DOWN" ? r2 : r1; - - frags = __frags(init_r); - - v_dir = vt_dir == "SPI_UP" ? 1 : -1; - r_dir = rt_dir == "CT_CLK" ? 1 : -1; - - angle_step = 360 / frags * r_dir; - initial_angle = atan2(level_dist / frags, 6.28318 * init_r / frags) * v_dir * r_dir; - - path_points = helix( - radius = radius, - levels = levels, - level_dist = level_dist, - vt_dir = vt_dir, - rt_dir = rt_dir - ); - - clk_a = r_dir == 1 ? 0 : 180; - angles = [for(i = [0:len(path_points) - 1]) [90 + initial_angle, 0, clk_a + angle_step * i]]; - - sections = cross_sections(shape_pts, path_points, angles, twist, scale); - - polysections( - sections, - triangles = triangles - ); - - // hook for testing - test_helix_extrude(sections); -} - -// override it to test -module test_helix_extrude(sections) { - -} - -/** -* shape_square.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-shape_square.html -* -**/ - - -function shape_square(size, corner_r = 0) = - let( - is_flt = __is_float(size), - x = is_flt ? size : size[0], - y = is_flt ? size : size[1] - ) - __trapezium( - length = x, - h = y, - round_r = corner_r - ); - - -function __shape_arc(radius, angle, width, width_mode = "LINE_CROSS") = - let( - w_offset = width_mode == "LINE_CROSS" ? [width / 2, -width / 2] : ( - width_mode == "LINE_INWARD" ? [0, -width] : [width, 0] - ), - frags = __frags(radius), - a_step = 360 / frags, - half_a_step = a_step / 2, - angles = __is_float(angle) ? [0, angle] : angle, - m = floor(angles[0] / a_step) + 1, - n = floor(angles[1] / a_step), - r_outer = radius + w_offset[0], - r_inner = radius + w_offset[1], - points = concat( - // outer arc path - [__ra_to_xy(__edge_r_begin(r_outer, angles[0], a_step, m), angles[0])], - m > n ? [] : [ - for(i = [m:n]) - __ra_to_xy(r_outer, a_step * i) - ], - angles[1] == a_step * n ? [] : [__ra_to_xy(__edge_r_end(r_outer, angles[1], a_step, n), angles[1])], - // inner arc path - angles[1] == a_step * n ? [] : [__ra_to_xy(__edge_r_end(r_inner, angles[1], a_step, n), angles[1])], - m > n ? [] : [ - for(i = [m:n]) - let(idx = (n + (m - i))) - __ra_to_xy(r_inner, a_step * idx) - - ], - [__ra_to_xy(__edge_r_begin(r_inner, angles[0], a_step, m), angles[0])] - ) - ) points; - -/** -* arc.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-arc.html -* -**/ - - -module arc(radius, angle, width, width_mode = "LINE_CROSS") { - polygon(__shape_arc(radius, angle, width, width_mode)); -} - -/** -* in_shape.scad -* -* @copyright Justin Lin, 2019 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-in_shape.html -* -**/ - - -function _in_shape_in_line_equation(edge, pt) = - let( - x1 = edge[0][0], - y1 = edge[0][1], - x2 = edge[1][0], - y2 = edge[1][1], - a = (y2 - y1) / (x2 - x1), - b = y1 - a * x1 - ) - (pt[1] == a * pt[0] + b); - -function _in_shape_in_any_edges_sub(edges, leng, pt, i, epsilon) = - leng == i ? false : ( - __in_line(edges[i], pt, epsilon) ? true : _in_shape_in_any_edges_sub(edges, leng, pt, i + 1, epsilon) - ); - -function _in_shape_in_any_edges(edges, pt, epsilon) = _in_shape_in_any_edges_sub(edges, len(edges), pt, 0, epsilon); - -function _in_shape_interpolate_x(y, p1, p2) = - p1[1] == p2[1] ? p1[0] : ( - p1[0] + (p2[0] - p1[0]) * (y - p1[1]) / (p2[1] - p1[1]) - ); - -function _in_shape_does_pt_cross(pts, i, j, pt) = - ((pts[i][1] > pt[1]) != (pts[j][1] > pt[1])) && - (pt[0] < _in_shape_interpolate_x(pt[1], pts[i], pts[j])); - - -function _in_shape_sub(shapt_pts, leng, pt, cond, i, j) = - j == leng ? cond : ( - _in_shape_does_pt_cross(shapt_pts, i, j, pt) ? - _in_shape_sub(shapt_pts, leng, pt, !cond, j, j + 1) : - _in_shape_sub(shapt_pts, leng, pt, cond, j, j + 1) - ); - -function in_shape(shapt_pts, pt, include_edge = false, epsilon = 0.0001) = - let( - leng = len(shapt_pts), - edges = __lines_from(shapt_pts, true) - ) - _in_shape_in_any_edges(edges, pt, epsilon) ? include_edge : - _in_shape_sub(shapt_pts, leng, pt, false, leng - 1, 0); - -function __lines_from(pts, closed = false) = - let(leng = len(pts)) - concat( - [for(i = [0:leng - 2]) [pts[i], pts[i + 1]]], - closed ? [[pts[len(pts) - 1], pts[0]]] : [] - ); - - -/** -* arc_shape.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-arc_path.html -* -**/ - - -function arc_path(radius, angle) = - let( - frags = __frags(radius), - a_step = 360 / frags, - angles = __is_float(angle) ? [0, angle] : angle, - m = floor(angles[0] / a_step) + 1, - n = floor(angles[1] / a_step), - points = concat([__ra_to_xy(__edge_r_begin(radius, angles[0], a_step, m), angles[0])], - m > n ? [] : [ - for(i = [m:n]) - __ra_to_xy(radius, a_step * i) - ], - angles[1] == a_step * n ? [] : [__ra_to_xy(__edge_r_end(radius, angles[1], a_step, n), angles[1])]) - ) points; - -/** -* sphere_spiral.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-sphere_spiral.html -* -**/ - -function sphere_spiral(radius, za_step, z_circles = 1, begin_angle = 0, end_angle = 0, vt_dir = "SPI_DOWN", rt_dir = "CT_CLK") = - [ - for(a = [begin_angle:za_step:90 * z_circles - end_angle]) - let( - ya = vt_dir == "SPI_DOWN" ? (-90 + 2 * a / z_circles) : (90 + 2 * a / z_circles), - za = (rt_dir == "CT_CLK" ? 1 : -1) * a, - ra = [0, ya, za] - ) - [rotate_p([radius, 0, 0], ra), ra] - ]; - -/** -* paths2sections.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-paths2sections.html -* -**/ - -function paths2sections(paths) = - let( - leng_path = len(paths[0]), - leng_paths = len(paths) - ) - [ - for(i = [0:leng_path - 1]) - [ - for(j = [0:leng_paths - 1]) - paths[j][i] - ] - ]; - -/** -* shape_trapezium.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-shape_trapezium.html -* -**/ - - -function shape_trapezium(length, h, corner_r = 0) = - __trapezium( - length = length, - h = h, - round_r = corner_r - ); - - -/** -* split_str.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-split_str.html -* -**/ - -function _split_t_by(idxs, t, ts = [], i = -1) = - i == -1 ? _split_t_by(idxs, t, [sub_str(t, 0, idxs[0])], i + 1) : ( - i == len(idxs) - 1 ? concat(ts, sub_str(t, idxs[i] + 1)) : - _split_t_by(idxs, t, concat(ts, sub_str(t, idxs[i] + 1, idxs[i + 1])), i + 1) - ); - -function split_str(t, delimiter) = - len(search(delimiter, t)) == 0 ? - [t] : _split_t_by(search(delimiter, t, 0)[0], t); - -/** -* bijection_offset.scad -* -* @copyright Justin Lin, 2019 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-bijection_offset.html -* -**/ - - -function _bijection_inward_edge_normal(edge) = - let( - pt1 = edge[0], - pt2 = edge[1], - dx = pt2[0] - pt1[0], - dy = pt2[1] - pt1[1], - edge_leng = norm([dx, dy]) - ) - [-dy / edge_leng, dx / edge_leng]; - -function _bijection_outward_edge_normal(edge) = -1 * _bijection_inward_edge_normal(edge); - -function _bijection_offset_edge(edge, dx, dy) = - let( - pt1 = edge[0], - pt2 = edge[1], - dxy = [dx, dy] - ) - [pt1 + dxy, pt2 + dxy]; - -function _bijection__bijection_offset_edges(edges, d) = - [ - for(edge = edges) - let( - ow_normal = _bijection_outward_edge_normal(edge), - dx = ow_normal[0] * d, - dy = ow_normal[1] * d - ) - _bijection_offset_edge(edge, dx, dy) - ]; - -function bijection_offset(pts, d, epsilon = 0.0001) = - let( - es = __lines_from(pts, true), - offset_es = _bijection__bijection_offset_edges(es, d), - leng = len(offset_es), - last_p = __line_intersection(offset_es[leng - 1], offset_es[0], epsilon) - ) - concat( - [ - for(i = [0:leng - 2]) - let( - this_edge = offset_es[i], - next_edge = offset_es[i + 1], - p = __line_intersection(this_edge, next_edge, epsilon) - ) - // p == p to avoid [nan, nan], because [nan, nan] != [nan, nan] - if(p != [] && p == p) p - ], - last_p != [] && last_p == last_p ? [last_p] : [] - ); - - -/** -* polytransversals.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-polytransversals.html -* -**/ - - -module polytransversals(transversals) { - polygon( - __polytransversals(transversals) - ); -} - -/** -* shape_pentagram.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-shape_ellipse.html -* -**/ - -function shape_pentagram(r) = - [ - [0, 1], [-0.224514, 0.309017], - [-0.951057, 0.309017], [-0.363271, -0.118034], - [-0.587785, -0.809017], [0, -0.381966], - [0.587785, -0.809017], [0.363271, -0.118034], - [0.951057, 0.309017], [0.224514, 0.309017] - ] * r; - -/** -* bend_extrude.scad -* -* @copyright Justin Lin, 2019 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-bend_extrude.html -* -**/ - -module bend_extrude(size, thickness, angle, frags = 24) { - x = size[0]; - y = size[1]; - frag_width = x / frags ; - frag_angle = angle / frags; - half_frag_width = 0.5 * frag_width; - half_frag_angle = 0.5 * frag_angle; - r = half_frag_width / sin(half_frag_angle); - s = (r - thickness) / r; - - module get_frag(i) { - offsetX = i * frag_width; - linear_extrude(thickness, scale = [s, 1]) - translate([-offsetX - half_frag_width, 0, 0]) - intersection() { - translate([x, 0, 0]) mirror([1, 0, 0]) children(); - translate([offsetX, 0, 0]) - square([frag_width, y]); - } - } - - offsetY = -r * cos(half_frag_angle) ; - rotate([180, 0, 180]) for(i = [0 : frags - 1]) { - rotate(i * frag_angle + half_frag_angle) - translate([0, offsetY, 0]) - rotate([-90, 0, 0]) - get_frag(i) - children(); - } - -} - - -/** -* hexagons.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-hexagons.html -* -**/ - -module hexagons(radius, spacing, levels) { - beginning_n = 2 * levels - 1; - offset_x = radius * cos(30); - offset_y = radius + radius * sin(30); - r_hexagon = radius - spacing / 2; - offset_step = 2 * offset_x; - center_offset = 2 * (offset_x - offset_x * levels); - - module hexagon() { - rotate(30) - circle(r_hexagon, $fn = 6); - } - - function hexagons_pts(hex_datum) = - let( - tx = hex_datum[0][0], - ty = hex_datum[0][1], - n = hex_datum[1], - offset_xs = [for(i = [0:n - 1]) i * offset_step + center_offset] - ) - [ - for(x = offset_xs) [x + tx, ty] - ]; - - module line_hexagons(hex_datum) { - tx = hex_datum[0][0]; - ty = hex_datum[0][1]; - n = hex_datum[1]; - - offset_xs = [for(i = [0:n - 1]) i * offset_step + center_offset]; - for(x = offset_xs) { - p = [x + tx, ty, 0]; - translate(p) - hexagon(); - } - } - - upper_hex_data = levels > 1 ? [ - for(i = [1:beginning_n - levels]) - let( - x = offset_x * i, - y = offset_y * i, - n = beginning_n - i - ) [[x, y], n] - ] : []; - - lower_hex_data = levels > 1 ? [ - for(hex_datum = upper_hex_data) - [[hex_datum[0][0], -hex_datum[0][1]], hex_datum[1]] - ] : []; - - total_hex_data = concat( - [ - [[0, 0], beginning_n] // first line - ], - upper_hex_data, - lower_hex_data - ); - - pts_all_lines = [ - for(hex_datum = total_hex_data) - hexagons_pts(hex_datum) - ]; - - for(pts_one_line = pts_all_lines) { - for(pt = pts_one_line) { - translate(pt) - hexagon(); - } - } - - test_each_hexagon(r_hexagon, pts_all_lines); -} - -// override it to test -module test_each_hexagon(hex_r, pts_all_lines) { - -} - -/** -* golden_spiral_extrude.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-golden_spiral_extrude.html -* -**/ - -module golden_spiral_extrude(shape_pts, from, to, point_distance, - rt_dir = "CT_CLK", twist = 0, scale = 1.0, triangles = "SOLID") { - - pts_angles = golden_spiral( - from = from, - to = to, - point_distance = point_distance, - rt_dir = rt_dir - ); - - pts = [for(pt_angle = pts_angles) pt_angle[0]]; - angles = [ - for(pt_angle = pts_angles) - [90, 0, pt_angle[1] + (rt_dir == "CT_CLK" ? 0 : -90)] - ]; - - sections = cross_sections( - shape_pts, - pts, angles, - twist = twist, - scale = scale - ); - - polysections( - sections, - triangles = triangles - ); - - // testing hook - test_golden_spiral_extrude(sections); -} - -// override it to test -module test_golden_spiral_extrude(sections) { - -} - -/** -* shape_superformula.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-shape_superformula.html -* -**/ - - -function _superformula_r(angle, m1, m2, n1, n2 = 1, n3 = 1, a = 1, b = 1) = - pow( - pow(abs(cos(m1 * angle / 4) / a), n2) + - pow(abs(sin(m2 * angle / 4) / b), n3), - - 1 / n1 - ); - -function shape_superformula(phi_step, m1, m2, n1, n2 = 1, n3 = 1, a = 1, b = 1) = - [ - for(phi = [0:phi_step:6.28318]) - let( - angle = __to_degree(phi), - r = _superformula_r(angle, m1, m2, n1, n2, n3, a, b) - - ) - __ra_to_xy(r, angle) - ]; - -/** -* archimedean_spiral_extrude.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-archimedean_spiral_extrude.html -* -**/ - -module archimedean_spiral_extrude(shape_pts, arm_distance, init_angle, point_distance, num_of_points, - rt_dir = "CT_CLK", twist = 0, scale = 1.0, triangles = "SOLID") { - points_angles = archimedean_spiral( - arm_distance = arm_distance, - init_angle = init_angle, - point_distance = point_distance, - num_of_points = num_of_points, - rt_dir = rt_dir - ); - - clk_a = rt_dir == "CT_CLK" ? 0 : 180; - - points = [for(pa = points_angles) pa[0]]; - angles = [ - for(pa = points_angles) - [90, 0, pa[1] + clk_a] - ]; - - sections = cross_sections(shape_pts, points, angles, twist, scale); - - polysections( - sections, - triangles = triangles - ); - - // testing hook - test_archimedean_spiral_extrude(sections); -} - -// override it to test -module test_archimedean_spiral_extrude(sections) { - -} - -function __is_float(value) = value + 0 != undef; - -/** -* multi_line_text.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-multi_line_text.html -* -**/ -module multi_line_text(lines, line_spacing = 15, size = 10, font = "Arial", halign = "left", valign = "baseline", direction = "ltr", language = "en", script = "latin"){ - to = len(lines) - 1; - inc = line_spacing; - offset_y = inc * to / 2; - union() { - for (i = [0 : to]) { - translate([0 , -i * inc + offset_y, 0]) - text(lines[i], size, font = font, valign = valign, halign = halign, direction = direction, language = language, script = script); - } - } -} - -function __pie_for_rounding(r, begin_a, end_a, frags) = - let( - sector_angle = end_a - begin_a, - step_a = sector_angle / frags, - is_integer = frags % 1 == 0 - ) - r < 0.00005 ? [[0, 0]] : concat([ - for(ang = [begin_a:step_a:end_a]) - [ - r * cos(ang), - r * sin(ang) - ] - ], - is_integer ? [] : [[ - r * cos(end_a), - r * sin(end_a) - ]] - ); - -function __to_3_elems_ang_vect(a) = - let(leng = len(a)) - leng == 3 ? a : ( - leng == 2 ? [a[0], a[1], 0] : [a[0], 0, 0] - ); - -function __to_ang_vect(a) = __is_float(a) ? [0, 0, a] : __to_3_elems_ang_vect(a); - -function __reverse(vt) = - let(leng = len(vt)) - [ - for(i = [0:leng - 1]) - vt[leng - 1 - i] - ]; - -function __to3d(p) = [p[0], p[1], 0]; - - -/** -* shape_glued2circles.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-shape_glued2circles.html -* -**/ - -function _glued2circles_pie_curve(radius, centre_dist, tangent_angle) = - let( - begin_ang = 90 + tangent_angle, - shape_pts = shape_pie(radius, [-begin_ang, begin_ang]) - ) - [ - for(i = [1:len(shape_pts) - 1]) - shape_pts[i] + [centre_dist / 2, 0] - ]; - -function _glued2circles_bezier(radius, centre_dist, tangent_angle, t_step, ctrl_p1) = - let( - ctrl_p = rotate_p([radius * tan(tangent_angle), -radius], tangent_angle), - ctrl_p2 = [-ctrl_p[0], ctrl_p[1]] + [centre_dist / 2, 0], - ctrl_p3 = [-ctrl_p2[0], ctrl_p2[1]], - ctrl_p4 = [-ctrl_p1[0], ctrl_p1[1]] - ) - bezier_curve( - t_step, - [ - ctrl_p1, - ctrl_p2, - ctrl_p3, - ctrl_p4 - ] - ); - -function _glued2circles_lower_half_curve(curve_pts, leng, i = 0) = - i < leng ? ( - curve_pts[leng - 1 - i][0] >= 0 ? - concat( - [curve_pts[leng - 1 - i]], - _glued2circles_lower_half_curve(curve_pts, leng, i + 1) - ) : - _glued2circles_lower_half_curve(curve_pts, leng, i + 1) - ) : []; - -function _glued2circles_half_glued_circle(radius, centre_dist, tangent_angle, t_step) = - let( - pie_curve_pts = _glued2circles_pie_curve(radius, centre_dist, tangent_angle), - curve_pts = _glued2circles_bezier(radius, centre_dist, tangent_angle, t_step, pie_curve_pts[0]), - lower_curve_pts = _glued2circles_lower_half_curve(curve_pts, len(curve_pts)), - leng_half_curve_pts = len(lower_curve_pts), - upper_curve_pts = [ - for(i = [0:leng_half_curve_pts - 1]) - let(pt = lower_curve_pts[leng_half_curve_pts - 1 - i]) - [pt[0], -pt[1]] - ] - ) concat( - lower_curve_pts, - pie_curve_pts, - upper_curve_pts - ); - -function shape_glued2circles(radius, centre_dist, tangent_angle = 30, t_step = 0.1) = - let( - half_glued_circles = _glued2circles_half_glued_circle(radius, centre_dist, tangent_angle, t_step), - leng_half_glued_circles = len(half_glued_circles), - left_half_glued_circles = [ - for(i = [0:leng_half_glued_circles - 1]) - let(pt = half_glued_circles[leng_half_glued_circles - 1 - i]) - [-pt[0], pt[1]] - ] - ) concat(half_glued_circles, left_half_glued_circles); - -/** -* pie.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-pie.html -* -**/ - - -module pie(radius, angle) { - polygon(__shape_pie(radius, angle)); -} - -/** -* in_polyline.scad -* -* @copyright Justin Lin, 2019 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-in_polyline.html -* -**/ - - -function _in_polyline_sub(pts, pt, epsilon, iend, i = 0) = - i == iend ? false : ( - __in_line([pts[i], pts[i + 1]], pt, epsilon) ? true : - _in_polyline_sub(pts, pt, epsilon, iend, i + 1) - ); - -function in_polyline(line_pts, pt, epsilon = 0.0001) = - _in_polyline_sub(line_pts, pt, epsilon, len(line_pts) - 1); - - -function __ra_to_xy(r, a) = [r * cos(a), r * sin(a)]; - /** * function_grapher.scad * @@ -2156,6 +361,9 @@ module function_grapher(points, thickness, style = "FACES", slicing = "SLASH") { rows = len(points); columns = len(points[0]); + yi_range = [0:rows - 2]; + xi_range = [0:columns - 2]; + // Increasing $fn will be slow when you use "LINES", "HULL_FACES" or "HULL_LINES". module faces() { @@ -2175,16 +383,16 @@ module function_grapher(points, thickness, style = "FACES", slicing = "SLASH") { leng_pts = len(top_pts); top_tri_faces1 = slicing == "SLASH" ? [ - for(yi = [0:rows - 2]) - for(xi = [0:columns - 2]) + for(yi = yi_range) + for(xi = xi_range) [ xy_to_index(xi, yi, columns), xy_to_index(xi + 1, yi + 1, columns), xy_to_index(xi + 1, yi, columns) ] ] : [ - for(yi = [0:rows - 2]) - for(xi = [0:columns - 2]) + for(yi = yi_range) + for(xi = xi_range) [ xy_to_index(xi, yi, columns), xy_to_index(xi, yi + 1, columns), @@ -2193,16 +401,16 @@ module function_grapher(points, thickness, style = "FACES", slicing = "SLASH") { ]; top_tri_faces2 = slicing == "SLASH" ? [ - for(yi = [0:rows - 2]) - for(xi = [0:columns - 2]) + for(yi = yi_range) + for(xi = xi_range) [ xy_to_index(xi, yi, columns), xy_to_index(xi, yi + 1, columns), xy_to_index(xi + 1, yi + 1, columns) ] ] : [ - for(yi = [0:rows - 2]) - for(xi = [0:columns - 2]) + for(yi = yi_range) + for(xi = xi_range) [ xy_to_index(xi, yi + 1, columns), xy_to_index(xi + 1, yi + 1, columns), @@ -2221,7 +429,7 @@ module function_grapher(points, thickness, style = "FACES", slicing = "SLASH") { ]; side_faces1 = [ - for(xi = [0:columns - 2]) + for(xi = xi_range) let( idx1 = xy_to_index(xi, 0, columns), idx2 = xy_to_index(xi + 1, 0, columns) @@ -2235,7 +443,7 @@ module function_grapher(points, thickness, style = "FACES", slicing = "SLASH") { ]; side_faces2 = [ - for(yi = [0:rows - 2]) + for(yi = yi_range) let( xi = columns - 1, idx1 = xy_to_index(xi, yi, columns), @@ -2250,7 +458,7 @@ module function_grapher(points, thickness, style = "FACES", slicing = "SLASH") { ]; side_faces3 = [ - for(xi = [0:columns - 2]) + for(xi = xi_range) let( yi = rows - 1, idx1 = xy_to_index(xi, yi, columns), @@ -2265,7 +473,7 @@ module function_grapher(points, thickness, style = "FACES", slicing = "SLASH") { ]; side_faces4 = [ - for(yi = [0:rows - 2]) + for(yi = yi_range) let( idx1 = xy_to_index(0, yi, columns), idx2 = xy_to_index(0, yi + 1, columns) @@ -2334,8 +542,8 @@ module function_grapher(points, thickness, style = "FACES", slicing = "SLASH") { if(style == "FACES") { faces(); } else { - for(yi = [0:rows - 2]) { - for(xi = [0:columns - 2]) { + for(yi = yi_range) { + for(xi = xi_range) { if(slicing == "SLASH") { tri_to_graph([ points[yi][xi], @@ -2367,13 +575,393 @@ module test_function_grapher_faces(points, faces) { } +/** +* bezier_curve.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-bezier_curve.html +* +**/ + + +function _combi(n, k) = + let( + bi_coef = [ + [1], // n = 0: for padding + [1,1], // n = 1: for Linear curves, how about drawing a line directly? + [1,2,1], // n = 2: for Quadratic curves + [1,3,3,1] // n = 3: for Cubic Bézier curves + ] + ) + n < len(bi_coef) ? bi_coef[n][k] : ( + k == 0 ? 1 : (_combi(n, k - 1) * (n - k + 1) / k) + ); + +function bezier_curve_coordinate(t, pn, n, i = 0) = + i == n + 1 ? 0 : + (_combi(n, i) * pn[i] * pow(1 - t, n - i) * pow(t, i) + + bezier_curve_coordinate(t, pn, n, i + 1)); + +function _bezier_curve_point(t, points) = + let(n = len(points) - 1) + [ + bezier_curve_coordinate( + t, + [for(p = points) p[0]], + n + ), + bezier_curve_coordinate( + t, + [for(p = points) p[1]], + n + ), + bezier_curve_coordinate( + t, + [for(p = points) p[2]], + n + ) + ]; + +function bezier_curve(t_step, points) = + let( + pts = concat([ + for(t = 0; t < ceil(1 / t_step); t = t + 1) + _bezier_curve_point(t * t_step, points) + ], [_bezier_curve_point(1, points)]) + ) + len(points[0]) == 3 ? pts : [for(pt = pts) __to2d(pt)]; + + +/** +* split_str.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-split_str.html +* +**/ + +function _split_t_by(idxs, t) = + let(leng = len(idxs)) + concat( + [sub_str(t, 0, idxs[0])], + [ + for(i = 0; i < leng; i = i + 1) + sub_str(t, idxs[i] + 1, idxs[i + 1]) + ] + ); + +function split_str(t, delimiter) = + len(search(delimiter, t)) == 0 ? + [t] : _split_t_by(search(delimiter, t, 0)[0], t); + +/** +* in_polyline.scad +* +* @copyright Justin Lin, 2019 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-in_polyline.html +* +**/ + + +function in_polyline(line_pts, pt, epsilon = 0.0001) = + let( + leng = len(line_pts), + iend = leng - 1, + maybe_last = [for(i = 0; i < iend && !__in_line([line_pts[i], line_pts[i + 1]], pt, epsilon); i = i + 1) i][leng - 2] + ) + is_undef(maybe_last); + + +function __trapezium(length, h, round_r) = + let( + r_half_trapezium = __half_trapezium(length / 2, h, round_r), + to = len(r_half_trapezium) - 1, + l_half_trapezium = [ + for(i = 0; i <= to; i = i + 1) + let(pt = r_half_trapezium[to - i]) + [-pt[0], pt[1]] + ] + ) + concat( + r_half_trapezium, + l_half_trapezium + ); + +/** +* hull_polyline3d.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/hull_polyline3d.html +* +**/ + +module hull_polyline3d(points, thickness) { + half_thickness = thickness / 2; + leng = len(points); + + module hull_line3d(index) { + point1 = points[index - 1]; + point2 = points[index]; + + hull() { + translate(point1) + sphere(half_thickness); + translate(point2) + sphere(half_thickness); + } + + // hook for testing + test_line_segment(index, point1, point2, half_thickness); + } + + module polyline3d_inner(index) { + if(index < leng) { + hull_line3d(index); + polyline3d_inner(index + 1); + } + } + + polyline3d_inner(1); +} + +// override it to test +module test_line_segment(index, point1, point2, radius) { + +} + +function __ra_to_xy(r, a) = [r * cos(a), r * sin(a)]; + +/** +* golden_spiral_extrude.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-golden_spiral_extrude.html +* +**/ + +module golden_spiral_extrude(shape_pts, from, to, point_distance, + rt_dir = "CT_CLK", twist = 0, scale = 1.0, triangles = "SOLID") { + + pts_angles = golden_spiral( + from = from, + to = to, + point_distance = point_distance, + rt_dir = rt_dir + ); + + pts = [for(pt_angle = pts_angles) pt_angle[0]]; + angles = [ + for(pt_angle = pts_angles) + [90, 0, pt_angle[1] + (rt_dir == "CT_CLK" ? 0 : -90)] + ]; + + sections = cross_sections( + shape_pts, + pts, angles, + twist = twist, + scale = scale + ); + + polysections( + sections, + triangles = triangles + ); + + // testing hook + test_golden_spiral_extrude(sections); +} + +// override it to test +module test_golden_spiral_extrude(sections) { + +} + +/** +* px_circle.scad +* +* @copyright Justin Lin, 2019 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-px_circle.html +* +**/ + +function _px_circle_y(f, y) = f >= 0 ? y - 1 : y; +function _px_circle_ddf_y(f, ddf_y) = f >= 0 ? ddf_y + 2 : ddf_y; +function _px_circle_f(f, ddf_y) = f >= 0 ? f + ddf_y : f; + +function _px_circle(f, ddf_x, ddf_y, x, y, filled) = + x >= y ? [] : + let( + ny = _px_circle_y(f, y), + nddf_y = _px_circle_ddf_y(f, ddf_y), + nx = x + 1, + nddf_x = ddf_x + 2, + nf = _px_circle_f(f, ddf_y) + nddf_x + ) + concat( + filled ? + concat( + [for(xi = -nx; xi <= nx; xi = xi + 1) [xi, -ny]], + [for(xi = -ny; xi <= ny; xi = xi + 1) [xi, -nx]], + [for(xi = -ny; xi <= ny; xi = xi + 1) [xi, nx]], + [for(xi = -nx; xi <= nx; xi = xi + 1) [xi, ny]] + ) + : + [ + [-nx, -ny], [nx, -ny], + [-ny, -nx], [ny, -nx], + [-ny, nx], [ny, nx], + [-nx, ny], [nx, ny] + ], + _px_circle(nf, nddf_x, nddf_y, nx, ny, filled) + ); + +function px_circle(radius, filled = false) = + let( + f = 1 - radius, + ddf_x = 1, + ddf_y = -2 * radius, + x = 0, + y = radius + ) + concat( + filled ? + concat( + [[0, radius], [0, -radius]], + [for(xi = -radius; xi <= radius; xi = xi + 1) [xi, 0]] + ) + : + [ + [0, -radius], + [-radius, 0], + [radius, 0], + [0, radius] + ], + _px_circle(f, ddf_x, ddf_y, x, y, filled) + ); + +function __m_shearing(sx, sy, sz) = + let( + sx_along_y = sx[0], + sx_along_z = sx[1], + sy_along_x = sy[0], + sy_along_z = sy[1], + sz_along_x = sz[0], + sz_along_y = sz[1] + ) + [ + [1, sx_along_y, sx_along_z, 0], + [sy_along_x, 1, sy_along_z, 0], + [sz_along_x, sz_along_y, 1, 0], + [0, 0, 0, 1] + ]; + +/** +* shape_ellipse.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-shape_ellipse.html +* +**/ + + +function shape_ellipse(axes) = + let( + frags = __frags(axes[0]), + step_a = 360 / frags, + a_end = 360 - step_a, + shape_pts = [ + for(a = 0; a <= a_end; a = a + step_a) + [axes[0] * cos(a), axes[1] * sin(a)] + ] + ) shape_pts; + +/** +* sort.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-sort.html +* +**/ + +function _sort(lt, i) = + let(leng = len(lt)) + leng <= 1 ? lt : + let( + pivot = lt[0], + before = [for(j = 1; j < leng; j = j + 1) if(lt[j][i] < pivot[i]) lt[j]], + after = [for(j = 1; j < leng; j = j + 1) if(lt[j][i] >= pivot[i]) lt[j]] + ) + concat(_sort(before, i), [pivot], _sort(after, i)); + +function sort(lt, by = "idx", idx = 0) = + let( + dict = [["x", 0], ["y", 1], ["z", 0], ["idx", idx]], + i = dict[search(by, dict)[0]][1] + ) + _sort(lt, i); + +/** +* stereographic_extrude.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-stereographic_extrude.html +* +**/ + +module stereographic_extrude(shadow_side_leng) { + half_side_length = shadow_side_leng / 2; + outer_sphere_r = half_side_length / 3; + a = atan(sqrt(2) * half_side_length / (2 * outer_sphere_r)); + inner_sphere_r = outer_sphere_r * sin(a); + + intersection() { + translate([0, 0, outer_sphere_r]) difference() { + sphere(outer_sphere_r); + sphere(outer_sphere_r / 2 + inner_sphere_r / 2); + + translate([0, 0, outer_sphere_r / 2]) + linear_extrude(outer_sphere_r) + circle(inner_sphere_r * cos(a)); + } + + linear_extrude(outer_sphere_r * 2, scale = 0.01) + children(); + } + + // hook for testing + test_stereographic_extrude_rs(outer_sphere_r, inner_sphere_r); +} + +// override for testing +module test_stereographic_extrude_rs(outer_sphere_r, inner_sphere_r) { + +} + /** * turtle3d.scad * * @copyright Justin Lin, 2017 * @license https://opensource.org/licenses/lgpl-3.0.html * -* @see https://openhome.cc/eGossip/OpenSCAD/lib-turtle3d.html +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-turtle3d.html * **/ @@ -2491,8 +1079,8 @@ function _turtle3d_zu_turn(turtle, a) = ); function _turtle3d_create_cmd(arg1, arg2) = - (arg1 == undef && arg2 == undef) ? _turtle3d_create_default() : ( - (arg1 != undef && arg2 != undef) ? _turtle3d_create(arg1, arg2) : undef + (is_undef(arg1) && is_undef(arg2)) ? _turtle3d_create_default() : ( + (!is_undef(arg1) && !is_undef(arg2)) ? _turtle3d_create(arg1, arg2) : undef ); function _turtle3d_chain_move(cmd, arg1, arg2) = @@ -2519,6 +1107,563 @@ function turtle3d(cmd, arg1, arg2) = _turtle3d_create_cmd(arg1, arg2) : _turtle3d_chain_move(cmd, arg1, arg2); +/** +* crystal_ball.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-crystal_ball.html +* +**/ + + +module crystal_ball(radius, theta = 360, phi = 180) { + phis = is_num(phi) ? [0, phi] : phi; + + frags = __frags(radius); + + shape_pts = shape_pie( + radius, + [90 - phis[1], 90 - phis[0]], + $fn = __nearest_multiple_of_4(frags) + ); + + ring_extrude( + shape_pts, + angle = theta, + radius = 0, + $fn = frags + ); + + // hook for testing + test_crystal_ball_pie(shape_pts); +} + +// override it to test +module test_crystal_ball_pie(shape_pts) { + +} + +/** +* rounded_square.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-rounded_square.html +* +**/ + + +module rounded_square(size, corner_r, center = false) { + is_flt = is_num(size); + x = is_flt ? size : size[0]; + y = is_flt ? size : size[1]; + + position = center ? [0, 0] : [x / 2, y / 2]; + points = __trapezium( + length = x, + h = y, + round_r = corner_r + ); + + translate(position) + polygon(points); + + // hook for testing + test_rounded_square(position, points); +} + +// override it to test +module test_rounded_square(position, points) { +} + +/** +* midpt_smooth.scad +* +* @copyright Justin Lin, 2019 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-midpt_smooth.html +* +**/ + +function _midpt_smooth_sub(points, iend, closed = false) = + concat( + [ + for(i = 0; i < iend; i = i + 1) + (points[i] + points[i + 1]) / 2 + ], + closed ? [(points[iend] + points[0]) / 2] : [] + ); + +function midpt_smooth(points, n, closed = false) = + let( + smoothed = _midpt_smooth_sub(points, len(points) - 1, closed) + ) + n == 1 ? smoothed : midpt_smooth(smoothed, n - 1, closed); + +/** +* ring_extrude.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-ring_extrude.html +* +**/ + + +module ring_extrude(shape_pts, radius, angle = 360, twist = 0, scale = 1.0, triangles = "SOLID") { + if(twist == 0 && scale == 1.0) { + rotate_extrude(angle = angle) + translate([radius, 0, 0]) + polygon(shape_pts); + } else { + a_step = 360 / __frags(radius); + + angles = is_num(angle) ? [0, angle] : angle; + + m = floor(angles[0] / a_step) + 1; + n = floor(angles[1] / a_step); + + leng = radius * cos(a_step / 2); + + begin_r = + leng / cos((m - 0.5) * a_step - angles[0]); + + end_r = + leng / cos((n + 0.5) * a_step - angles[1]); + + angs = concat( + [[90, 0, angles[0]]], + m > n ? [] : [for(i = [m:n]) [90, 0, a_step * i]] + ); + pts = concat( + [__ra_to_xy(begin_r, angles[0])], + m > n ? [] : [for(i = [m:n]) __ra_to_xy(radius, a_step * i)] + ); + + is_angle_frag_end = angs[len(angs) - 1][2] == angles[1]; + + all_angles = is_angle_frag_end ? + angs : + concat(angs, [[90, 0, angles[1]]]); + + all_points = is_angle_frag_end ? + pts : + concat(pts, [__ra_to_xy(end_r, angles[1])]); + + sections = cross_sections(shape_pts, all_points, all_angles, twist, scale); + + polysections( + sections, + triangles = triangles + ); + + // hook for testing + test_ring_extrude(sections); + } +} + +// Override it to test +module test_ring_extrude(sections) { + +} + +/** +* shear.scad +* +* @copyright Justin Lin, 2019 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-shear.html +* +**/ + + +module shear(sx = [0, 0], sy = [0, 0], sz = [0, 0]) { + multmatrix(__m_shearing(sx, sy, sz)) children(); +} + +/** +* shape_trapezium.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-shape_trapezium.html +* +**/ + + +function shape_trapezium(length, h, corner_r = 0) = + __trapezium( + length = length, + h = h, + round_r = corner_r + ); + + +/** +* polysections.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-polysections.html +* +**/ + + +module polysections(sections, triangles = "SOLID") { + + function side_indexes(sects, begin_idx = 0) = + let( + leng_sects = len(sects), + leng_pts_sect = len(sects[0]), + range_j = [begin_idx:leng_pts_sect:begin_idx + (leng_sects - 2) * leng_pts_sect], + range_i = [0:leng_pts_sect - 1] + ) + concat( + [ + for(j = range_j) + for(i = range_i) + [ + j + i, + j + (i + 1) % leng_pts_sect, + j + (i + 1) % leng_pts_sect + leng_pts_sect + ] + ], + [ + for(j = range_j) + for(i = range_i) + [ + j + i, + j + (i + 1) % leng_pts_sect + leng_pts_sect , + j + i + leng_pts_sect + ] + ] + ); + + function search_at(f_sect, p, leng_pts_sect, i = 0) = + i < leng_pts_sect ? + (p == f_sect[i] ? i : search_at(f_sect, p, leng_pts_sect, i + 1)) : -1; + + function the_same_after_twisting(f_sect, l_sect, leng_pts_sect) = + let( + found_at_i = search_at(f_sect, l_sect[0], leng_pts_sect) + ) + found_at_i <= 0 ? false : + l_sect == concat( + [for(i = found_at_i; i < leng_pts_sect; i = i + 1) f_sect[i]], + [for(i = 0; i < found_at_i; i = i + 1) f_sect[i]] + ); + + function to_v_pts(sects) = + [ + for(sect = sects) + for(pt = sect) + pt + ]; + + module solid_sections(sects) { + + leng_sects = len(sects); + leng_pts_sect = len(sects[0]); + first_sect = sects[0]; + last_sect = sects[leng_sects - 1]; + + v_pts = [ + for(sect = sects) + for(pt = sect) + pt + ]; + + begin_end_the_same = + first_sect == last_sect || + the_same_after_twisting(first_sect, last_sect, leng_pts_sect); + + if(begin_end_the_same) { + f_idxes = side_indexes(sects); + + polyhedron( + v_pts, + f_idxes + ); + + // hook for testing + test_polysections_solid(v_pts, f_idxes); + } else { + range_i = [0:leng_pts_sect - 1]; + first_idxes = [for(i = range_i) leng_pts_sect - 1 - i]; + last_idxes = [ + for(i = range_i) + i + leng_pts_sect * (leng_sects - 1) + ]; + + f_idxes = concat([first_idxes], side_indexes(sects), [last_idxes]); + + polyhedron( + v_pts, + f_idxes + ); + + // hook for testing + test_polysections_solid(v_pts, f_idxes); + } + } + + module hollow_sections(sects) { + leng_sects = len(sects); + leng_sect = len(sects[0]); + half_leng_sect = leng_sect / 2; + half_leng_v_pts = leng_sects * half_leng_sect; + + function strip_sects(begin_idx, end_idx) = + [ + for(i = 0; i < leng_sects; i = i + 1) + [ + for(j = begin_idx; j <= end_idx; j = j + 1) + sects[i][j] + ] + ]; + + function first_idxes() = + [ + for(i = 0; i < half_leng_sect; i = i + 1) + [ + i, + i + half_leng_v_pts, + (i + 1) % half_leng_sect + half_leng_v_pts, + (i + 1) % half_leng_sect + ] + ]; + + function last_idxes(begin_idx) = + [ + for(i = 0; i < half_leng_sect; i = i + 1) + [ + begin_idx + i, + begin_idx + (i + 1) % half_leng_sect, + begin_idx + (i + 1) % half_leng_sect + half_leng_v_pts, + begin_idx + i + half_leng_v_pts + ] + ]; + + outer_sects = strip_sects(0, half_leng_sect - 1); + inner_sects = strip_sects(half_leng_sect, leng_sect - 1); + + outer_v_pts = to_v_pts(outer_sects); + inner_v_pts = to_v_pts(inner_sects); + + outer_idxes = side_indexes(outer_sects); + inner_idxes = [ + for(idxes = side_indexes(inner_sects, half_leng_v_pts)) + __reverse(idxes) + ]; + + first_outer_sect = outer_sects[0]; + last_outer_sect = outer_sects[leng_sects - 1]; + first_inner_sect = inner_sects[0]; + last_inner_sect = inner_sects[leng_sects - 1]; + + leng_pts_sect = len(first_outer_sect); + + begin_end_the_same = + (first_outer_sect == last_outer_sect && first_inner_sect == last_inner_sect) || + ( + the_same_after_twisting(first_outer_sect, last_outer_sect, leng_pts_sect) && + the_same_after_twisting(first_inner_sect, last_inner_sect, leng_pts_sect) + ); + + v_pts = concat(outer_v_pts, inner_v_pts); + + if(begin_end_the_same) { + f_idxes = concat(outer_idxes, inner_idxes); + + polyhedron( + v_pts, + f_idxes + ); + + // hook for testing + test_polysections_solid(v_pts, f_idxes); + } else { + first_idxes = first_idxes(); + last_idxes = last_idxes(half_leng_v_pts - half_leng_sect); + + f_idxes = concat(first_idxes, outer_idxes, inner_idxes, last_idxes); + + polyhedron( + v_pts, + f_idxes + ); + + // hook for testing + test_polysections_solid(v_pts, f_idxes); + } + } + + module triangles_defined_sections() { + module tri_sections(tri1, tri2) { + hull() polyhedron( + points = concat(tri1, tri2), + faces = [ + [0, 1, 2], + [3, 5, 4], + [1, 3, 4], [2, 1, 4], [2, 3, 0], + [0, 3, 1], [2, 4, 5], [2, 5, 3] + ] + ); + } + + module two_sections(section1, section2) { + for(idx = triangles) { + tri_sections( + [ + section1[idx[0]], + section1[idx[1]], + section1[idx[2]] + ], + [ + section2[idx[0]], + section2[idx[1]], + section2[idx[2]] + ] + ); + } + } + + for(i = [0:len(sections) - 2]) { + two_sections( + sections[i], + sections[i + 1] + ); + } + } + + if(triangles == "SOLID") { + solid_sections(sections); + } else if(triangles == "HOLLOW") { + hollow_sections(sections); + } + else { + triangles_defined_sections(); + } +} + +// override it to test + +module test_polysections_solid(points, faces) { + +} + +/** +* archimedean_spiral.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-archimedean_spiral.html +* +**/ + +function _radian_step(b, theta, l) = + let(r_square = pow(b * theta, 2)) + acos((2 * r_square - pow(l, 2)) / (2 * r_square)) / 180 * PI; + +function _find_radians(b, point_distance, radians, n, count = 1) = + let(pre_radians = radians[count - 1]) + count == n ? radians : ( + _find_radians( + b, + point_distance, + concat( + radians, + [pre_radians + _radian_step(b, pre_radians, point_distance)] + ), + n, + count + 1) + ); + +function archimedean_spiral(arm_distance, init_angle, point_distance, num_of_points, rt_dir = "CT_CLK") = + let(b = arm_distance / (2 * PI), init_radian = init_angle * PI / 180) + [ + for(theta = _find_radians(b, point_distance, [init_radian], num_of_points)) + let(r = b * theta, a = (rt_dir == "CT_CLK" ? 1 : -1) * theta * 57.2958) + [[r * cos(a), r * sin(a)], a] + ]; + +/** +* golden_spiral.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-golden_spiral.html +* +**/ + +function _fast_fibonacci_sub(nth) = + let( + _f = _fast_fibonacci_2_elems(floor(nth / 2)), + a = _f[0], + b = _f[1], + c = a * (b * 2 - a), + d = a * a + b * b + ) + nth % 2 == 0 ? [c, d] : [d, c + d]; + +function _fast_fibonacci_2_elems(nth) = + nth == 0 ? [0, 1] : _fast_fibonacci_sub(nth); + +function _fast_fibonacci(nth) = + _fast_fibonacci_2_elems(nth)[0]; + +function _remove_same_pts(pts1, pts2) = + pts1[len(pts1) - 1] == pts2[0] ? + concat(pts1, [for(i = 1; i < len(pts2); i = i + 1) pts2[i]]) : + concat(pts1, pts2); + +function _golden_spiral_from_ls_or_eql_to(from, to, point_distance, rt_dir) = + let( + f1 = _fast_fibonacci(from), + f2 = _fast_fibonacci(from + 1), + fn = floor(f1 * 6.28312 / point_distance), + $fn = fn + 4 - (fn % 4), + circle_pts = circle_path(radius = f1, n = $fn / 4 + 1), + len_pts = len(circle_pts), + a_step = 360 / $fn * rt_dir, + range_i = [0:len_pts - 1], + arc_points_angles = (rt_dir == 1 ? [ + for(i = range_i) + [circle_pts[i], a_step * i] + ] : [ + for(i = range_i) let(idx = len_pts - i - 1) + [circle_pts[idx], a_step * i] + ]), + offset = f2 - f1 + ) _remove_same_pts( + arc_points_angles, + [ + for(pt_a = _golden_spiral(from + 1, to, point_distance, rt_dir)) + [ + rotate_p(pt_a[0], [0, 0, 90 * rt_dir]) + + (rt_dir == 1 ? [0, -offset, 0] : [-offset, 0, 0]), + pt_a[1] + 90 * rt_dir + ] + ] + ); + +function _golden_spiral(from, to, point_distance, rt_dir) = + from <= to ? + _golden_spiral_from_ls_or_eql_to(from, to, point_distance, rt_dir) : []; + +function golden_spiral(from, to, point_distance, rt_dir = "CT_CLK") = + _golden_spiral(from, to, point_distance, (rt_dir == "CT_CLK" ? 1 : -1)); + /** * shape_taiwan.scad * @@ -2530,22 +1675,1952 @@ function turtle3d(cmd, arg1, arg2) = **/ function shape_taiwan(h, distance = 0) = - let(tw = [[3.85724, 6.24078], [3.7902, 6.25779], [3.73596, 6.26288], [3.62807, 6.24587], [3.59581, 6.2602], [3.55429, 6.32386], [3.51698, 6.4571], [3.50768, 6.5361], [3.51188, 6.58284], [3.53917, 6.63708], [3.48981, 6.66934], [2.78286, 6.83905], [2.7218, 6.86112], [2.68441, 6.90272], [2.61063, 6.96209], [2.64288, 7.05549], [2.61062, 7.06568], [2.56396, 7.06058], [2.50281, 7.04109], [2.44849, 7.15647], [2.29319, 7.37123], [2.22438, 7.42555], [2.05644, 7.44248], [1.88674, 7.40509], [1.73901, 7.32879], [1.63795, 7.238], [1.58868, 7.14974], [1.54463, 7.0555], [1.5149, 7.0411], [1.48526, 7.01895], [1.53658, 6.9725], [1.58825, 6.92909], [1.63096, 6.86281], [1.61348, 6.80387], [1.57757, 6.83721], [1.53949, 6.89116], [1.48525, 6.87393], [1.43851, 6.87393], [1.40381, 6.86623], [1.37408, 6.85174], [1.28068, 6.77282], [1.20682, 6.7457], [0.723984, 6.65659], [0.586451, 6.60741], [0.5152, 6.57094], [0.458435, 6.52167], [0.393838, 6.47922], [0.108666, 6.38843], [-0.002506, 6.2925], [-0.110307, 6.16693], [-0.278327, 5.89785], [-0.312266, 5.80452], [-0.319942, 5.74076], [-0.35978, 5.72804], [-0.398773, 5.69411], [-0.431113, 5.64921], [-0.443073, 5.60508], [-0.45317, 5.54563], [-0.477762, 5.51429], [-0.504966, 5.48196], [-0.527025, 5.4379], [-0.511683, 5.32413], [-0.544022, 5.28008], [-0.630518, 5.10523], [-0.652506, 5.02118], [-0.721317, 4.96517], [-0.751047, 4.87851], [-0.807895, 4.81922], [-0.849502, 4.76313], [-0.835106, 4.67916], [-0.94535, 4.70123], [-1.03193, 4.67664], [-1.10318, 4.62476], [-1.16685, 4.55856], [-1.18724, 4.52125], [-1.20679, 4.47981], [-1.23643, 4.44755], [-1.33927, 4.41782], [-1.36462, 4.37621], [-1.38844, 4.28037], [-1.47747, 4.11993], [-1.51477, 4.03419], [-1.52674, 3.93321], [-1.55638, 3.87122], [-1.87389, 3.52162], [-1.92308, 3.43757], [-1.96721, 3.28479], [-2.11055, 3.03862], [-2.15224, 2.84946], [-2.18703, 2.75092], [-2.23874, 2.70864], [-2.2481, 2.65676], [-2.43313, 2.44284], [-2.47482, 2.40393], [-2.48998, 2.36148], [-2.49681, 2.20617], [-2.51727, 2.15951], [-2.59526, 2.09828], [-2.61312, 2.05583], [-2.62237, 2.00926], [-2.64705, 1.98728], [-2.68183, 1.97279], [-2.71915, 1.94559], [-2.76589, 1.90137], [-2.80741, 1.82768], [-2.89576, 1.58074], [-2.9601, 1.46267], [-3.00171, 1.34223], [-3.03396, 1.29978], [-3.14261, 1.19451], [-3.16223, 1.14945], [-3.18683, 1.04173], [-3.21142, 0.994987], [-3.30988, 0.906048], [-3.32504, 0.864443], [-3.42105, 0.738702], [-3.43797, 0.692212], [-3.47452, 0.558807], [-3.54409, 0.411083], [-3.62553, 0.283068], [-3.69434, 0.142925], [-3.72407, -0.047077], [-3.71634, -0.135425], [-3.67474, -0.317847], [-3.65948, -0.475761], [-3.62302, -0.539348], [-3.61029, -0.588533], [-3.62554, -0.628538], [-3.65703, -0.687068], [-3.61029, -0.73878], [-3.64002, -0.795629], [-3.57542, -0.918676], [-3.67902, -1.14784], [-3.62553, -1.18944], [-3.59589, -1.2046], [-3.60515, -1.24376], [-3.6476, -1.28781], [-3.68162, -1.37186], [-3.72138, -1.38205], [-3.74597, -1.40925], [-3.79785, -1.54426], [-3.80458, -1.58157], [-3.81731, -1.61121], [-3.84956, -1.65526], [-3.87677, -1.70958], [-3.8665, -1.75893], [-3.84714, -1.80812], [-3.83434, -1.86665], [-3.85397, -1.90666], [-3.89633, -1.91845], [-3.93532, -1.94052], [-3.94552, -2.0025], [-3.90315, -2.05169], [-3.83687, -2.10846], [-3.91452, -2.12525], [-3.92486, -2.16746], [-3.8021, -2.21718], [-3.78004, -2.24169], [-3.79537, -2.28599], [-3.84194, -2.30292], [-3.9014, -2.31052], [-3.94553, -2.3325], [-3.90902, -2.38984], [-3.81228, -2.42599], [-3.7487, -2.45311], [-3.7359, -2.49042], [-3.61032, -2.51249], [-3.51439, -2.52698], [-3.49737, -2.60598], [-3.53645, -2.69921], [-3.61031, -2.75101], [-3.55085, -2.813], [-3.52197, -2.86732], [-3.47455, -3.17194], [-3.46268, -3.20175], [-3.42108, -3.27805], [-3.36173, -3.36723], [-3.3667, -3.40353], [-3.39137, -3.45802], [-3.39137, -3.50468], [-3.37605, -3.57332], [-3.3048, -3.72879], [-3.22849, -3.84755], [-3.18689, -3.9332], [-3.16473, -4.02239], [-3.18175, -4.08606], [-3.21401, -4.15723], [-3.18942, -4.22848], [-3.1377, -4.29316], [-2.99756, -4.4237], [-2.91612, -4.51458], [-2.85675, -4.62575], [-2.84478, -4.76572], [-2.64282, -4.92119], [-2.55624, -4.90831], [-2.51219, -4.92877], [-2.47733, -4.95075], [-2.40355, -5.01441], [-2.33222, -5.06116], [-2.17691, -5.13485], [-2.10053, -5.19944], [-2.05126, -5.27328], [-2.00199, -5.30293], [-1.87641, -5.40147], [-1.84416, -5.44552], [-1.77804, -5.59577], [-1.69399, -5.70181], [-1.66687, -5.74611], [-1.35963, -6.53694], [-1.36899, -6.58351], [-1.4063, -6.638], [-1.41556, -6.68466], [-1.41556, -6.84915], [-1.42322, -6.93076], [-1.41556, -6.96992], [-1.33, -7.11073], [-1.34945, -7.21845], [-1.34692, -7.25315], [-1.28999, -7.29989], [-1.23921, -7.31522], [-1.20181, -7.27783], [-1.19675, -7.17685], [-1.07362, -7.20658], [-0.953101, -7.2609], [-0.849593, -7.33982], [-0.778259, -7.44248], [-0.775729, -7.35413], [-0.795186, -7.21416], [-0.797786, -7.08606], [-0.736641, -7.02913], [-0.685014, -6.99014], [-0.645009, -6.89851], [-0.620417, -6.78565], [-0.637343, -5.77062], [-0.612751, -5.52192], [-0.590692, -5.43534], [-0.443136, -5.1799], [-0.371802, -4.92362], [-0.341989, -4.73344], [-0.29036, -4.64283], [-0.16723, -4.48735], [-0.128151, -4.41105], [-0.046711, -4.20395], [-0.014539, -4.16235], [0.027066, -4.14297], [0.191803, -3.96039], [0.441265, -3.79565], [0.515127, -3.72608], [0.588904, -3.63285], [0.62032, -3.58105], [0.640788, -3.5317], [0.643228, -3.48757], [0.633124, -3.39173], [0.640794, -3.35189], [0.689979, -3.29336], [0.9039, -3.11338], [0.923353, -3.07093], [1.08363, -2.84522], [1.11605, -2.75342], [1.16262, -2.55407], [1.23396, -2.42344], [1.26116, -2.33518], [1.27809, -2.30031], [1.31035, -2.26637], [1.38421, -2.21213], [1.41638, -2.17987], [1.49024, -2.02701], [1.50464, -1.87935], [1.50212, -1.72405], [1.52671, -1.54937], [1.55897, -1.45589], [1.59897, -1.37942], [1.70669, -1.23616], [1.74147, -1.16044], [1.98243, 0.226167], [2.05637, 0.376416], [2.18195, 0.989965], [2.27788, 1.25316], [2.32959, 1.50186], [2.33469, 1.60107], [2.34741, 1.65447], [2.40173, 1.74366], [2.42118, 1.79798], [2.38391, 1.88363], [2.36176, 1.9185], [2.33473, 1.99994], [2.33213, 2.07136], [2.3542, 2.13747], [2.46798, 2.30473], [2.51203, 2.49221], [2.55625, 2.58553], [2.59356, 2.62284], [2.71147, 2.72138], [2.69968, 2.75364], [2.72175, 2.78497], [2.793, 2.8419], [2.89145, 2.97513], [2.98064, 3.06078], [2.97805, 3.26778], [2.98485, 3.3638], [2.99757, 3.41297], [3.01702, 3.44775], [3.03412, 3.48936], [3.02732, 3.59547], [3.03152, 3.64474], [3.14008, 3.76771], [3.23348, 3.82464], [3.27332, 3.8611], [3.26572, 3.90356], [3.23852, 3.94517], [3.22673, 3.98929], [3.23343, 4.02904], [3.32515, 4.08085], [3.33955, 4.16659], [3.31748, 4.26758], [3.2784, 4.34405], [3.3056, 4.3635], [3.37526, 4.38649], [3.39869, 4.42513], [3.32514, 4.42541], [3.22669, 4.4874], [3.17237, 4.58324], [3.16977, 4.70636], [3.19192, 4.7675], [3.19432, 4.8294], [3.14261, 5.06624], [3.14001, 5.17909], [3.14781, 5.29709], [3.1724, 5.41583], [3.20634, 5.51943], [3.25384, 5.59329], [3.54153, 5.94036], [3.62558, 6.01431], [3.94553, 6.17215], [3.91327, 6.21106]] / 15 * h) - distance == 0 ? tw : [for(i = [0 : len(tw) - 1]) if(norm(tw[i] - tw[i + 1]) > distance) tw[i]]; - - -function __line_intersection(line_pts1, line_pts2, epsilon = 0.0001) = let( - a1 = line_pts1[0], - a2 = line_pts1[1], - b1 = line_pts2[0], - b2 = line_pts2[1], - a = a2 - a1, - b = b2 - b1, - s = b1 - a1 + tw = [[3.85724, 6.24078], [3.7902, 6.25779], [3.73596, 6.26288], [3.62807, 6.24587], [3.59581, 6.2602], [3.55429, 6.32386], [3.51698, 6.4571], [3.50768, 6.5361], [3.51188, 6.58284], [3.53917, 6.63708], [3.48981, 6.66934], [2.78286, 6.83905], [2.7218, 6.86112], [2.68441, 6.90272], [2.61063, 6.96209], [2.64288, 7.05549], [2.61062, 7.06568], [2.56396, 7.06058], [2.50281, 7.04109], [2.44849, 7.15647], [2.29319, 7.37123], [2.22438, 7.42555], [2.05644, 7.44248], [1.88674, 7.40509], [1.73901, 7.32879], [1.63795, 7.238], [1.58868, 7.14974], [1.54463, 7.0555], [1.5149, 7.0411], [1.48526, 7.01895], [1.53658, 6.9725], [1.58825, 6.92909], [1.63096, 6.86281], [1.61348, 6.80387], [1.57757, 6.83721], [1.53949, 6.89116], [1.48525, 6.87393], [1.43851, 6.87393], [1.40381, 6.86623], [1.37408, 6.85174], [1.28068, 6.77282], [1.20682, 6.7457], [0.723984, 6.65659], [0.586451, 6.60741], [0.5152, 6.57094], [0.458435, 6.52167], [0.393838, 6.47922], [0.108666, 6.38843], [-0.002506, 6.2925], [-0.110307, 6.16693], [-0.278327, 5.89785], [-0.312266, 5.80452], [-0.319942, 5.74076], [-0.35978, 5.72804], [-0.398773, 5.69411], [-0.431113, 5.64921], [-0.443073, 5.60508], [-0.45317, 5.54563], [-0.477762, 5.51429], [-0.504966, 5.48196], [-0.527025, 5.4379], [-0.511683, 5.32413], [-0.544022, 5.28008], [-0.630518, 5.10523], [-0.652506, 5.02118], [-0.721317, 4.96517], [-0.751047, 4.87851], [-0.807895, 4.81922], [-0.849502, 4.76313], [-0.835106, 4.67916], [-0.94535, 4.70123], [-1.03193, 4.67664], [-1.10318, 4.62476], [-1.16685, 4.55856], [-1.18724, 4.52125], [-1.20679, 4.47981], [-1.23643, 4.44755], [-1.33927, 4.41782], [-1.36462, 4.37621], [-1.38844, 4.28037], [-1.47747, 4.11993], [-1.51477, 4.03419], [-1.52674, 3.93321], [-1.55638, 3.87122], [-1.87389, 3.52162], [-1.92308, 3.43757], [-1.96721, 3.28479], [-2.11055, 3.03862], [-2.15224, 2.84946], [-2.18703, 2.75092], [-2.23874, 2.70864], [-2.2481, 2.65676], [-2.43313, 2.44284], [-2.47482, 2.40393], [-2.48998, 2.36148], [-2.49681, 2.20617], [-2.51727, 2.15951], [-2.59526, 2.09828], [-2.61312, 2.05583], [-2.62237, 2.00926], [-2.64705, 1.98728], [-2.68183, 1.97279], [-2.71915, 1.94559], [-2.76589, 1.90137], [-2.80741, 1.82768], [-2.89576, 1.58074], [-2.9601, 1.46267], [-3.00171, 1.34223], [-3.03396, 1.29978], [-3.14261, 1.19451], [-3.16223, 1.14945], [-3.18683, 1.04173], [-3.21142, 0.994987], [-3.30988, 0.906048], [-3.32504, 0.864443], [-3.42105, 0.738702], [-3.43797, 0.692212], [-3.47452, 0.558807], [-3.54409, 0.411083], [-3.62553, 0.283068], [-3.69434, 0.142925], [-3.72407, -0.047077], [-3.71634, -0.135425], [-3.67474, -0.317847], [-3.65948, -0.475761], [-3.62302, -0.539348], [-3.61029, -0.588533], [-3.62554, -0.628538], [-3.65703, -0.687068], [-3.61029, -0.73878], [-3.64002, -0.795629], [-3.57542, -0.918676], [-3.67902, -1.14784], [-3.62553, -1.18944], [-3.59589, -1.2046], [-3.60515, -1.24376], [-3.6476, -1.28781], [-3.68162, -1.37186], [-3.72138, -1.38205], [-3.74597, -1.40925], [-3.79785, -1.54426], [-3.80458, -1.58157], [-3.81731, -1.61121], [-3.84956, -1.65526], [-3.87677, -1.70958], [-3.8665, -1.75893], [-3.84714, -1.80812], [-3.83434, -1.86665], [-3.85397, -1.90666], [-3.89633, -1.91845], [-3.93532, -1.94052], [-3.94552, -2.0025], [-3.90315, -2.05169], [-3.83687, -2.10846], [-3.91452, -2.12525], [-3.92486, -2.16746], [-3.8021, -2.21718], [-3.78004, -2.24169], [-3.79537, -2.28599], [-3.84194, -2.30292], [-3.9014, -2.31052], [-3.94553, -2.3325], [-3.90902, -2.38984], [-3.81228, -2.42599], [-3.7487, -2.45311], [-3.7359, -2.49042], [-3.61032, -2.51249], [-3.51439, -2.52698], [-3.49737, -2.60598], [-3.53645, -2.69921], [-3.61031, -2.75101], [-3.55085, -2.813], [-3.52197, -2.86732], [-3.47455, -3.17194], [-3.46268, -3.20175], [-3.42108, -3.27805], [-3.36173, -3.36723], [-3.3667, -3.40353], [-3.39137, -3.45802], [-3.39137, -3.50468], [-3.37605, -3.57332], [-3.3048, -3.72879], [-3.22849, -3.84755], [-3.18689, -3.9332], [-3.16473, -4.02239], [-3.18175, -4.08606], [-3.21401, -4.15723], [-3.18942, -4.22848], [-3.1377, -4.29316], [-2.99756, -4.4237], [-2.91612, -4.51458], [-2.85675, -4.62575], [-2.84478, -4.76572], [-2.64282, -4.92119], [-2.55624, -4.90831], [-2.51219, -4.92877], [-2.47733, -4.95075], [-2.40355, -5.01441], [-2.33222, -5.06116], [-2.17691, -5.13485], [-2.10053, -5.19944], [-2.05126, -5.27328], [-2.00199, -5.30293], [-1.87641, -5.40147], [-1.84416, -5.44552], [-1.77804, -5.59577], [-1.69399, -5.70181], [-1.66687, -5.74611], [-1.35963, -6.53694], [-1.36899, -6.58351], [-1.4063, -6.638], [-1.41556, -6.68466], [-1.41556, -6.84915], [-1.42322, -6.93076], [-1.41556, -6.96992], [-1.33, -7.11073], [-1.34945, -7.21845], [-1.34692, -7.25315], [-1.28999, -7.29989], [-1.23921, -7.31522], [-1.20181, -7.27783], [-1.19675, -7.17685], [-1.07362, -7.20658], [-0.953101, -7.2609], [-0.849593, -7.33982], [-0.778259, -7.44248], [-0.775729, -7.35413], [-0.795186, -7.21416], [-0.797786, -7.08606], [-0.736641, -7.02913], [-0.685014, -6.99014], [-0.645009, -6.89851], [-0.620417, -6.78565], [-0.637343, -5.77062], [-0.612751, -5.52192], [-0.590692, -5.43534], [-0.443136, -5.1799], [-0.371802, -4.92362], [-0.341989, -4.73344], [-0.29036, -4.64283], [-0.16723, -4.48735], [-0.128151, -4.41105], [-0.046711, -4.20395], [-0.014539, -4.16235], [0.027066, -4.14297], [0.191803, -3.96039], [0.441265, -3.79565], [0.515127, -3.72608], [0.588904, -3.63285], [0.62032, -3.58105], [0.640788, -3.5317], [0.643228, -3.48757], [0.633124, -3.39173], [0.640794, -3.35189], [0.689979, -3.29336], [0.9039, -3.11338], [0.923353, -3.07093], [1.08363, -2.84522], [1.11605, -2.75342], [1.16262, -2.55407], [1.23396, -2.42344], [1.26116, -2.33518], [1.27809, -2.30031], [1.31035, -2.26637], [1.38421, -2.21213], [1.41638, -2.17987], [1.49024, -2.02701], [1.50464, -1.87935], [1.50212, -1.72405], [1.52671, -1.54937], [1.55897, -1.45589], [1.59897, -1.37942], [1.70669, -1.23616], [1.74147, -1.16044], [1.98243, 0.226167], [2.05637, 0.376416], [2.18195, 0.989965], [2.27788, 1.25316], [2.32959, 1.50186], [2.33469, 1.60107], [2.34741, 1.65447], [2.40173, 1.74366], [2.42118, 1.79798], [2.38391, 1.88363], [2.36176, 1.9185], [2.33473, 1.99994], [2.33213, 2.07136], [2.3542, 2.13747], [2.46798, 2.30473], [2.51203, 2.49221], [2.55625, 2.58553], [2.59356, 2.62284], [2.71147, 2.72138], [2.69968, 2.75364], [2.72175, 2.78497], [2.793, 2.8419], [2.89145, 2.97513], [2.98064, 3.06078], [2.97805, 3.26778], [2.98485, 3.3638], [2.99757, 3.41297], [3.01702, 3.44775], [3.03412, 3.48936], [3.02732, 3.59547], [3.03152, 3.64474], [3.14008, 3.76771], [3.23348, 3.82464], [3.27332, 3.8611], [3.26572, 3.90356], [3.23852, 3.94517], [3.22673, 3.98929], [3.23343, 4.02904], [3.32515, 4.08085], [3.33955, 4.16659], [3.31748, 4.26758], [3.2784, 4.34405], [3.3056, 4.3635], [3.37526, 4.38649], [3.39869, 4.42513], [3.32514, 4.42541], [3.22669, 4.4874], [3.17237, 4.58324], [3.16977, 4.70636], [3.19192, 4.7675], [3.19432, 4.8294], [3.14261, 5.06624], [3.14001, 5.17909], [3.14781, 5.29709], [3.1724, 5.41583], [3.20634, 5.51943], [3.25384, 5.59329], [3.54153, 5.94036], [3.62558, 6.01431], [3.94553, 6.17215], [3.91327, 6.21106]] / 15 * h, + leng = len(tw) ) - abs(cross(a, b)) < epsilon ? [] : // they are parallel or conincident edges - a1 + a * cross(s, b) / cross(a, b); + distance == 0 ? tw : [for(i = 0; i < leng; i = i + 1) if(norm(tw[i] - tw[i + 1]) > distance) tw[i]]; + + +/** +* multi_line_text.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-multi_line_text.html +* +**/ +module multi_line_text(lines, line_spacing = 15, size = 10, font = "Arial", halign = "left", valign = "baseline", direction = "ltr", language = "en", script = "latin"){ + to = len(lines) - 1; + inc = line_spacing; + offset_y = inc * to / 2; + union() { + for (i = [0 : to]) { + translate([0 , -i * inc + offset_y, 0]) + text(lines[i], size, font = font, valign = valign, halign = halign, direction = direction, language = language, script = script); + } + } +} + +/** +* px_line.scad +* +* @copyright Justin Lin, 2019 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-px_line.html +* +**/ + + +function _px_line_zsgn(a) = a == 0 ? a : a / abs(a); + +// x-dominant +function _px_line_xdominant_y(y, yd, sy) = yd >= 0 ? y + sy : y; +function _px_line_xdominant_yd(yd, ax, ay) = (yd >= 0 ? yd - ax : yd) + ay; +function _px_line_xdominant_z(z, zd, sz) = zd >= 0 ? z + sz : z; +function _px_line_xdominant_zd(zd, ax, az) = (zd >= 0 ? zd - ax : zd) + az; + +function _px_line_xdominant(start, end, a, s) = + let( + x = start[0], + y = start[1], + z = start[2], + ax = a[0], + ay = a[1], + az = a[2], + sx = s[0], + sy = s[1], + sz = s[2], + shrx = floor(ax / 2), + yd = ay - shrx, + zd = az - shrx, + endx = end[0] + ) + concat( + [start], + _px_line_xdominant_sub( + x + sx, + _px_line_xdominant_y(y, yd, sy), + _px_line_xdominant_z(z, zd, sz), + endx, + a, + s, + _px_line_xdominant_yd(yd, ax, ay), + _px_line_xdominant_zd(zd, ax, az) + ) + ); + +function _px_line_xdominant_sub(x, y, z, endx, a, s, yd, zd) = + let( + ax = a[0], + ay = a[1], + az = a[2], + sx = s[0], + sy = s[1], + sz = s[2] + ) + x == endx ? [] : + concat([[x, y, z]], + _px_line_xdominant_sub( + x + sx, + _px_line_xdominant_y(y, yd, sy), + _px_line_xdominant_z(z, zd, sz), + endx, + a, + s, + _px_line_xdominant_yd(yd, ax, ay), + _px_line_xdominant_zd(zd, ax, az) + ) + ); + +// y-dominant +function _px_line_ydominant_x(x, xd, sx) = xd >= 0 ? x + sx : x; +function _px_line_ydominant_xd(xd, ax, ay) = (xd >= 0 ? xd - ay : xd) + ax; +function _px_line_ydominant_z(z, zd, sz) = zd >= 0 ? z + sz : z; +function _px_line_ydominant_zd(zd, ay, az) = (zd >= 0 ? zd - ay : zd) + az; + +function _px_line_ydominant(start, end, a, s) = + let( + x = start[0], + y = start[1], + z = start[2], + ax = a[0], + ay = a[1], + az = a[2], + sx = s[0], + sy = s[1], + sz = s[2], + shry = floor(ay / 2), + xd = ax - shry, + zd = az - shry, + endy = end[1] + ) + concat( + [start], + _px_line_ydominant_sub( + _px_line_ydominant_x(x, xd, sx), + y + sy, + _px_line_ydominant_z(z, zd, sz), + endy, + a, + s, + _px_line_ydominant_xd(xd, ax, ay), + _px_line_ydominant_zd(zd, ay, az) + ) + ); + +function _px_line_ydominant_sub(x, y, z, endy, a, s, xd, zd) = + let( + ax = a[0], + ay = a[1], + az = a[2], + sx = s[0], + sy = s[1], + sz = s[2] + ) + y == endy ? [] : + concat([[x, y, z]], + _px_line_ydominant_sub( + _px_line_ydominant_x(x, xd, sx), + y + sy, + _px_line_ydominant_z(z, zd, sz), + endy, + a, + s, + _px_line_ydominant_xd(xd, ax, ay), + _px_line_ydominant_zd(zd, ay, az) + ) + ); + +// z-dominant +function _px_line_zdominant_x(x, xd, sx) = xd >= 0 ? x + sx : x; +function _px_line_zdominant_xd(xd, ax, az) = (xd >= 0 ? xd - az : xd) + ax; + +function _px_line_zdominant_y(y, yd, sy) = yd >= 0 ? y + sy : y; +function _px_line_zdominant_yd(yd, ay, az) = (yd >= 0 ? yd - az : yd) + ay; + +function _px_line_zdominant(start, end, a, s) = + let( + x = start[0], + y = start[1], + z = start[2], + ax = a[0], + ay = a[1], + az = a[2], + sx = s[0], + sy = s[1], + sz = s[2], + shrz = floor(az / 2), + xd = ax - shrz, + yd = ay - shrz, + endz = end[2] + ) + concat( + [start], + _px_line_zdominant_sub( + _px_line_zdominant_x(x, xd, sx), + _px_line_zdominant_y(y, yd, sy), + z + sz, + endz, + a, + s, + _px_line_zdominant_xd(xd, ax, az), + _px_line_zdominant_yd(yd, ay, az) + ) + ); + +function _px_line_zdominant_sub(x, y, z, endz, a, s, xd, yd) = + let( + ax = a[0], + ay = a[1], + az = a[2], + sx = s[0], + sy = s[1], + sz = s[2] + ) + z == endz ? [] : + concat([[x, y, z]], + _px_line_zdominant_sub( + _px_line_zdominant_x(x, xd, sx), + _px_line_zdominant_y(y, yd, sy), + z + sz, + endz, + a, + s, + _px_line_zdominant_xd(xd, ax, az), + _px_line_zdominant_yd(yd, ay, az) + ) + ); + +function px_line(p1, p2) = + let( + is_2d = len(p1) == 2, + start_pt = is_2d ? __to3d(p1) : p1, + end_pt = is_2d ? __to3d(p2) : p2, + dt = end_pt - start_pt, + ax = floor(abs(dt[0]) * 2), + ay = floor(abs(dt[1]) * 2), + az = floor(abs(dt[2]) * 2), + sx = _px_line_zsgn(dt[0]), + sy = _px_line_zsgn(dt[1]), + sz = _px_line_zsgn(dt[2]), + points = ax >= max(ay, az) ? _px_line_xdominant(start_pt, end_pt, [ax, ay, az], [sx, sy, sz]) : ( + ay >= max(ax, az) ? _px_line_ydominant(start_pt, end_pt, [ax, ay, az], [sx, sy, sz]) : + _px_line_zdominant(start_pt, end_pt, [ax, ay, az], [sx, sy, sz]) + ) + ) + is_2d ? [for(pt = points) __to2d(pt)] : points; + +/** +* hull_polyline2d.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/hull_polyline2d.html +* +**/ + +module hull_polyline2d(points, width) { + half_width = width / 2; + leng = len(points); + + module hull_line2d(index) { + point1 = points[index - 1]; + point2 = points[index]; + + hull() { + translate(point1) + circle(half_width); + translate(point2) + circle(half_width); + } + + // hook for testing + test_line_segment(index, point1, point2, half_width); + } + + module polyline2d_inner(index) { + if(index < leng) { + hull_line2d(index); + polyline2d_inner(index + 1); + } + } + + polyline2d_inner(1); +} + +// override it to test +module test_line_segment(index, point1, point2, radius) { + +} + +/** +* bezier_smooth.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-bezier_curve.html +* +**/ + + +function _corner_ctrl_pts(round_d, p1, p2, p3) = + let( + _ya_za_1 = __angy_angz(p1, p2), + _ya_za_2 = __angy_angz(p3, p2), + + dz1 = sin(_ya_za_1[0]) * round_d, + dxy1 = cos(_ya_za_1[0]) * round_d, + dy1 = sin(_ya_za_1[1]) * dxy1, + dx1 = cos(_ya_za_1[1]) * dxy1, + + dz2 = sin(_ya_za_2[0]) * round_d, + dxy2 = cos(_ya_za_2[0]) * round_d, + dy2 = sin(_ya_za_2[1]) * dxy2, + dx2 = cos(_ya_za_2[1]) * dxy2 + ) + [ + p2 - [dx1, dy1, dz1], + p2, + p2 - [dx2, dy2, dz2] + ]; + + +function _bezier_corner(round_d, t_step, p1, p2, p3) = + bezier_curve(t_step, _corner_ctrl_pts(round_d, p1, p2, p3)); + +function _recursive_bezier_smooth(pts, round_d, t_step, leng) = + let(end_i = leng - 2) + [ + for(i = 0; i < end_i; i = i + 1) + each _bezier_corner(round_d, t_step, pts[i], pts[i + 1], pts[i + 2]) + ]; + + +function bezier_smooth(path_pts, round_d, t_step = 0.1, closed = false) = + let( + pts = len(path_pts[0]) == 3 ? path_pts : [for(p = path_pts) __to3d(p)], + leng = len(pts), + middle_pts = _recursive_bezier_smooth(pts, round_d, t_step, leng), + pth_pts = closed ? + concat( + _recursive_bezier_smooth( + [pts[leng - 1], pts[0], pts[1]], + round_d, t_step, 3 + ), + middle_pts, + _recursive_bezier_smooth( + [pts[leng - 2], pts[leng - 1], pts[0]], + round_d, t_step, 3 + ) + ) : + concat( + [pts[0]], + middle_pts, + [pts[leng - 1]] + ) + ) + len(path_pts[0]) == 2 ? [for(p = pth_pts) __to2d(p)] : pth_pts; + +/** +* starburst.scad +* +* @copyright Justin Lin, 2019 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-starburst.html +* +**/ + +module starburst(r1, r2, n, height) { + a = 180 / n; + + p0 = [0, 0, 0]; + p1 = [r2 * cos(a), r2 * sin(a), 0]; + p2 = [r1, 0, 0]; + p3 = [0, 0, height]; + + module half_burst() { + polyhedron(points = [p0, p1, p2, p3], + faces = [ + [0, 2, 1], + [0, 1, 3], + [0, 3, 2], + [2, 1, 3] + ] + ); + } + + module burst() { + hull() { + half_burst(); + mirror([0, 1,0]) half_burst(); + } + } + + union() { + for(i = [0 : n - 1]) { + rotate(2 * a * i) burst(); + } + } +} + +/** +* turtle2d.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-turtle2d.html +* +**/ + +function _turtle2d_turtle(x, y, angle) = [[x, y], angle]; + +function _turtle2d_set_point(turtle, point) = [point, _turtle2d_get_angle(turtle)]; + +function _turtle2d_set_x(turtle, x) = [[x, _turtle2d_get_y(turtle)], _turtle2d_get_angle(turtle)]; +function _turtle2d_set_y(turtle, y) = [[_turtle2d_get_x(turtle), y], _turtle2d_get_angle(turtle)]; +function _turtle2d_set_angle(turtle, angle) = [_turtle2d_get_pt(turtle), angle]; + +function _turtle2d_forward(turtle, leng) = + _turtle2d_turtle( + _turtle2d_get_x(turtle) + leng * cos(_turtle2d_get_angle(turtle)), + _turtle2d_get_y(turtle) + leng * sin(_turtle2d_get_angle(turtle)), + _turtle2d_get_angle(turtle) + ); + +function _turtle2d_turn(turtle, angle) = [_turtle2d_get_pt(turtle), _turtle2d_get_angle(turtle) + angle]; + +function _turtle2d_get_x(turtle) = turtle[0][0]; +function _turtle2d_get_y(turtle) = turtle[0][1]; +function _turtle2d_get_pt(turtle) = turtle[0]; +function _turtle2d_get_angle(turtle) = turtle[1]; + +function _turtle2d_three_args_command(cmd, arg1, arg2, arg3) = + cmd == "create" ? _turtle2d_turtle(arg1, arg2, arg3) : _turtle2d_two_args_command(cmd, arg1, arg2); + +function _turtle2d_two_args_command(cmd, arg1, arg2) = + is_undef(arg2) ? _turtle2d_one_arg_command(cmd, arg1) : ( + cmd == "pt" ? _turtle2d_set_point(arg1, arg2) : ( + cmd == "x" ? _turtle2d_set_x(arg1, arg2) : ( + cmd == "y" ? _turtle2d_set_y(arg1, arg2) : ( + cmd == "angle" ? _turtle2d_set_angle(arg1, arg2) : ( + cmd == "forward" ? _turtle2d_forward(arg1, arg2) : ( + cmd == "turn" ? _turtle2d_turn(arg1, arg2) : undef + ) + ) + ) + ) + ) + ); + +function _turtle2d_one_arg_command(cmd, arg) = + cmd == "x" ? _turtle2d_get_x(arg) : ( + cmd == "y" ? _turtle2d_get_y(arg) : ( + cmd == "angle" ? _turtle2d_get_angle(arg) : ( + cmd == "pt" ? _turtle2d_get_pt(arg) : undef + ) + ) + ); + +function turtle2d(cmd, arg1, arg2, arg3) = + _turtle2d_three_args_command(cmd, arg1, arg2, arg3); + + + +/** +* shape_glued2circles.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-shape_glued2circles.html +* +**/ + +function _glued2circles_pie_curve(radius, centre_dist, tangent_angle) = + let( + begin_ang = 90 + tangent_angle, + shape_pts = shape_pie(radius, [-begin_ang, begin_ang]), + leng = len(shape_pts) + ) + [ + for(i = 1; i < leng; i = i + 1) + shape_pts[i] + [centre_dist / 2, 0] + ]; + +function _glued2circles_bezier(radius, centre_dist, tangent_angle, t_step, ctrl_p1) = + let( + ctrl_p = rotate_p([radius * tan(tangent_angle), -radius], tangent_angle), + ctrl_p2 = [-ctrl_p[0], ctrl_p[1]] + [centre_dist / 2, 0], + ctrl_p3 = [-ctrl_p2[0], ctrl_p2[1]], + ctrl_p4 = [-ctrl_p1[0], ctrl_p1[1]] + ) + bezier_curve( + t_step, + [ + ctrl_p1, + ctrl_p2, + ctrl_p3, + ctrl_p4 + ] + ); + +function _glued2circles_lower_half_curve(curve_pts, leng) = + [ + for(i = 0; i < leng; i = i + 1) + let(p = curve_pts[leng - 1 - i]) + if(p[0] >= 0) p + ]; + +function _glued2circles_half_glued_circle(radius, centre_dist, tangent_angle, t_step) = + let( + pie_curve_pts = _glued2circles_pie_curve(radius, centre_dist, tangent_angle), + curve_pts = _glued2circles_bezier(radius, centre_dist, tangent_angle, t_step, pie_curve_pts[0]), + lower_curve_pts = _glued2circles_lower_half_curve(curve_pts, len(curve_pts)), + leng_half_curve_pts = len(lower_curve_pts), + upper_curve_pts = [ + for(i = 0; i < leng_half_curve_pts; i = i + 1) + let(pt = lower_curve_pts[leng_half_curve_pts - 1 - i]) + [pt[0], -pt[1]] + ] + ) concat( + lower_curve_pts, + pie_curve_pts, + upper_curve_pts + ); + +function shape_glued2circles(radius, centre_dist, tangent_angle = 30, t_step = 0.1) = + let( + half_glued_circles = _glued2circles_half_glued_circle(radius, centre_dist, tangent_angle, t_step), + leng_half_glued_circles = len(half_glued_circles), + left_half_glued_circles = [ + for(i = 0; i < leng_half_glued_circles; i = i + 1) + let(pt = half_glued_circles[leng_half_glued_circles - 1 - i]) + [-pt[0], pt[1]] + ] + ) concat(half_glued_circles, left_half_glued_circles); + +function __m_scaling_to_3_elems_scaling_vect(s) = + let(leng = len(s)) + leng == 3 ? s : ( + leng == 2 ? [s[0], s[1], 1] : [s[0], 1, 1] + ); + +function __m_scaling_to_scaling_vect(s) = is_num(s) ? [s, s, s] : __m_scaling_to_3_elems_scaling_vect(s); + +function __m_scaling(s) = + let(v = __m_scaling_to_scaling_vect(s)) + [ + [v[0], 0, 0, 0], + [0, v[1], 0, 0], + [0, 0, v[2], 0], + [0, 0, 0, 1] + ]; + +/** +* hollow_out.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-hollow_out.html +* +**/ + +module hollow_out(shell_thickness) { + difference() { + children(); + offset(delta = -shell_thickness) children(); + } +} + +/** +* shape_square.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-shape_square.html +* +**/ + + +function shape_square(size, corner_r = 0) = + let( + is_flt = is_num(size), + x = is_flt ? size : size[0], + y = is_flt ? size : size[1] + ) + __trapezium( + length = x, + h = y, + round_r = corner_r + ); + + +/** +* triangulate.scad +* +* @copyright Justin Lin, 2019 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-triangulate.html +* +**/ + +function _triangulate_in_triangle(p0, p1, p2, p) = + let( + v0 = p0 - p, + v1 = p1 - p, + v2 = p2 - p, + c0 = cross(v0, v1), + c1 = cross(v1, v2), + c2 = cross(v2, v0) + ) + (c0 > 0 && c1 > 0 && c2 > 0) || (c0 < 0 && c1 < 0 && c2 < 0); + +function _triangulate_snipable(shape_pts, u, v, w, n, indices, epsilon = 0.0001) = + let( + a = shape_pts[indices[u]], + b = shape_pts[indices[v]], + c = shape_pts[indices[w]], + ax = a[0], + ay = a[1], + bx = b[0], + by = b[1], + cx = c[0], + cy = c[1] + ) + epsilon > (((bx - ax) * (cy - ay)) - ((by - ay) * (cx - ax))) ? + false : _triangulate_snipable_sub(shape_pts, n, u, v, w, a, b, c, indices); + +function _triangulate_snipable_sub(shape_pts, n, u, v, w, a, b, c, indices, p = 0) = + p == n ? true : ( + ((p == u) || (p == v) || (p == w)) ? _triangulate_snipable_sub(shape_pts, n, u, v, w, a, b, c, indices, p + 1) : ( + _triangulate_in_triangle(a, b, c, shape_pts[indices[p]]) ? + false : _triangulate_snipable_sub(shape_pts, n, u, v, w, a, b, c, indices, p + 1) + ) + ); + +// remove the elem at idx v from indices +function _triangulate_remove_v(indices, v, num_of_vertices) = + let( + nv_minuns_one = num_of_vertices - 1 + ) + v == 0 ? [for(i = 1; i <= nv_minuns_one; i = i + 1) indices[i]] : ( + v == nv_minuns_one ? [for(i = 0; i < v; i = i + 1) indices[i]] : concat( + [for(i = 0; i < v; i = i + 1) indices[i]], + [for(i = v + 1; i <= nv_minuns_one; i = i + 1) indices[i]] + ) + ); + +function _triangulate_zero_or_value(num_of_vertices, value) = + num_of_vertices <= value ? 0 : value; + +function _triangulate_real_triangulate_sub(shape_pts, collector, indices, v, num_of_vertices, count, epsilon) = + let( + // idxes of three consecutive vertices + u = _triangulate_zero_or_value(num_of_vertices, v), + vi = _triangulate_zero_or_value(num_of_vertices, u + 1), + w = _triangulate_zero_or_value(num_of_vertices, vi + 1) + ) + _triangulate_snipable(shape_pts, u, vi, w, num_of_vertices, indices, epsilon) ? + _triangulate_snip(shape_pts, collector, indices, u, vi, w, num_of_vertices, count, epsilon) : + _triangulate_real_triangulate(shape_pts, collector, indices, vi, num_of_vertices, count, epsilon); + +function _triangulate_snip(shape_pts, collector, indices, u, v, w, num_of_vertices, count, epsilon) = + let( + a = indices[u], + b = indices[v], + c = indices[w], + new_nv = num_of_vertices - 1 + ) + _triangulate_real_triangulate( + shape_pts, + concat(collector, [[a, b, c]]), + _triangulate_remove_v(indices, v, num_of_vertices), + v, + new_nv, + 2 * new_nv, + epsilon + ); + +function _triangulate_real_triangulate(shape_pts, collector, indices, v, num_of_vertices, count, epsilon) = + count <= 0 ? [] : ( + num_of_vertices == 2 ? + collector : _triangulate_real_triangulate_sub(shape_pts, collector, indices, v, num_of_vertices, count - 1, epsilon) + ); + +function triangulate(shape_pts, epsilon = 0.0001) = + let( + num_of_vertices = len(shape_pts), + v = num_of_vertices - 1, + indices = [for(vi = 0; vi <= v; vi = vi + 1) vi], + count = 2 * num_of_vertices + ) + num_of_vertices < 3 ? [] : _triangulate_real_triangulate(shape_pts, [], indices, v, num_of_vertices, count, epsilon); + + +/** +* shape_superformula.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-shape_superformula.html +* +**/ + + +function _superformula_r(angle, m1, m2, n1, n2 = 1, n3 = 1, a = 1, b = 1) = + pow( + pow(abs(cos(m1 * angle / 4) / a), n2) + + pow(abs(sin(m2 * angle / 4) / b), n3), + - 1 / n1 + ); + +function shape_superformula(phi_step, m1, m2, n1, n2 = 1, n3 = 1, a = 1, b = 1) = + let(tau = PI * 2) + [ + for(phi = 0; phi <= tau; phi = phi + phi_step) + let( + angle = __to_degree(phi), + r = _superformula_r(angle, m1, m2, n1, n2, n3, a, b) + ) + __ra_to_xy(r, angle) + ]; + +/** +* path_extrude.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-path_extrude.html +* +**/ + + +module path_extrude(shape_pts, path_pts, triangles = "SOLID", twist = 0, scale = 1.0, closed = false, method = "AXIS_ANGLE") { + sh_pts = len(shape_pts[0]) == 3 ? shape_pts : [for(p = shape_pts) __to3d(p)]; + pth_pts = len(path_pts[0]) == 3 ? path_pts : [for(p = path_pts) __to3d(p)]; + + len_path_pts = len(pth_pts); + len_path_pts_minus_one = len_path_pts - 1; + + module axis_angle_path_extrude() { + twist_step_a = twist / len_path_pts; + + function scale_pts(pts, s) = [ + for(p = pts) [p[0] * s[0], p[1] * s[1], p[2] * s[2]] + ]; + + function translate_pts(pts, t) = [ + for(p = pts) [p[0] + t[0], p[1] + t[1], p[2] + t[2]] + ]; + + function rotate_pts(pts, a, v) = [for(p = pts) rotate_p(p, a, v)]; + + scale_step_vt = is_num(scale) ? + let(s = (scale - 1) / len_path_pts_minus_one) [s, s, s] : + [ + (scale[0] - 1) / len_path_pts_minus_one, + (scale[1] - 1) / len_path_pts_minus_one, + is_undef(scale[2]) ? 0 : (scale[2] - 1) / len_path_pts_minus_one + ]; + + // get rotation matrice for sections + + function local_ang_vects(j) = + [ + for(i = j; i > 0; i = i - 1) + let( + vt0 = pth_pts[i] - pth_pts[i - 1], + vt1 = pth_pts[i + 1] - pth_pts[i], + a = acos((vt0 * vt1) / (norm(vt0) * norm(vt1))), + v = cross(vt0, vt1) + ) + [a, v] + ]; + + rot_matrice = [ + for(ang_vect = local_ang_vects(len_path_pts - 2)) + __m_rotation(ang_vect[0], ang_vect[1]) + ]; + + leng_rot_matrice = len(rot_matrice); + leng_rot_matrice_minus_one = leng_rot_matrice - 1; + leng_rot_matrice_minus_two= leng_rot_matrice - 2; + + identity_matrix = [ + [1, 0, 0, 0], + [0, 1, 0, 0], + [0, 0, 1, 0], + [0, 0, 0, 1] + ]; + + function cumulated_rot_matrice(i) = + leng_rot_matrice == 0 ? [identity_matrix] : ( + leng_rot_matrice == 1 ? [rot_matrice[0], identity_matrix] : + ( + i == leng_rot_matrice_minus_two ? + [ + rot_matrice[leng_rot_matrice_minus_one], + rot_matrice[leng_rot_matrice_minus_two] * rot_matrice[leng_rot_matrice_minus_one] + ] + : cumulated_rot_matrice_sub(i)) + ); + + function cumulated_rot_matrice_sub(i) = + let( + matrice = cumulated_rot_matrice(i + 1), + curr_matrix = rot_matrice[i], + prev_matrix = matrice[len(matrice) - 1] + ) + concat(matrice, [curr_matrix * prev_matrix]); + + cumu_rot_matrice = cumulated_rot_matrice(0); + + // get all sections + + function init_section(a, s) = + let(angleyz = __angy_angz(pth_pts[0], pth_pts[1])) + rotate_pts( + rotate_pts( + rotate_pts( + scale_pts(sh_pts, s), a + ), [90, 0, -90] + ), [0, -angleyz[0], angleyz[1]] + ); + + function local_rotate_section(j, init_a, init_s) = + j == 0 ? + init_section(init_a, init_s) : + local_rotate_section_sub(j, init_a, init_s); + + function local_rotate_section_sub(j, init_a, init_s) = + let( + vt0 = pth_pts[j] - pth_pts[j - 1], + vt1 = pth_pts[j + 1] - pth_pts[j], + ms = cumu_rot_matrice[j - 1] + ) + [ + for(p = init_section(init_a, init_s)) + [ + [ms[0][0], ms[0][1], ms[0][2]] * p, + [ms[1][0], ms[1][1], ms[1][2]] * p, + [ms[2][0], ms[2][1], ms[2][2]] * p + ] + ]; + + sections = + let( + fst_section = + translate_pts(local_rotate_section(0, 0, [1, 1, 1]), pth_pts[0]), + end_i = len_path_pts - 1, + remain_sections = [ + for(i = 0; i < end_i; i = i + 1) + translate_pts( + local_rotate_section(i, i * twist_step_a, [1, 1, 1] + scale_step_vt * i), + pth_pts[i + 1] + ) + ] + ) concat([fst_section], remain_sections); + + calculated_sections = + closed && pth_pts[0] == pth_pts[len_path_pts_minus_one] ? + concat(sections, [sections[0]]) : // round-robin + sections; + + polysections( + calculated_sections, + triangles = triangles + ); + + // hook for testing + test_path_extrude(sections); + } + + module euler_angle_path_extrude() { + scale_step_vt = is_num(scale) ? + [(scale - 1) / len_path_pts_minus_one, (scale - 1) / len_path_pts_minus_one] : + [(scale[0] - 1) / len_path_pts_minus_one, (scale[1] - 1) / len_path_pts_minus_one]; + + scale_step_x = scale_step_vt[0]; + scale_step_y = scale_step_vt[1]; + twist_step = twist / len_path_pts_minus_one; + + function section(p1, p2, i) = + let( + length = norm(p1 - p2), + angy_angz = __angy_angz(p1, p2), + ay = -angy_angz[0], + az = angy_angz[1] + ) + [ + for(p = sh_pts) + let(scaled_p = [p[0] * (1 + scale_step_x * i), p[1] * (1 + scale_step_y * i), p[2]]) + rotate_p( + rotate_p( + rotate_p(scaled_p, twist_step * i), [90, 0, -90] + ) + [i == 0 ? 0 : length, 0, 0], + [0, ay, az] + ) + p1 + ]; + + path_extrude_inner = + [ + for(i = 1; i < len_path_pts; i = i + 1) + section(pth_pts[i - 1], pth_pts[i], i) + ]; + + calculated_sections = + closed && pth_pts[0] == pth_pts[len_path_pts_minus_one] ? + concat(path_extrude_inner, [path_extrude_inner[0]]) : // round-robin + concat([section(pth_pts[0], pth_pts[1], 0)], path_extrude_inner); + + polysections( + calculated_sections, + triangles = triangles + ); + + // hook for testing + test_path_extrude(calculated_sections); + } + + if(method == "AXIS_ANGLE") { + axis_angle_path_extrude(); + } + else if(method == "EULER_ANGLE") { + euler_angle_path_extrude(); + } +} + +// override to test +module test_path_extrude(sections) { + +} + +function __polytransversals(transversals) = + let( + leng_trs = len(transversals), + leng_tr = len(transversals[0]), + lefts = [ + for(i = 1; i < leng_trs - 1; i = i + 1) + let(tr = transversals[leng_trs - i]) + tr[0] + ], + rights = [ + for(i = 1; i < leng_trs - 1; i = i + 1) + let(tr = transversals[i]) + tr[leng_tr - 1] + ] + ) concat( + transversals[0], + rights, + __reverse(transversals[leng_trs - 1]), + lefts + ); + +/** +* box_extrude.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-box_extrude.html +* +**/ + +module box_extrude(height, shell_thickness, offset_mode = "delta", chamfer = false) { + linear_extrude(shell_thickness) + children(); + + linear_extrude(height) + difference() { + children(); + if(offset_mode == "delta") { + offset(delta = -shell_thickness, chamfer = chamfer) + children(); + } else { + offset(r = -shell_thickness) + children(); + } + } +} + + + +/** +* polytransversals.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-polytransversals.html +* +**/ + + +module polytransversals(transversals) { + polygon( + __polytransversals(transversals) + ); +} + +function __m_rotation_q_rotation(a, v) = + let( + half_a = a / 2, + axis = v / norm(v), + s = sin(half_a), + x = s * axis[0], + y = s * axis[1], + z = s * axis[2], + w = cos(half_a), + + x2 = x + x, + y2 = y + y, + z2 = z + z, + + xx = x * x2, + yx = y * x2, + yy = y * y2, + zx = z * x2, + zy = z * y2, + zz = z * z2, + wx = w * x2, + wy = w * y2, + wz = w * z2 + ) + [ + [1 - yy - zz, yx - wz, zx + wy, 0], + [yx + wz, 1 - xx - zz, zy - wx, 0], + [zx - wy, zy + wx, 1 - xx - yy, 0], + [0, 0, 0, 1] + ]; + +function __m_rotation_xRotation(a) = + let(c = cos(a), s = sin(a)) + [ + [1, 0, 0, 0], + [0, c, -s, 0], + [0, s, c, 0], + [0, 0, 0, 1] + ]; + +function __m_rotation_yRotation(a) = + let(c = cos(a), s = sin(a)) + [ + [c, 0, s, 0], + [0, 1, 0, 0], + [-s, 0, c, 0], + [0, 0, 0, 1] + ]; + +function __m_rotation_zRotation(a) = + let(c = cos(a), s = sin(a)) + [ + [c, -s, 0, 0], + [s, c, 0, 0], + [0, 0, 1, 0], + [0, 0, 0, 1] + ]; + +function __m_rotation_xyz_rotation(a) = + let(ang = __to_ang_vect(a)) + __m_rotation_zRotation(ang[2]) * __m_rotation_yRotation(ang[1]) * __m_rotation_xRotation(ang[0]); + +function __m_rotation(a, v) = + (a == 0 || a == [0, 0, 0] || a == [0] || a == [0, 0]) ? [ + [1, 0, 0, 0], + [0, 1, 0, 0], + [0, 0, 1, 0], + [0, 0, 0, 1] + ] : (is_undef(v) ? __m_rotation_xyz_rotation(a) : __m_rotation_q_rotation(a, v)); + +/** +* shape_arc.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-shape_arc.html +* +**/ + + +function shape_arc(radius, angle, width, width_mode = "LINE_CROSS") = + __shape_arc(radius, angle, width, width_mode); + +/** +* slice.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-slice.html +* +**/ + +function slice(lt, begin, end) = + let(ed = is_undef(end) ? len(lt) : end) + [for(i = begin; i < ed; i = i + 1) lt[i]]; + + +/** +* shape_path_extend.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-path_extend.html +* +**/ + + +function _shape_path_extend_az(p1, p2) = + let( + x1 = p1[0], + y1 = p1[1], + x2 = p2[0], + y2 = p2[1] + ) -90 + atan2((y2 - y1), (x2 - x1)); + +function _shape_path_first_stroke(stroke_pts, path_pts) = + let( + p1 = path_pts[0], + p2 = path_pts[1], + a = _shape_path_extend_az(p1, p2) + ) + [ + for(p = stroke_pts) + rotate_p(p, a) + p1 + ]; + +function _shape_path_extend_stroke(stroke_pts, p1, p2, scale_step, i) = + let( + leng = norm(__to3d(p2) - __to3d(p1)), + a = _shape_path_extend_az(p1, p2) + ) + [ + for(p = stroke_pts) + rotate_p(p * (1 + scale_step * i) + [0, leng], a) + p1 + ]; + +function _shape_path_extend_inner(stroke_pts, path_pts, leng_path_pts, scale_step) = + [ + for(i = 1; i < leng_path_pts; i = i + 1) + _shape_path_extend_stroke( + stroke_pts, + path_pts[i - 1], + path_pts[i ], + scale_step, + i + ) + ]; + +function shape_path_extend(stroke_pts, path_pts, scale = 1.0, closed = false) = + let( + leng_path_pts = len(path_pts), + scale_step = (scale - 1) / (leng_path_pts - 1), + strokes = _shape_path_extend_inner(stroke_pts, path_pts, leng_path_pts, scale_step) + ) + closed && path_pts[0] == path_pts[leng_path_pts - 1] ? + __polytransversals(concat(strokes, [strokes[0]])) : + __polytransversals( + concat([_shape_path_first_stroke(stroke_pts, path_pts)], strokes) + ); + + + +function __frags(radius) = $fn > 0 ? + ($fn >= 3 ? $fn : 3) : + max(min(360 / $fa, radius * PI * 2 / $fs), 5); + +/** +* circle_path.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-circle_path.html +* +**/ + + +function circle_path(radius, n) = + let( + _frags = __frags(radius), + step_a = 360 / _frags, + end_a = 360 - step_a * ((is_undef(n) || n > _frags) ? 1 : _frags - n + 1) + ) + [ + for(a = 0; a <= end_a; a = a + step_a) + [radius * cos(a), radius * sin(a)] + ]; + + +/** +* archimedean_spiral_extrude.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-archimedean_spiral_extrude.html +* +**/ + +module archimedean_spiral_extrude(shape_pts, arm_distance, init_angle, point_distance, num_of_points, + rt_dir = "CT_CLK", twist = 0, scale = 1.0, triangles = "SOLID") { + points_angles = archimedean_spiral( + arm_distance = arm_distance, + init_angle = init_angle, + point_distance = point_distance, + num_of_points = num_of_points, + rt_dir = rt_dir + ); + + clk_a = rt_dir == "CT_CLK" ? 0 : 180; + + points = [for(pa = points_angles) pa[0]]; + angles = [ + for(pa = points_angles) + [90, 0, pa[1] + clk_a] + ]; + + sections = cross_sections(shape_pts, points, angles, twist, scale); + + polysections( + sections, + triangles = triangles + ); + + // testing hook + test_archimedean_spiral_extrude(sections); +} + +// override it to test +module test_archimedean_spiral_extrude(sections) { + +} + +/** +* voronoi2d.scad +* +* @copyright Justin Lin, 2019 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-voronoi2d.html +* +**/ + +module voronoi2d(points, spacing = 1, r = 0, delta = 0, chamfer = false, region_type = "square") { + xs = [for(p = points) p[0]]; + ys = [for(p = points) abs(p[1])]; + + region_size = max([(max(xs) - min(xs) / 2), (max(ys) - min(ys)) / 2]); + half_region_size = 0.5 * region_size; + offset_leng = spacing * 0.5 + half_region_size; + + function normalize(v) = v / norm(v); + + module region(pt) { + intersection_for(p = points) { + if(pt != p) { + v = p - pt; + translate((pt + p) / 2 - normalize(v) * offset_leng) + rotate(atan2(v[1], v[0])) + if(region_type == "square") { + square(region_size, center = true); + } + else if(region_type == "circle") { + circle(region_size / 2); + } + + } + } + } + + for(p = points) { + if(r != 0) { + offset(r) region(p); + } + else { + offset(delta = delta, chamfer = chamfer) region(p); + } + } +} + +/** +* bend_extrude.scad +* +* @copyright Justin Lin, 2019 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-bend_extrude.html +* +**/ + +module bend_extrude(size, thickness, angle, frags = 24) { + x = size[0]; + y = size[1]; + frag_width = x / frags ; + frag_angle = angle / frags; + half_frag_width = 0.5 * frag_width; + half_frag_angle = 0.5 * frag_angle; + r = half_frag_width / sin(half_frag_angle); + s = (r - thickness) / r; + + module get_frag(i) { + offsetX = i * frag_width; + linear_extrude(thickness, scale = [s, 1]) + translate([-offsetX - half_frag_width, 0, 0]) + intersection() { + translate([x, 0, 0]) mirror([1, 0, 0]) children(); + translate([offsetX, 0, 0]) + square([frag_width, y]); + } + } + + offsetY = -r * cos(half_frag_angle) ; + rotate([180, 0, 180]) for(i = [0 : frags - 1]) { + rotate(i * frag_angle + half_frag_angle) + translate([0, offsetY, 0]) + rotate([-90, 0, 0]) + get_frag(i) + children(); + } + +} + + +/** +* line2d.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-line2d.html +* +**/ + + +module line2d(p1, p2, width, p1Style = "CAP_SQUARE", p2Style = "CAP_SQUARE") { + half_width = 0.5 * width; + + atan_angle = atan2(p2[1] - p1[1], p2[0] - p1[0]); + leng = sqrt(pow(p2[0] - p1[0], 2) + pow(p2[1] - p1[1], 2)); + + frags = __nearest_multiple_of_4(__frags(half_width)); + + module square_end(point) { + translate(point) + rotate(atan_angle) + square(width, center = true); + + // hook for testing + test_line2d_cap(point, "CAP_SQUARE"); + } + + module round_end(point) { + translate(point) + rotate(atan_angle) + circle(half_width, $fn = frags); + + // hook for testing + test_line2d_cap(point, "CAP_ROUND"); + } + + if(p1Style == "CAP_SQUARE") { + square_end(p1); + } else if(p1Style == "CAP_ROUND") { + round_end(p1); + } + + translate(p1) + rotate(atan_angle) + translate([0, -width / 2]) + square([leng, width]); + + if(p2Style == "CAP_SQUARE") { + square_end(p2); + } else if(p2Style == "CAP_ROUND") { + round_end(p2); + } + + // hook for testing + test_line2d_line(atan_angle, leng, width, frags); +} + +// override them to test +module test_line2d_cap(point, style) { +} + +module test_line2d_line(angle, length, width, frags) { +} + + + +/** +* bezier_surface.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-bezier_surface.html +* +**/ + +function bezier_surface(t_step, ctrl_pts) = + let(pts = [ + for(i = 0; i < len(ctrl_pts); i = i + 1) + bezier_curve(t_step, ctrl_pts[i]) + ]) + [for(x = 0; x < len(pts[0]); x = x + 1) + bezier_curve(t_step, + [for(y = [0:len(pts) - 1]) pts[y][x]] + ) + ]; + +/** +* m_translation.scad +* +* @copyright Justin Lin, 2019 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-m_translation.html +* +**/ + +function _to_3_elems_translation_vect(v) = + let(leng = len(v)) + leng == 3 ? v : ( + leng == 2 ? [v[0], v[1], 0] : [v[0], 0, 0] + ); + +function _to_translation_vect(v) = is_num(v) ? [v, 0, 0] : _to_3_elems_translation_vect(v); + +function m_translation(v) = + let(vt = _to_translation_vect(v)) + [ + [1, 0, 0, vt[0]], + [0, 1, 0, vt[1]], + [0, 0, 1, vt[2]], + [0, 0, 0, 1] + ]; + +/** +* helix.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-helix.html +* +**/ + + +function helix(radius, levels, level_dist, vt_dir = "SPI_DOWN", rt_dir = "CT_CLK") = + let( + is_flt = is_num(radius), + r1 = is_flt ? radius : radius[0], + r2 = is_flt ? radius : radius[1], + init_r = vt_dir == "SPI_DOWN" ? r2 : r1, + _frags = __frags(init_r), + h = level_dist * levels, + vt_d = vt_dir == "SPI_DOWN" ? 1 : -1, + rt_d = rt_dir == "CT_CLK" ? 1 : -1, + r_diff = (r1 - r2) * vt_d, + h_step = level_dist / _frags * vt_d, + r_step = r_diff / (levels * _frags), + a_step = 360 / _frags * rt_d, + begin_r = vt_dir == "SPI_DOWN" ? r2 : r1, + begin_h = vt_dir == "SPI_DOWN" ? h : 0, + end_i = _frags * levels + ) + [ + for(i = 0; i <= end_i; i = i + 1) + let(r = begin_r + r_step * i, a = a_step * i) + [r * cos(a), r * sin(a), begin_h - h_step * i] + ]; + +/** +* polyline2d.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-polyline2d.html +* +**/ + +module polyline2d(points, width, startingStyle = "CAP_SQUARE", endingStyle = "CAP_SQUARE") { + leng_pts = len(points); + + module line_segment(index) { + styles = index == 1 ? [startingStyle, "CAP_ROUND"] : ( + index == leng_pts - 1 ? ["CAP_BUTT", endingStyle] : [ + "CAP_BUTT", "CAP_ROUND" + ] + ); + + p1 = points[index - 1]; + p2 = points[index]; + p1Style = styles[0]; + p2Style = styles[1]; + + line2d(points[index - 1], points[index], width, + p1Style = p1Style, p2Style = p2Style); + + // hook for testing + test_line_segment(index, p1, p2, width, p1Style, p2Style); + } + + module polyline2d_inner(index) { + if(index < leng_pts) { + line_segment(index); + polyline2d_inner(index + 1); + } + } + + polyline2d_inner(1); +} + +// override it to test +module test_line_segment(index, point1, point2, width, p1Style, p2Style) { + +} + +/** +* reverse.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-reverse.html +* +**/ + + +function reverse(lt) = __reverse(lt); + +function __to_degree(phi) = 180 / PI * phi; + +/** +* px_cylinder.scad +* +* @copyright Justin Lin, 2019 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-px_cylinder.html +* +**/ + +function _px_cylinder_px_circle(radius, filled, thickness) = + let(range = [-radius: radius - 1]) + filled ? [ + for(y = range) + for(x = range) + let(v = [x, y]) + if(norm(v) < radius) v + ] : + let(ishell = radius * radius - 2 * thickness * radius) + [ + for(y = range) + for(x = range) + let( + v = [x, y], + leng = norm(v) + ) + if(leng < radius && (leng * leng) > ishell) v + ]; + +function _px_cylinder_diff_r(r, h, filled, thickness) = + let( + r1 = r[0], + r2 = r[1] + ) + r1 == r2 ? _px_cylinder_same_r(r1, h, filled, thickness) : + let(dr = (r2 - r1) / (h - 1)) + [ + for(i = 0; i < h; i = i + 1) + let(r = round(r1 + dr * i)) + each [ + for(pt = _px_cylinder_px_circle(r, filled, thickness)) + [pt[0], pt[1], i] + ] + ]; + +function _px_cylinder_same_r(r, h, filled, thickness) = + let(c = _px_cylinder_px_circle(r, filled, thickness)) + [ + for(i = 0; i < h; i = i + 1) + each [ + for(pt = c) + [pt[0], pt[1], i] + ] + ]; + +function px_cylinder(r, h, filled = false, thickness = 1) = + is_num(r) ? + _px_cylinder_same_r(r, h, filled, thickness) : + _px_cylinder_diff_r(r, h, filled, thickness); + +/** +* ellipse_extrude.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-ellipse_extrude.html +* +**/ + +module ellipse_extrude(semi_minor_axis, height, center = false, convexity = 10, twist = 0, slices = 20) { + h = is_undef(height) ? semi_minor_axis : ( + // `semi_minor_axis` is always equal to or greater than `height`. + height > semi_minor_axis ? semi_minor_axis : height + ); + angle = asin(h / semi_minor_axis) / slices; + + f_extrude = [ + for(i = 1; i <= slices; i = i + 1) + [ + cos(angle * i) / cos(angle * (i - 1)), + semi_minor_axis * sin(angle * i) + ] + ]; + len_f_extrude = len(f_extrude); + + accm_fs = + [ + for(i = 0, pre_f = 1; i < len_f_extrude; pre_f = pre_f * f_extrude[i][0], i = i + 1) + pre_f * f_extrude[i][0] + ]; + + child_fs = concat([1], accm_fs); + pre_zs = concat( + [0], + [ + for(i = 0; i < len_f_extrude; i = i + 1) + f_extrude[i][1] + ] + ); + + module extrude() { + for(i = [0:len_f_extrude - 1]) { + f = f_extrude[i][0]; + z = f_extrude[i][1]; + + translate([0, 0, pre_zs[i]]) + rotate(-twist / slices * i) + linear_extrude( + z - pre_zs[i], + convexity = convexity, + twist = twist / slices, + slices = 1, + scale = f + ) scale(child_fs[i]) children(); + } + } + + center_offset = [0, 0, center == true ? -h / 2 : 0]; + translate(center_offset) + extrude() + children(); + + // hook for testing + test_ellipse_extrude_fzc(child_fs, pre_zs, center_offset); +} + +// override for testing +module test_ellipse_extrude_fzc(child_fs, pre_zs, center_offset) { + +} + +/** +* parse_number.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-parse_number.html +* +**/ + +function _str_to_int(t) = + let( + dict = [["0", 0], ["1", 1], ["2", 2], ["3", 3], ["4", 4], ["5", 5], ["6", 6], ["7", 7], ["8", 8], ["9", 9]], + n = dict[search(t, dict)[0]][1] + ) n; + +function _parse_positive_int(t, value = 0, i = 0) = + i == len(t) ? value : _parse_positive_int(t, value * pow(10, i) + _str_to_int(t[i]), i + 1); + +function _parse_positive_decimal(t, value = 0, i = 0) = + i == len(t) ? value : _parse_positive_decimal(t, value + _str_to_int(t[i]) * pow(10, -(i + 1)), i + 1); + +function _parse_positive_number(t) = + len(search(".", t)) == 0 ? _parse_positive_int(t) : + _parse_positive_int(split_str(t, ".")[0]) + _parse_positive_decimal(split_str(t, ".")[1]); + +function parse_number(t) = + t[0] == "-" ? -_parse_positive_number(sub_str(t, 1, len(t))) : _parse_positive_number(t); + + + +/** +* cross_sections.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-cross_sections.html +* +**/ + + +function cross_sections(shape_pts, path_pts, angles, twist = 0, scale = 1.0) = + let( + len_path_pts_minus_one = len(path_pts) - 1, + sh_pts = len(shape_pts[0]) == 3 ? shape_pts : [for(p = shape_pts) __to3d(p)], + pth_pts = len(path_pts[0]) == 3 ? path_pts : [for(p = path_pts) __to3d(p)], + scale_step_vt = is_num(scale) ? + [(scale - 1) / len_path_pts_minus_one, (scale - 1) / len_path_pts_minus_one] : + [(scale[0] - 1) / len_path_pts_minus_one, (scale[1] - 1) / len_path_pts_minus_one] + , + scale_step_x = scale_step_vt[0], + scale_step_y = scale_step_vt[1], + twist_step = twist / len_path_pts_minus_one + ) + [ + for(i = 0; i <= len_path_pts_minus_one; i = i + 1) + [ + for(p = sh_pts) + let(scaled_p = [p[0] * (1 + scale_step_x * i), p[1] * (1 + scale_step_y * i), p[2]]) + rotate_p( + rotate_p(scaled_p, twist_step * i) + , angles[i] + ) + pth_pts[i] + ] + ]; + + +/** +* rounded_cube.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-rounded_cube.html +* +**/ + + +module rounded_cube(size, corner_r, center = false) { + is_flt = is_num(size); + x = is_flt ? size : size[0]; + y = is_flt ? size : size[1]; + z = is_flt ? size : size[2]; + + corner_frags = __nearest_multiple_of_4(__frags(corner_r)); + edge_d = corner_r * cos(180 / corner_frags); + + half_x = x / 2; + half_y = y / 2; + half_z = z / 2; + + half_l = half_x - edge_d; + half_w = half_y - edge_d; + half_h = half_z - edge_d; + + half_cube_leng = size / 2; + half_leng = half_cube_leng - edge_d; + + corners = [ + for(z = [1, -1]) + for(y = [1, -1]) + for(x = [1, -1]) + [half_l * x, half_w * y, half_h * z] + ]; + + module corner(i) { + translate(corners[i]) + sphere(corner_r, $fn = corner_frags); + } + + center_pts = center ? [0, 0, 0] : [half_x, half_y, half_z]; + + // Don't use `hull() for(...) {...}` because it's slow. + translate(center_pts) hull() { + corner(0); + corner(1); + corner(2); + corner(3); + corner(4); + corner(5); + corner(6); + corner(7); + } + + // hook for testing + test_rounded_edge_corner_center(corner_frags, corners, center_pts); +} + +// override it to test +module test_rounded_edge_corner_center(corner_frags, corners, center_pts) { + +} + +function __edge_r_begin(orig_r, a, a_step, m) = + let(leng = orig_r * cos(a_step / 2)) + leng / cos((m - 0.5) * a_step - a); + +function __edge_r_end(orig_r, a, a_step, n) = + let(leng = orig_r * cos(a_step / 2)) + leng / cos((n + 0.5) * a_step - a); + +/** +* voronoi3d.scad +* +* @copyright Justin Lin, 2019 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-voronoi3d.html +* +**/ + + +// slow but workable + +module voronoi3d(points, space_size = "auto", spacing = 1) { + xs = [for(p = points) p[0]]; + ys = [for(p = points) abs(p[1])]; + zs = [for(p = points) abs(p[2])]; + + space_size = max([max(xs) - min(xs), max(ys) - min(ys), max(zs) - min(zs)]); + half_space_size = 0.5 * space_size; + offset_leng = spacing * 0.5 + half_space_size; + + function normalize(v) = v / norm(v); + + module space(pt) { + intersection_for(p = points) { + if(pt != p) { + v = p - pt; + ryz = __angy_angz(p, pt); + + translate((pt + p) / 2 - normalize(v) * offset_leng) + rotate([0, -ryz[0], ryz[1]]) + cube([space_size, space_size * 2, space_size * 2], center = true); + } + } + } + + for(p = points) { + space(p); + } +} + +/** +* torus_knot.scad +* +* @copyright Justin Lin, 2019 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-torus_knot.html +* +**/ + +function torus_knot(p, q, phi_step) = + let(tau = PI * 2) + [ + for(phi = 0; phi < tau; phi = phi + phi_step) + let( + degree = phi * 180 / PI, + r = cos(q * degree) + 2, + x = r * cos(p * degree), + y = r * sin(p * degree), + z = -sin(q * degree) + ) + [x, y, z] + ]; + +/** +* m_rotation.scad +* +* @copyright Justin Lin, 2019 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-m_rotation.html +* +**/ + + +function m_rotation(a, v) = __m_rotation(a, v); + +function __nearest_multiple_of_4(n) = + let( + remain = n % 4 + ) + (remain / 4) > 0.5 ? n - remain + 4 : n - remain; + + +/** +* shape_cyclicpolygon.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-shape_cyclicpolygon.html +* +**/ + + +function shape_cyclicpolygon(sides, circle_r, corner_r) = + let( + frag_a = 360 / sides, + corner_a = (180 - frag_a), + corner_circle_a = 180 - corner_a, + half_corner_circle_a = corner_circle_a / 2, + corner_circle_center = circle_r - corner_r / sin(corner_a / 2), + first_corner = [ + for( + pt = __pie_for_rounding( + corner_r, + -half_corner_circle_a, + half_corner_circle_a, + __frags(corner_r) * corner_circle_a / 360 + ) + ) + [pt[0] + corner_circle_center, pt[1]] + ] + + ) + concat( + first_corner, + [ + for(side = 1; side < sides; side = side + 1) + for(pt = first_corner) + let( + a = frag_a * side, + x = pt[0], + y = pt[1], + sina = sin(a), + cosa = cos(a) + ) + [ + x * cosa - y * sina, + x * sina + y * cosa + ] + ] + ); /** * shape_star.scad @@ -2561,21 +3636,51 @@ function __outer_points_shape_starburst(r1, r2, n) = let( a = 360 / n ) - [for(i = [0:n-1]) [r1 * cos(a * i), r1 * sin(a * i)]]; + [for(i = 0; i < n; i = i + 1) [r1 * cos(a * i), r1 * sin(a * i)]]; + function __inner_points_shape_starburst(r1, r2, n) = let ( a = 360 / n, half_a = a / 2 ) - [for(i = [0:n-1]) [r2 * cos(a * i + half_a), r2 * sin(a * i + half_a)]]; + [for(i = 0; i < n; i = i + 1) [r2 * cos(a * i + half_a), r2 * sin(a * i + half_a)]]; -function __one_by_one_shape_starburst(outer_points, inner_points, i = 0) = - len(outer_points) == i ? [] : - concat([outer_points[i], inner_points[i]], __one_by_one_shape_starburst(outer_points, inner_points, i + 1)); +function shape_starburst(r1, r2, n) = + let( + outer_points = __outer_points_shape_starburst(r1, r2, n), + inner_points = __inner_points_shape_starburst(r1, r2, n), + leng = len(outer_points) + ) + [for(i = 0; i < leng; i = i + 1) each [outer_points[i], inner_points[i]]]; -function shape_starburst(r1, r2, n) = __one_by_one_shape_starburst( - __outer_points_shape_starburst(r1, r2, n), __inner_points_shape_starburst(r1, r2, n) -); +function __to2d(p) = [p[0], p[1]]; + +/** +* m_mirror.scad +* +* @copyright Justin Lin, 2019 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-m_mirror.html +* +**/ + +function m_mirror(v) = + let( + nv = v / norm(v), + txx = -2* nv[0] * nv[0], + txy = -2* nv[0] * nv[1], + txz = -2* nv[0] * nv[2], + tyy = -2* nv[1] * nv[1], + tyz = -2* nv[1] * nv[2], + tzz = -2* nv[2] * nv[2] + ) + [ + [1 + txx, txy, txz, 0], + [txy, 1 + tyy, tyz, 0], + [txz, tyz, 1 + tzz, 0], + [0, 0, 0, 1] + ]; /** * line3d.scad @@ -2653,572 +3758,92 @@ module test_line3d_cap(p, r, frags, cap_leng, angles) { } -/** -* golden_spiral.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-golden_spiral.html -* -**/ - -function _fast_fibonacci_sub(nth) = +function __pie_for_rounding(r, begin_a, end_a, frags) = let( - _f = _fast_fibonacci_2_elems(floor(nth / 2)), - a = _f[0], - b = _f[1], - c = a * (b * 2 - a), - d = a * a + b * b - ) - nth % 2 == 0 ? [c, d] : [d, c + d]; - -function _fast_fibonacci_2_elems(nth) = - nth == 0 ? [0, 1] : _fast_fibonacci_sub(nth); - -function _fast_fibonacci(nth) = - _fast_fibonacci_2_elems(nth)[0]; - -function _remove_same_pts(pts1, pts2) = - pts1[len(pts1) - 1] == pts2[0] ? - concat(pts1, [for(i = [1:len(pts2) - 1]) pts2[i]]) : - concat(pts1, pts2); - -function _golden_spiral_from_ls_or_eql_to(from, to, point_distance, rt_dir) = - let( - f1 = _fast_fibonacci(from), - f2 = _fast_fibonacci(from + 1), - fn = floor(f1 * 6.28312 / point_distance), - $fn = fn + 4 - (fn % 4), - circle_pts = circle_path(radius = f1, n = $fn / 4 + 1), - len_pts = len(circle_pts), - a_step = 360 / $fn * rt_dir, - arc_points_angles = (rt_dir == 1 ? [ - for(i = [0:len_pts - 1]) - [circle_pts[i], a_step * i] - ] : [ - for(i = [0:len_pts - 1]) let(idx = len_pts - i - 1) - [circle_pts[idx], a_step * i] - ]), - offset = f2 - f1 - ) _remove_same_pts( - arc_points_angles, - [ - for(pt_a = _golden_spiral(from + 1, to, point_distance, rt_dir)) - [ - rotate_p(pt_a[0], [0, 0, 90 * rt_dir]) + - (rt_dir == 1 ? [0, -offset, 0] : [-offset, 0, 0]), - pt_a[1] + 90 * rt_dir - ] - ] - ); - -function _golden_spiral(from, to, point_distance, rt_dir) = - from <= to ? - _golden_spiral_from_ls_or_eql_to(from, to, point_distance, rt_dir) : []; - -function golden_spiral(from, to, point_distance, rt_dir = "CT_CLK") = - _golden_spiral(from, to, point_distance, (rt_dir == "CT_CLK" ? 1 : -1)); - -/** -* m_cumulate.scad -* -* @copyright Justin Lin, 2019 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-m_cumulate.html -* -**/ - -function _m_cumulate(matrice, i) = - i == len(matrice) - 2 ? - matrice[i] * matrice[i + 1] : - matrice[i] * _m_cumulate(matrice, i + 1); - -function m_cumulate(matrice) = - len(matrice) == 1 ? matrice[0] : _m_cumulate(matrice, 0); - - - -/** -* voronoi3d.scad -* -* @copyright Justin Lin, 2019 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-voronoi3d.html -* -**/ - - -// slow but workable - -module voronoi3d(points, space_size = "auto", spacing = 1) { - xs = [for(p = points) p[0]]; - ys = [for(p = points) abs(p[1])]; - zs = [for(p = points) abs(p[2])]; - - space_size = max([max(xs) - min(xs), max(ys) - min(ys), max(zs) - min(zs)]); - half_space_size = 0.5 * space_size; - offset_leng = spacing * 0.5 + half_space_size; - - function normalize(v) = v / norm(v); - - module space(pt) { - intersection_for(p = points) { - if(pt != p) { - v = p - pt; - ryz = __angy_angz(p, pt); - - translate((pt + p) / 2 - normalize(v) * offset_leng) - rotate([0, -ryz[0], ryz[1]]) - cube([space_size, space_size * 2, space_size * 2], center = true); - } - } - } - - for(p = points) { - space(p); - } -} - -/** -* crystal_ball.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-crystal_ball.html -* -**/ - - -module crystal_ball(radius, theta = 360, phi = 180) { - phis = __is_float(phi) ? [0, phi] : phi; - - frags = __frags(radius); - - shape_pts = shape_pie( - radius, - [90 - phis[1], 90 - phis[0]], - $fn = __nearest_multiple_of_4(frags) + sector_angle = end_a - begin_a, + step_a = sector_angle / frags, + is_integer = frags % 1 == 0 + ) + r < 0.00005 ? [[0, 0]] : concat([ + for(ang = begin_a; ang <= end_a; ang = ang + step_a) + [ + r * cos(ang), + r * sin(ang) + ] + ], + is_integer ? [] : [[ + r * cos(end_a), + r * sin(end_a) + ]] ); - // _hole_r = 0.0005 for avoiding warnings when using 2015.03 - // I downloaded 2017.01.20 and found that the problem is solved. - _hole_r = version_num() >= 20170120 ? 0 : 0.0005; - ring_extrude( - shape_pts, - angle = theta, - radius = _hole_r, - $fn = frags - ); +function __angy_angz(p1, p2) = + let( + dx = p2[0] - p1[0], + dy = p2[1] - p1[1], + dz = p2[2] - p1[2], + ya = atan2(dz, sqrt(dx * dx + dy * dy)), + za = atan2(dy, dx) + ) [ya, za]; - // hook for testing - test_crystal_ball_pie(shape_pts); -} +function __tr__corner_t_leng_lt_zero(frags, t_sector_angle, l1, l2, h, round_r) = + let(t_height = tan(t_sector_angle) * l1 - round_r / sin(90 - t_sector_angle) - h / 2) + [ + for(pt = __pie_for_rounding(round_r, 90 - t_sector_angle, 90, frags * t_sector_angle / 180)) + [pt[0], pt[1] + t_height] + ]; -// override it to test -module test_crystal_ball_pie(shape_pts) { - -} - -/** -* rounded_extrude.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-rounded_extrude.html -* -**/ - - -module rounded_extrude(size, round_r, angle = 90, twist = 0, convexity = 10) { - - is_flt = __is_float(size); - x = is_flt ? size : size[0]; - y = is_flt ? size : size[1]; - - q_corner_frags = __frags(round_r) / 4; - - step_a = angle / q_corner_frags; - twist_step = twist / q_corner_frags; - - module layers(pre_x, pre_y, pre_h = 0, i = 1) { - module one_layer(current_a) { - wx = pre_x; - wy = pre_y; - - h = (round_r - pre_h) - round_r * cos(current_a); - - d_leng = - round_r * (sin(current_a) - sin(step_a * (i - 1))); - - sx = (d_leng * 2 + wx) / wx; - sy = (d_leng * 2 + wy) / wy; - - translate([0, 0, pre_h]) - rotate(-twist_step * (i - 1)) - linear_extrude( - h, - slices = 1, - scale = [sx, sy], - convexity = convexity, - twist = twist_step - ) scale([wx / x, wy / y]) - children(); - - test_rounded_extrude_data(i, wx, wy, pre_h, sx, sy); - - layers(wx * sx, wy * sy, h + pre_h, i + 1) - children(); - - } - - if(i <= q_corner_frags) { - one_layer(i * step_a) - children(); - } else if(i - q_corner_frags < 1) { - one_layer(q_corner_frags * step_a) - children(); - } - } - - layers(x, y) - children(); -} - -module test_rounded_extrude_data(i, wx, wy, pre_h, sx, sy) { - -} - -/** -* along_with.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-along_with.html -* -**/ - - -// Becuase of improving the performance, this module requires m_rotation.scad which doesn't require in dotSCAD 1.0. -// For backward compatibility, I directly include m_rotation here. - -module along_with(points, angles, twist = 0, scale = 1.0, method = "AXIS_ANGLE") { - leng_points = len(points); - leng_points_minus_one = leng_points - 1; - twist_step_a = twist / leng_points; - - angles_defined = angles != undef; - - scale_step_vt = __is_float(scale) ? - scale_step() : - [ - (scale[0] - 1) / leng_points_minus_one, - (scale[1] - 1) / leng_points_minus_one, - scale[2] == undef ? 0 : (scale[2] - 1) / leng_points_minus_one - ]; - - - function scale_step() = - let(s = (scale - 1) / leng_points_minus_one) - [s, s, s]; - - - /* - Sadly, children(n) cannot be used with inner modules - so I have to do things in the first level. Ugly!! - */ - - // >>> begin: modules and functions for "AXIS-ANGLE" - - // get rotation matrice for sections - identity_matrix = [ - [1, 0, 0, 0], - [0, 1, 0, 0], - [0, 0, 1, 0], - [0, 0, 0, 1] +function __tr_corner_t_leng_gt_or_eq_zero(frags, t_sector_angle, t_leng, h, round_r) = + let(offset_y = h / 2 - round_r) + [ + for(pt = __pie_for_rounding(round_r, 90 - t_sector_angle, 90, frags * t_sector_angle / 360)) + [pt[0] + t_leng, pt[1] + offset_y] ]; - function axis_angle_local_ang_vects(j) = - j == 0 ? [] : axis_angle_local_ang_vects_sub(j); - - function axis_angle_local_ang_vects_sub(j) = - let( - vt0 = points[j] - points[j - 1], - vt1 = points[j + 1] - points[j], - a = acos((vt0 * vt1) / (norm(vt0) * norm(vt1))), - v = cross(vt0, vt1) - ) - concat([[a, v]], axis_angle_local_ang_vects(j - 1)); +function __tr_corner(frags, b_ang, l1, l2, h, round_r) = + let(t_leng = l2 - round_r * tan(b_ang / 2)) + t_leng >= 0 ? + __tr_corner_t_leng_gt_or_eq_zero(frags, b_ang, t_leng, h, round_r) : + __tr__corner_t_leng_lt_zero(frags, b_ang, l1, l2, h, round_r); - function axis_angle_cumulated_rot_matrice(i, rot_matrice) = - let( - leng_rot_matrice = len(rot_matrice), - leng_rot_matrice_minus_one = leng_rot_matrice - 1, - leng_rot_matrice_minus_two = leng_rot_matrice - 2 - ) - leng_rot_matrice == 0 ? [identity_matrix] : ( - leng_rot_matrice == 1 ? [rot_matrice[0], identity_matrix] : ( - i == leng_rot_matrice_minus_two ? - [ - rot_matrice[leng_rot_matrice_minus_one], - rot_matrice[leng_rot_matrice_minus_two] * rot_matrice[leng_rot_matrice_minus_one] - ] - : axis_angle_cumulated_rot_matrice_sub(i, rot_matrice) - ) - ); +function __tr__corner_b_leng_lt_zero(frags, b_sector_angle, l1, l2, h, round_r) = + let( + reversed = __tr__corner_t_leng_lt_zero(frags, b_sector_angle, l2, l1, h, round_r), + leng = len(reversed) + ) + [ + for(i = [0:leng - 1]) + let(pt = reversed[leng - 1 - i]) + [pt[0], -pt[1]] + ]; - function axis_angle_cumulated_rot_matrice_sub(i, rot_matrice) = - let( - matrice = axis_angle_cumulated_rot_matrice(i + 1, rot_matrice), - curr_matrix = rot_matrice[i], - prev_matrix = matrice[len(matrice) - 1] - ) - concat(matrice, [curr_matrix * prev_matrix]); +function __br_corner_b_leng_gt_or_eq_zero(frags, b_sector_angle, l1, l2, b_leng, h, round_r) = + let(half_h = h / 2) + [ + for(pt = __pie_for_rounding(round_r, -90, -90 + b_sector_angle, frags * b_sector_angle / 360)) + [pt[0] + b_leng, pt[1] + round_r - half_h] + ]; - // align modules +function __br_corner(frags, b_ang, l1, l2, h, round_r) = + let(b_leng = l1 - round_r / tan(b_ang / 2)) + b_leng >= 0 ? + __br_corner_b_leng_gt_or_eq_zero(frags, 180 - b_ang, l1, l2, b_leng, h, round_r) : + __tr__corner_b_leng_lt_zero(frags, 180 - b_ang, l1, l2, h, round_r); - module axis_angle_align_with_pts_angles(i) { - translate(points[i]) - rotate(angles[i]) - rotate(twist_step_a * i) - scale([1, 1, 1] + scale_step_vt * i) - children(0); - } - - module axis_angle_align_with_pts_init(a, s) { - angleyz = __angy_angz(__to3d(points[0]), __to3d(points[1])); - - rotate([0, -angleyz[0], angleyz[1]]) - rotate([90, 0, -90]) - rotate(a) - scale(s) - children(0); - } - - module axis_angle_align_with_pts_local_rotate(j, init_a, init_s, cumu_rot_matrice) { - if(j == 0) { // first child - axis_angle_align_with_pts_init(init_a, init_s) - children(0); - } - else { - multmatrix(cumu_rot_matrice[j - 1]) - axis_angle_align_with_pts_init(init_a, init_s) - children(0); - } - } - - // <<< end: modules and functions for "AXIS-ANGLE" - - - // >>> begin: modules and functions for "EULER-ANGLE" - - function _euler_angle_path_angles(pts, end_i, i = 0) = - i == end_i ? - [] : - concat( - [__angy_angz(pts[i], pts[i + 1])], - _euler_angle_path_angles(pts, end_i, i + 1) - ); - - function euler_angle_path_angles(children) = - let( - pts = len(points[0]) == 3 ? points : [for(pt = points) __to3d(pt)], - end_i = children == 1 ? leng_points_minus_one : children - 1, - angs = _euler_angle_path_angles(pts, end_i) - ) - concat( - [[0, -angs[0][0], angs[0][1]]], - [for(a = angs) [0, -a[0], a[1]]] - ); - - module euler_angle_align(i, angs) { - translate(points[i]) - rotate(angs[i]) - rotate(angles_defined ? [0, 0, 0] : [90, 0, -90]) - rotate(twist_step_a * i) - scale([1, 1, 1] + scale_step_vt * i) - children(0); - } - - // <<< end: modules and functions for "EULER-ANGLE" - - if(method == "AXIS_ANGLE") { - if(angles_defined) { - if($children == 1) { - for(i = [0:leng_points_minus_one]) { - axis_angle_align_with_pts_angles(i) children(0); - } - } else { - for(i = [0:min(leng_points, $children) - 1]) { - axis_angle_align_with_pts_angles(i) children(i); - } - } - } - else { - cumu_rot_matrice = axis_angle_cumulated_rot_matrice(0, [ - for(ang_vect = axis_angle_local_ang_vects(leng_points - 2)) - m_rotation(ang_vect[0], ang_vect[1]) - ]); - - translate(points[0]) - axis_angle_align_with_pts_local_rotate(0, 0, [1, 1, 1], cumu_rot_matrice) - children(0); - - if($children == 1) { - for(i = [0:leng_points - 2]) { - translate(points[i + 1]) - axis_angle_align_with_pts_local_rotate(i, i * twist_step_a, [1, 1, 1] + scale_step_vt * i, cumu_rot_matrice) - children(0); - } - } else { - for(i = [0:min(leng_points, $children) - 2]) { - translate(points[i + 1]) - axis_angle_align_with_pts_local_rotate(i, i * twist_step_a, [1, 1, 1] + scale_step_vt * i, cumu_rot_matrice) - children(i + 1); - } - } - } - } - else if(method == "EULER_ANGLE") { - angs = angles_defined ? angles : euler_angle_path_angles($children); - - if($children == 1) { - for(i = [0:leng_points_minus_one]) { - euler_angle_align(i, angs) children(0); - } - - } else { - for(i = [0:min(leng_points, $children) - 1]) { - euler_angle_align(i, angs) children(i); - } - } - } -} - -/** -* stereographic_extrude.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-stereographic_extrude.html -* -**/ - -module stereographic_extrude(shadow_side_leng) { - half_side_length = shadow_side_leng / 2; - outer_sphere_r = half_side_length / 3; - a = atan(sqrt(2) * half_side_length / (2 * outer_sphere_r)); - inner_sphere_r = outer_sphere_r * sin(a); - - intersection() { - translate([0, 0, outer_sphere_r]) difference() { - sphere(outer_sphere_r); - sphere(outer_sphere_r / 2 + inner_sphere_r / 2); - - translate([0, 0, outer_sphere_r / 2]) - linear_extrude(outer_sphere_r) - circle(inner_sphere_r * cos(a)); - } - - linear_extrude(outer_sphere_r * 2, scale = 0.01) - children(); - } - - // hook for testing - test_stereographic_extrude_rs(outer_sphere_r, inner_sphere_r); -} - -// override for testing -module test_stereographic_extrude_rs(outer_sphere_r, inner_sphere_r) { - -} - -/** -* sub_str.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-sub_str.html -* -**/ - -function _sub_str(t, begin, end) = - begin == end ? "" : str(t[begin], sub_str(t, begin + 1, end)); - -function sub_str(t, begin, end) = - end == undef ? _sub_str(t, begin, len(t)) : _sub_str(t, begin, end); - - -/** -* hollow_out.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-hollow_out.html -* -**/ - -module hollow_out(shell_thickness) { - difference() { - children(); - offset(delta = -shell_thickness) children(); - } -} - -/** -* voronoi2d.scad -* -* @copyright Justin Lin, 2019 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-voronoi2d.html -* -**/ - -module voronoi2d(points, spacing = 1, r = 0, delta = 0, chamfer = false, region_type = "square") { - xs = [for(p = points) p[0]]; - ys = [for(p = points) abs(p[1])]; - - region_size = max([(max(xs) - min(xs) / 2), (max(ys) - min(ys)) / 2]); - half_region_size = 0.5 * region_size; - offset_leng = spacing * 0.5 + half_region_size; - - function normalize(v) = v / norm(v); - - module region(pt) { - intersection_for(p = points) { - if(pt != p) { - v = p - pt; - translate((pt + p) / 2 - normalize(v) * offset_leng) - rotate(atan2(v[1], v[0])) - if(region_type == "square") { - square(region_size, center = true); - } - else if(region_type == "circle") { - circle(region_size / 2); - } - - } - } - } - - for(p = points) { - if(r != 0) { - offset(r) region(p); - } - else { - offset(delta = delta, chamfer = chamfer) region(p); - } - } -} +function __half_trapezium(length, h, round_r) = + let( + is_flt = is_num(length), + l1 = is_flt ? length : length[0], + l2 = is_flt ? length : length[1], + frags = __frags(round_r), + b_ang = atan2(h, l1 - l2), + br_corner = __br_corner(frags, b_ang, l1, l2, h, round_r), + tr_corner = __tr_corner(frags, b_ang, l1, l2, h, round_r) + ) + concat( + br_corner, + tr_corner + ); /** * sphere_spiral_extrude.scad @@ -3269,56 +3894,68 @@ module test_sphere_spiral_extrude(sections) { } /** -* rounded_cylinder.scad +* m_scaling.scad * -* @copyright Justin Lin, 2017 +* @copyright Justin Lin, 2019 * @license https://opensource.org/licenses/lgpl-3.0.html * -* @see https://openhome.cc/eGossip/OpenSCAD/lib-rounded_cylinder.html +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-m_scaling.html * **/ -module rounded_cylinder(radius, h, round_r, convexity = 2, center = false) { - r_corners = __half_trapezium(radius, h, round_r); - - shape_pts = concat( - [[0, -h/2]], - r_corners, - [[0, h/2]] - ); +function m_scaling(s) = __m_scaling(s); - center_pt = center ? [0, 0, 0] : [0, 0, h/2]; +/** +* shape_pentagram.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-shape_ellipse.html +* +**/ - translate(center ? [0, 0, 0] : [0, 0, h/2]) - rotate(180) - rotate_extrude(convexity = convexity) - polygon(shape_pts); +function shape_pentagram(r) = + [ + [0, 1], [-0.224514, 0.309017], + [-0.951057, 0.309017], [-0.363271, -0.118034], + [-0.587785, -0.809017], [0, -0.381966], + [0.587785, -0.809017], [0.363271, -0.118034], + [0.951057, 0.309017], [0.224514, 0.309017] + ] * r; - // hook for testing - test_center_half_trapezium(center_pt, shape_pts); -} - -// override it to test -module test_center_half_trapezium(center_pt, shape_pts) { - -} - - -function __trapezium(length, h, round_r) = +function __shape_arc(radius, angle, width, width_mode = "LINE_CROSS") = let( - r_half_trapezium = __half_trapezium(length / 2, h, round_r), - to = len(r_half_trapezium) - 1, - l_half_trapezium = [ - for(i = [0:to]) - let(pt = r_half_trapezium[to - i]) - [-pt[0], pt[1]] - ] - ) - concat( - r_half_trapezium, - l_half_trapezium - ); + w_offset = width_mode == "LINE_CROSS" ? [width / 2, -width / 2] : ( + width_mode == "LINE_INWARD" ? [0, -width] : [width, 0] + ), + frags = __frags(radius), + a_step = 360 / frags, + half_a_step = a_step / 2, + angles = is_num(angle) ? [0, angle] : angle, + m = floor(angles[0] / a_step) + 1, + n = floor(angles[1] / a_step), + r_outer = radius + w_offset[0], + r_inner = radius + w_offset[1], + points = concat( + // outer arc path + [__ra_to_xy(__edge_r_begin(r_outer, angles[0], a_step, m), angles[0])], + m > n ? [] : [ + for(i = m; i <= n; i = i + 1) __ra_to_xy(r_outer, a_step * i) + ], + angles[1] == a_step * n ? [] : [__ra_to_xy(__edge_r_end(r_outer, angles[1], a_step, n), angles[1])], + // inner arc path + angles[1] == a_step * n ? [] : [__ra_to_xy(__edge_r_end(r_inner, angles[1], a_step, n), angles[1])], + m > n ? [] : [ + for(i = m; i <= n; i = i + 1) + let(idx = (n + (m - i))) + __ra_to_xy(r_inner, a_step * idx) + + ], + [__ra_to_xy(__edge_r_begin(r_inner, angles[0], a_step, m), angles[0])] + ) + ) points; /** * path_scaling_sections.scad @@ -3338,11 +3975,12 @@ function path_scaling_sections(shape_pts, edge_path) = scaling_matrice = [ for(p = edge_path) let(s = norm([p[0], p[1], 0]) / base_leng) - m_scaling([s, s, 1]) - ] + __m_scaling([s, s, 1]) + ], + leng_edge_path = len(edge_path) ) __reverse([ - for(i = [0:len(edge_path) - 1]) + for(i = 0; i < leng_edge_path; i = i + 1) [ for(p = shape_pts) let(scaled_p = scaling_matrice[i] * [p[0], p[1], edge_path[i][2], 1]) @@ -3350,76 +3988,352 @@ function path_scaling_sections(shape_pts, edge_path) = ] ]); -function __to_degree(phi) = 180 / 3.14159 * phi; +/** +* m_shearing.scad +* +* @copyright Justin Lin, 2019 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-m_shearing.html +* +**/ + + +function m_shearing(sx = [0, 0], sy = [0, 0], sz = [0, 0]) = __m_shearing(sx, sy, sz); + +function __line_intersection(line_pts1, line_pts2, epsilon = 0.0001) = + let( + a1 = line_pts1[0], + a2 = line_pts1[1], + b1 = line_pts2[0], + b2 = line_pts2[1], + a = a2 - a1, + b = b2 - b1, + s = b1 - a1 + ) + abs(cross(a, b)) < epsilon ? [] : // they are parallel or conincident edges + a1 + a * cross(s, b) / cross(a, b); /** -* bezier_smooth.scad +* px_sphere.scad +* +* @copyright Justin Lin, 2019 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-px_sphere.html +* +**/ + +function px_sphere(radius, filled = false, thickness = 1) = + let(range = [-radius: radius - 1]) + filled ? [ + for(z = range) + for(y = range) + for(x = range) + let(v = [x, y, z]) + if(norm(v) < radius) v + ] : + let(ishell = radius * radius - 2 * thickness * radius) + [ + for(z = range) + for(y = range) + for(x = range) + let( + v = [x, y, z], + leng = norm(v) + ) + if(leng < radius && (leng * leng) > ishell) v + ]; + + +/** +* in_shape.scad +* +* @copyright Justin Lin, 2019 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-in_shape.html +* +**/ + + +function _in_shape_in_line_equation(edge, pt) = + let( + x1 = edge[0][0], + y1 = edge[0][1], + x2 = edge[1][0], + y2 = edge[1][1], + a = (y2 - y1) / (x2 - x1), + b = y1 - a * x1 + ) + (pt[1] == a * pt[0] + b); + +function _in_shape_in_any_edges(edges, pt, epsilon) = + let( + leng = len(edges), + maybe_last = [for(i = 0; i < leng && !__in_line(edges[i], pt, epsilon); i = i + 1) i][leng - 1] + ) + is_undef(maybe_last); + +function _in_shape_interpolate_x(y, p1, p2) = + p1[1] == p2[1] ? p1[0] : ( + p1[0] + (p2[0] - p1[0]) * (y - p1[1]) / (p2[1] - p1[1]) + ); + +function _in_shape_does_pt_cross(pts, i, j, pt) = + ((pts[i][1] > pt[1]) != (pts[j][1] > pt[1])) && + (pt[0] < _in_shape_interpolate_x(pt[1], pts[i], pts[j])); + + +function _in_shape_sub(shapt_pts, leng, pt, cond, i, j) = + j == leng ? cond : ( + _in_shape_does_pt_cross(shapt_pts, i, j, pt) ? + _in_shape_sub(shapt_pts, leng, pt, !cond, j, j + 1) : + _in_shape_sub(shapt_pts, leng, pt, cond, j, j + 1) + ); + +function in_shape(shapt_pts, pt, include_edge = false, epsilon = 0.0001) = + let( + leng = len(shapt_pts), + edges = __lines_from(shapt_pts, true) + ) + _in_shape_in_any_edges(edges, pt, epsilon) ? include_edge : + _in_shape_sub(shapt_pts, leng, pt, false, leng - 1, 0); + +/** +* sphere_spiral.scad * * @copyright Justin Lin, 2017 * @license https://opensource.org/licenses/lgpl-3.0.html * -* @see https://openhome.cc/eGossip/OpenSCAD/lib-bezier_curve.html +* @see https://openhome.cc/eGossip/OpenSCAD/lib-sphere_spiral.html +* +**/ + +function sphere_spiral(radius, za_step, z_circles = 1, begin_angle = 0, end_angle = 0, vt_dir = "SPI_DOWN", rt_dir = "CT_CLK") = + let( + a_end = 90 * z_circles - end_angle + ) + [ + for(a = begin_angle; a <= a_end; a = a + za_step) + let( + ya = vt_dir == "SPI_DOWN" ? (-90 + 2 * a / z_circles) : (90 + 2 * a / z_circles), + za = (rt_dir == "CT_CLK" ? 1 : -1) * a, + ra = [0, ya, za] + ) + [rotate_p([radius, 0, 0], ra), ra] + ]; + +function __shape_pie(radius, angle) = + let( + frags = __frags(radius), + a_step = 360 / frags, + leng = radius * cos(a_step / 2), + angles = is_num(angle) ? [0:angle] : angle, + m = floor(angles[0] / a_step) + 1, + n = floor(angles[1] / a_step), + edge_r_begin = leng / cos((m - 0.5) * a_step - angles[0]), + edge_r_end = leng / cos((n + 0.5) * a_step - angles[1]), + shape_pts = concat( + [[0, 0], __ra_to_xy(edge_r_begin, angles[0])], + m > n ? [] : [ + for(i = m; i <= n; i = i + 1) + let(a = a_step * i) + __ra_to_xy(radius, a) + ], + angles[1] == a_step * n ? [] : [__ra_to_xy(edge_r_end, angles[1])] + ) + ) shape_pts; + +/** +* bijection_offset.scad +* +* @copyright Justin Lin, 2019 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-bijection_offset.html +* +**/ + + +function _bijection_inward_edge_normal(edge) = + let( + pt1 = edge[0], + pt2 = edge[1], + dx = pt2[0] - pt1[0], + dy = pt2[1] - pt1[1], + edge_leng = norm([dx, dy]) + ) + [-dy / edge_leng, dx / edge_leng]; + +function _bijection_outward_edge_normal(edge) = -1 * _bijection_inward_edge_normal(edge); + +function _bijection_offset_edge(edge, dx, dy) = + let( + pt1 = edge[0], + pt2 = edge[1], + dxy = [dx, dy] + ) + [pt1 + dxy, pt2 + dxy]; + +function _bijection__bijection_offset_edges(edges, d) = + [ + for(edge = edges) + let( + ow_normal = _bijection_outward_edge_normal(edge), + dx = ow_normal[0] * d, + dy = ow_normal[1] * d + ) + _bijection_offset_edge(edge, dx, dy) + ]; + +function bijection_offset(pts, d, epsilon = 0.0001) = + let( + es = __lines_from(pts, true), + offset_es = _bijection__bijection_offset_edges(es, d), + leng = len(offset_es), + last_p = __line_intersection(offset_es[leng - 1], offset_es[0], epsilon) + ) + concat( + [ + for(i = 0; i < leng - 1; i = i + 1) + let( + this_edge = offset_es[i], + next_edge = offset_es[i + 1], + p = __line_intersection(this_edge, next_edge, epsilon) + ) + // p == p to avoid [nan, nan], because [nan, nan] != [nan, nan] + if(p != [] && p == p) p + ], + last_p != [] && last_p == last_p ? [last_p] : [] + ); + + +/** +* arc_shape.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-arc_path.html * **/ -function _corner_ctrl_pts(round_d, p1, p2, p3) = +function arc_path(radius, angle) = let( - _ya_za_1 = __angy_angz(p1, p2), - _ya_za_2 = __angy_angz(p3, p2), - - dz1 = sin(_ya_za_1[0]) * round_d, - dxy1 = cos(_ya_za_1[0]) * round_d, - dy1 = sin(_ya_za_1[1]) * dxy1, - dx1 = cos(_ya_za_1[1]) * dxy1, - - dz2 = sin(_ya_za_2[0]) * round_d, - dxy2 = cos(_ya_za_2[0]) * round_d, - dy2 = sin(_ya_za_2[1]) * dxy2, - dx2 = cos(_ya_za_2[1]) * dxy2 + frags = __frags(radius), + a_step = 360 / frags, + angles = is_num(angle) ? [0, angle] : angle, + m = floor(angles[0] / a_step) + 1, + n = floor(angles[1] / a_step), + points = concat([__ra_to_xy(__edge_r_begin(radius, angles[0], a_step, m), angles[0])], + m > n ? [] : [ + for(i = m; i <= n; i = i + 1) + __ra_to_xy(radius, a_step * i) + ], + angles[1] == a_step * n ? [] : [__ra_to_xy(__edge_r_end(radius, angles[1], a_step, n), angles[1])]) + ) points; + +/** +* helix_extrude.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-helix_extrude.html +* +**/ + + +module helix_extrude(shape_pts, radius, levels, level_dist, + vt_dir = "SPI_DOWN", rt_dir = "CT_CLK", + twist = 0, scale = 1.0, triangles = "SOLID") { + + function reverse(vt) = + let(leng = len(vt)) + [ + for(i = 0; i < leng; i = i + 1) + vt[leng - 1 - i] + ]; + + is_flt = is_num(radius); + r1 = is_flt ? radius : radius[0]; + r2 = is_flt ? radius : radius[1]; + + init_r = vt_dir == "SPI_DOWN" ? r2 : r1; + + frags = __frags(init_r); + + v_dir = vt_dir == "SPI_UP" ? 1 : -1; + r_dir = rt_dir == "CT_CLK" ? 1 : -1; + + angle_step = 360 / frags * r_dir; + initial_angle = atan2(level_dist / frags, PI * 2 * init_r / frags) * v_dir * r_dir; + + path_points = helix( + radius = radius, + levels = levels, + level_dist = level_dist, + vt_dir = vt_dir, + rt_dir = rt_dir + ); + + clk_a = r_dir == 1 ? 0 : 180; + angles = [for(i = 0; i < len(path_points); i = i + 1) [90 + initial_angle, 0, clk_a + angle_step * i]]; + + sections = cross_sections(shape_pts, path_points, angles, twist, scale); + + polysections( + sections, + triangles = triangles + ); + + // hook for testing + test_helix_extrude(sections); +} + +// override it to test +module test_helix_extrude(sections) { + +} + +/** +* paths2sections.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-paths2sections.html +* +**/ + +function paths2sections(paths) = + let( + leng_path = len(paths[0]), + leng_paths = len(paths) ) [ - p2 - [dx1, dy1, dz1], - p2, - p2 - [dx2, dy2, dz2] + for(i = 0; i < leng_path; i = i + 1) + [ + for(j = 0; j < leng_paths; j = j + 1) + paths[j][i] + ] ]; - - -function _bezier_corner(round_d, t_step, p1, p2, p3) = - bezier_curve(t_step, _corner_ctrl_pts(round_d, p1, p2, p3)); -function _recursive_bezier_smooth(pts, round_d, t_step, leng, i = 0) = - i <= leng - 3 ? - concat( - _bezier_corner(round_d, t_step, pts[i], pts[i + 1], pts[i + 2]), - _recursive_bezier_smooth(pts, round_d, t_step, leng, i + 1) - ) - : []; - -function bezier_smooth(path_pts, round_d, t_step = 0.1, closed = false) = - let( - pts = len(path_pts[0]) == 3 ? path_pts : [for(p = path_pts) __to3d(p)], - leng = len(pts), - middle_pts = _recursive_bezier_smooth(pts, round_d, t_step, leng), - pth_pts = closed ? - concat( - _recursive_bezier_smooth( - [pts[leng - 1], pts[0], pts[1]], - round_d, t_step, 3 - ), - middle_pts, - _recursive_bezier_smooth( - [pts[leng - 2], pts[leng - 1], pts[0]], - round_d, t_step, 3 - ) - ) : - concat( - [pts[0]], - middle_pts, - [pts[leng - 1]] - ) - ) - len(path_pts[0]) == 2 ? [for(p = pth_pts) __to2d(p)] : pth_pts; +/** +* shape_pie.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-shape_pie.html +* +**/ + + +function shape_pie(radius, angle) = + __shape_pie(radius, angle); function __in_line(line_pts, pt, epsilon = 0.0001) = let( @@ -3430,45 +4344,56 @@ function __in_line(line_pts, pt, epsilon = 0.0001) = ) (norm(cross(v1, v2)) < epsilon) && ((v1 * v2) <= epsilon); -function __nearest_multiple_of_4(n) = - let( - remain = n % 4 - ) - (remain / 4) > 0.5 ? n - remain + 4 : n - remain; - - /** -* hull_polyline3d.scad +* pie.scad * * @copyright Justin Lin, 2017 * @license https://opensource.org/licenses/lgpl-3.0.html * -* @see https://openhome.cc/eGossip/OpenSCAD/hull_polyline3d.html +* @see https://openhome.cc/eGossip/OpenSCAD/lib-pie.html * **/ -module hull_polyline3d(points, thickness) { - half_thickness = thickness / 2; - leng = len(points); - - module hull_line3d(index) { - point1 = points[index - 1]; - point2 = points[index]; + +module pie(radius, angle) { + polygon(__shape_pie(radius, angle)); +} - hull() { - translate(point1) - sphere(half_thickness); - translate(point2) - sphere(half_thickness); - } +/** +* polyline3d.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-polyline3d.html +* +**/ + +module polyline3d(points, thickness, startingStyle = "CAP_CIRCLE", endingStyle = "CAP_CIRCLE") { + leng_pts = len(points); + + module line_segment(index) { + styles = index == 1 ? [startingStyle, "CAP_BUTT"] : ( + index == leng_pts - 1 ? ["CAP_SPHERE", endingStyle] : [ + "CAP_SPHERE", "CAP_BUTT" + ] + ); + + p1 = points[index - 1]; + p2 = points[index]; + p1Style = styles[0]; + p2Style = styles[1]; + + line3d(p1, p2, thickness, + p1Style = p1Style, p2Style = p2Style); // hook for testing - test_line_segment(index, point1, point2, half_thickness); + test_line3d_segment(index, p1, p2, thickness, p1Style, p2Style); } module polyline3d_inner(index) { - if(index < leng) { - hull_line3d(index); + if(index < leng_pts) { + line_segment(index); polyline3d_inner(index + 1); } } @@ -3477,295 +4402,280 @@ module hull_polyline3d(points, thickness) { } // override it to test -module test_line_segment(index, point1, point2, radius) { +module test_line3d_segment(index, point1, point2, thickness, p1Style, p2Style) { } /** -* ellipse_extrude.scad +* trim_shape.scad +* +* @copyright Justin Lin, 2019 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib-trim_shape.html +* +**/ + + +function _trim_shape_any_intersection_sub(lines, line, lines_leng, i, epsilon) = + let( + p = __line_intersection(lines[i], line, epsilon) + ) + (p != [] && __in_line(line, p, epsilon) && __in_line(lines[i], p, epsilon)) ? [i, p] : _trim_shape_any_intersection(lines, line, lines_leng, i + 1, epsilon); + +// return [idx, [x, y]] or [] +function _trim_shape_any_intersection(lines, line, lines_leng, i, epsilon) = + i == lines_leng ? [] : _trim_shape_any_intersection_sub(lines, line, lines_leng, i, epsilon); + +function _trim_sub(lines, leng, epsilon) = + let( + current_line = lines[0], + next_line = lines[1], + lines_from_next = [for(j = 1; j < leng; j = j + 1) lines[j]], + lines_from_next2 = [for(j = 2; j < leng; j = j + 1) lines[j]], + current_p = current_line[0], + leng_lines_from_next2 = len(lines_from_next2), + inter_p = _trim_shape_any_intersection(lines_from_next2, current_line, leng_lines_from_next2, 0, epsilon) + ) + // no intersecting pt, collect current_p and trim remain lines + inter_p == [] ? (concat([current_p], _trim_shape_trim_lines(lines_from_next, epsilon))) : ( + // collect current_p, intersecting pt and the last pt + (leng == 3 || (inter_p[0] == (leng_lines_from_next2 - 1))) ? [current_p, inter_p[1], lines[leng - 1]] : ( + // collect current_p, intersecting pt and trim remain lines + concat([current_p, inter_p[1]], + _trim_shape_trim_lines([for(i = inter_p[0] + 1; i < leng_lines_from_next2; i = i + 1) lines_from_next2[i]], epsilon) + ) + ) + ); + +function _trim_shape_trim_lines(lines, epsilon) = + let(leng = len(lines)) + leng > 2 ? _trim_sub(lines, leng, epsilon) : _trim_shape_collect_pts_from(lines, leng); + +function _trim_shape_collect_pts_from(lines, leng) = + concat([for(line = lines) line[0]], [lines[leng - 1][1]]); + +function trim_shape(shape_pts, from, to, epsilon = 0.0001) = + let( + pts = [for(i = from; i <= to; i = i + 1) shape_pts[i]], + trimmed = _trim_shape_trim_lines(__lines_from(pts), epsilon) + ) + len(shape_pts) == len(trimmed) ? trimmed : trim_shape(trimmed, 0, len(trimmed) - 1, epsilon); + + +function __to3d(p) = [p[0], p[1], 0]; + +/** +* along_with.scad * * @copyright Justin Lin, 2017 * @license https://opensource.org/licenses/lgpl-3.0.html * -* @see https://openhome.cc/eGossip/OpenSCAD/lib-ellipse_extrude.html +* @see https://openhome.cc/eGossip/OpenSCAD/lib-along_with.html * -**/ +**/ + -module ellipse_extrude(semi_minor_axis, height, center = false, convexity = 10, twist = 0, slices = 20) { - h = height == undef ? semi_minor_axis : ( - // `semi_minor_axis` is always equal to or greater than `height`. - height > semi_minor_axis ? semi_minor_axis : height - ); - angle = asin(h / semi_minor_axis) / slices; +module along_with(points, angles, twist = 0, scale = 1.0, method = "AXIS_ANGLE") { + leng_points = len(points); + leng_points_minus_one = leng_points - 1; + twist_step_a = twist / leng_points; - function f_extrude(i = 1) = - i <= slices ? - concat( - [ - [ - cos(angle * i) / cos(angle * (i - 1)), - semi_minor_axis * sin(angle * i) - ] - ], - f_extrude(i + 1) - ) : []; + angles_defined = !is_undef(angles); - fzs = f_extrude(); - len_fzs = len(fzs); - - function accm_fs(pre_f = 1, i = 0) = - i < len_fzs ? - concat( - [pre_f * fzs[i][0]], - accm_fs(pre_f * fzs[i][0], i + 1) - ) : []; - - child_fs = concat([1], accm_fs()); - pre_zs = concat( - [0], + scale_step_vt = is_num(scale) ? + let(s = (scale - 1) / leng_points_minus_one) [s, s, s] : [ - for(i = [0:len_fzs - 1]) - fzs[i][1] - ] - ); + (scale[0] - 1) / leng_points_minus_one, + (scale[1] - 1) / leng_points_minus_one, + is_undef(scale[2]) ? 0 : (scale[2] - 1) / leng_points_minus_one + ]; - module extrude() { - for(i = [0:len_fzs - 1]) { - f = fzs[i][0]; - z = fzs[i][1]; + /* + Sadly, children(n) cannot be used with inner modules + so I have to do things in the first level. Ugly!! + */ - translate([0, 0, pre_zs[i]]) - rotate(-twist / slices * i) - linear_extrude( - z - pre_zs[i], - convexity = convexity, - twist = twist / slices, - slices = 1, - scale = f - ) scale(child_fs[i]) children(); - } - } - - center_offset = [0, 0, center == true ? -h / 2 : 0]; - translate(center_offset) - extrude() - children(); + // >>> begin: modules and functions for "AXIS-ANGLE" - // hook for testing - test_ellipse_extrude_fzc(child_fs, pre_zs, center_offset); -} - -// override for testing -module test_ellipse_extrude_fzc(child_fs, pre_zs, center_offset) { - -} - -/** -* log.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-log.html -* -**/ - -/* - The accepted values are "OFF" (-1), "INFO" (20), - "WARNING" (30), "ERROR" (40) or positive integers. -*/ -$log_level = "INFO"; - -module log(level = "INFO", level_color) { - default_level_ints = [ - ["OFF", -1], - ["INFO", 20], - ["WARNING", 30], - ["ERROR", 40] - ]; - - default_level_colors = [ - ["INFO", "green"], - ["WARNING", "orange"], - ["ERROR", "red"] + // get rotation matrice for sections + identity_matrix = [ + [1, 0, 0, 0], + [0, 1, 0, 0], + [0, 0, 1, 0], + [0, 0, 0, 1] ]; - /* - The built-in lookup function require integer keys. - I overwrite it so that using string keys is ok. - */ - function lookup(key, mappings, i = 0) = - i == len(mappings) ? key : ( - key == mappings[i][0] ? - mappings[i][1] : - lookup(key, mappings, i + 1) + function axis_angle_local_ang_vects(j) = + [ + for(i = j; i > 0; i = i - 1) + let( + vt0 = points[i] - points[i - 1], + vt1 = points[i + 1] - points[i], + a = acos((vt0 * vt1) / (norm(vt0) * norm(vt1))), + v = cross(vt0, vt1) + ) + [a, v] + ]; + + function axis_angle_cumulated_rot_matrice(i, rot_matrice) = + let( + leng_rot_matrice = len(rot_matrice), + leng_rot_matrice_minus_one = leng_rot_matrice - 1, + leng_rot_matrice_minus_two = leng_rot_matrice - 2 + ) + leng_rot_matrice == 0 ? [identity_matrix] : ( + leng_rot_matrice == 1 ? [rot_matrice[0], identity_matrix] : ( + i == leng_rot_matrice_minus_two ? + [ + rot_matrice[leng_rot_matrice_minus_one], + rot_matrice[leng_rot_matrice_minus_two] * rot_matrice[leng_rot_matrice_minus_one] + ] + : axis_angle_cumulated_rot_matrice_sub(i, rot_matrice) + ) ); - if($log_level != "OFF") { - argu_level = lookup(level, default_level_ints); - golbal_level = lookup( - $log_level == undef ? "INFO" : $log_level, - default_level_ints - ); + function axis_angle_cumulated_rot_matrice_sub(i, rot_matrice) = + let( + matrice = axis_angle_cumulated_rot_matrice(i + 1, rot_matrice), + curr_matrix = rot_matrice[i], + prev_matrix = matrice[len(matrice) - 1] + ) + concat(matrice, [curr_matrix * prev_matrix]); - if(argu_level >= golbal_level) { - c = level_color == undef ? lookup(level, default_level_colors) : level_color; - lv = str(len(level) == undef ? "LEVEL " : "", level); + // align modules + + module axis_angle_align_with_pts_angles(i) { + translate(points[i]) + rotate(angles[i]) + rotate(twist_step_a * i) + scale([1, 1, 1] + scale_step_vt * i) + children(0); + } + + module axis_angle_align_with_pts_init(a, s) { + angleyz = __angy_angz(__to3d(points[0]), __to3d(points[1])); + rotate([0, -angleyz[0], angleyz[1]]) + rotate([90, 0, -90]) + rotate(a) + scale(s) + children(0); + } + + module axis_angle_align_with_pts_local_rotate(j, init_a, init_s, cumu_rot_matrice) { + if(j == 0) { // first child + axis_angle_align_with_pts_init(init_a, init_s) + children(0); + } + else { + multmatrix(cumu_rot_matrice[j - 1]) + axis_angle_align_with_pts_init(init_a, init_s) + children(0); + } + } + + // <<< end: modules and functions for "AXIS-ANGLE" + + + // >>> begin: modules and functions for "EULER-ANGLE" + + function _euler_angle_path_angles(pts, end_i) = + [for(i = 0; i < end_i; i = i + 1) __angy_angz(pts[i], pts[i + 1])]; - // level text - echo( - str( - "", - "", - lv, - "", - "" - ) - ); - - // echo - for(i = [0:$children - 1]) { - children(i); + function euler_angle_path_angles(children) = + let( + pts = len(points[0]) == 3 ? points : [for(pt = points) __to3d(pt)], + end_i = children == 1 ? leng_points_minus_one : children - 1, + angs = _euler_angle_path_angles(pts, end_i) + ) + concat( + [[0, -angs[0][0], angs[0][1]]], + [for(a = angs) [0, -a[0], a[1]]] + ); + + module euler_angle_align(i, angs) { + translate(points[i]) + rotate(angs[i]) + rotate(angles_defined ? [0, 0, 0] : [90, 0, -90]) + rotate(twist_step_a * i) + scale([1, 1, 1] + scale_step_vt * i) + children(0); + } + + // <<< end: modules and functions for "EULER-ANGLE" + + if(method == "AXIS_ANGLE") { + if(angles_defined) { + if($children == 1) { + for(i = [0:leng_points_minus_one]) { + axis_angle_align_with_pts_angles(i) children(0); + } + } else { + for(i = [0:min(leng_points, $children) - 1]) { + axis_angle_align_with_pts_angles(i) children(i); + } + } + } + else { + cumu_rot_matrice = axis_angle_cumulated_rot_matrice(0, [ + for(ang_vect = axis_angle_local_ang_vects(leng_points - 2)) + __m_rotation(ang_vect[0], ang_vect[1]) + ]); + + translate(points[0]) + axis_angle_align_with_pts_local_rotate(0, 0, [1, 1, 1], cumu_rot_matrice) + children(0); + + if($children == 1) { + for(i = [0:leng_points - 2]) { + translate(points[i + 1]) + axis_angle_align_with_pts_local_rotate(i, i * twist_step_a, [1, 1, 1] + scale_step_vt * i, cumu_rot_matrice) + children(0); + } + } else { + for(i = [0:min(leng_points, $children) - 2]) { + translate(points[i + 1]) + axis_angle_align_with_pts_local_rotate(i, i * twist_step_a, [1, 1, 1] + scale_step_vt * i, cumu_rot_matrice) + children(i + 1); + } + } + } + } + else if(method == "EULER_ANGLE") { + angs = angles_defined ? angles : euler_angle_path_angles($children); + + if($children == 1) { + for(i = [0:leng_points_minus_one]) { + euler_angle_align(i, angs) children(0); + } + } else { + for(i = [0:min(leng_points, $children) - 1]) { + euler_angle_align(i, angs) children(i); } } - } -} -function __m_shearing(sx, sy, sz) = - let( - sx_along_y = sx[0], - sx_along_z = sx[1], - sy_along_x = sy[0], - sy_along_z = sy[1], - sz_along_x = sz[0], - sz_along_y = sz[1] - ) - [ - [1, sx_along_y, sx_along_z, 0], - [sy_along_x, 1, sy_along_z, 0], - [sz_along_x, sz_along_y, 1, 0], - [0, 0, 0, 1] - ]; - -function __edge_r_begin(orig_r, a, a_step, m) = - let(leng = orig_r * cos(a_step / 2)) - leng / cos((m - 0.5) * a_step - a); - -function __edge_r_end(orig_r, a, a_step, n) = - let(leng = orig_r * cos(a_step / 2)) - leng / cos((n + 0.5) * a_step - a); - -/** -* ring_extrude.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-ring_extrude.html -* -**/ - - -module ring_extrude(shape_pts, radius, angle = 360, twist = 0, scale = 1.0, triangles = "SOLID") { - if(angle == 360 && twist == 0 && scale == 1.0) { - rotate_extrude() - translate([radius, 0, 0]) - polygon(shape_pts); - } else { - a_step = 360 / __frags(radius); - - angles = __is_float(angle) ? [0, angle] : angle; - - m = floor(angles[0] / a_step) + 1; - n = floor(angles[1] / a_step); - - leng = radius * cos(a_step / 2); - - begin_r = - leng / cos((m - 0.5) * a_step - angles[0]); - - end_r = - leng / cos((n + 0.5) * a_step - angles[1]); - - angs = concat( - [[90, 0, angles[0]]], - m > n ? [] : [for(i = [m:n]) [90, 0, a_step * i]] - ); - pts = concat( - [__ra_to_xy(begin_r, angles[0])], - m > n ? [] : [for(i = [m:n]) __ra_to_xy(radius, a_step * i)] - ); - - is_angle_frag_end = angs[len(angs) - 1][2] == angles[1]; - - all_angles = is_angle_frag_end ? - angs : - concat(angs, [[90, 0, angles[1]]]); - - all_points = is_angle_frag_end ? - pts : - concat(pts, [__ra_to_xy(end_r, angles[1])]); - - sections = cross_sections(shape_pts, all_points, all_angles, twist, scale); - - polysections( - sections, - triangles = triangles - ); - - // hook for testing - test_ring_extrude(sections); + test_along_with_angles(angs); } } -// Override it to test -module test_ring_extrude(sections) { +module test_along_with_angles(angles) { } /** -* shape_ellipse.scad +* arc.scad * * @copyright Justin Lin, 2017 * @license https://opensource.org/licenses/lgpl-3.0.html * -* @see https://openhome.cc/eGossip/OpenSCAD/lib-shape_ellipse.html +* @see https://openhome.cc/eGossip/OpenSCAD/lib-arc.html * -**/ +**/ -function shape_ellipse(axes) = - let( - frags = __frags(axes[0]), - step_a = 360 / frags, - shape_pts = [ - for(a = [0:step_a:360 - step_a]) - [axes[0] * cos(a), axes[1] * sin(a)] - ] - ) shape_pts; - -function __shape_pie(radius, angle) = - let( - frags = __frags(radius), - a_step = 360 / frags, - leng = radius * cos(a_step / 2), - angles = __is_float(angle) ? [0:angle] : angle, - m = floor(angles[0] / a_step) + 1, - n = floor(angles[1] / a_step), - edge_r_begin = leng / cos((m - 0.5) * a_step - angles[0]), - edge_r_end = leng / cos((n + 0.5) * a_step - angles[1]), - shape_pts = concat( - [[0, 0], __ra_to_xy(edge_r_begin, angles[0])], - m > n ? [] : [ - for(i = [m:n]) - let(a = a_step * i) - __ra_to_xy(radius, a) - ], - angles[1] == a_step * n ? [] : [__ra_to_xy(edge_r_end, angles[1])] - ) - ) shape_pts; - -function __to2d(p) = [p[0], p[1]]; +module arc(radius, angle, width, width_mode = "LINE_CROSS") { + polygon(__shape_arc(radius, angle, width, width_mode)); +} /** * rotate_p.scad @@ -3852,568 +4762,34 @@ function _q_rotate_p(p, a, v) = ); function rotate_p(point, a, v) = - v == undef ? _rotate_p(point, a) : _q_rotate_p(point, a, v); + is_undef(v) ? _rotate_p(point, a) : _q_rotate_p(point, a, v); /** -* shape_path_extend.scad +* sub_str.scad * * @copyright Justin Lin, 2017 * @license https://opensource.org/licenses/lgpl-3.0.html * -* @see https://openhome.cc/eGossip/OpenSCAD/lib-path_extend.html +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-sub_str.html * -**/ +**/ - -function _shape_path_extend_az(p1, p2) = - let( - x1 = p1[0], - y1 = p1[1], - x2 = p2[0], - y2 = p2[1] - ) -90 + atan2((y2 - y1), (x2 - x1)); - -function _shape_path_first_stroke(stroke_pts, path_pts) = - let( - p1 = path_pts[0], - p2 = path_pts[1], - a = _shape_path_extend_az(p1, p2) - ) - [ - for(p = stroke_pts) - rotate_p(p, a) + p1 - ]; - -function _shape_path_extend_stroke(stroke_pts, p1, p2, scale_step, i) = - let( - leng = norm(__to3d(p2) - __to3d(p1)), - a = _shape_path_extend_az(p1, p2) - ) - [ - for(p = stroke_pts) - rotate_p(p * (1 + scale_step * i) + [0, leng], a) + p1 - ]; +function _sub_str(t, begin, end) = + begin == end ? "" : str(t[begin], sub_str(t, begin + 1, end)); -function _shape_path_extend_inner(stroke_pts, path_pts, leng_path_pts, scale_step, index) = - index == leng_path_pts ? [] : - concat( - [ - _shape_path_extend_stroke( - stroke_pts, - path_pts[index - 1], - path_pts[index], - scale_step, - index - ) - ], - _shape_path_extend_inner( - stroke_pts, - path_pts, - leng_path_pts, - scale_step, - index + 1 - ) - ); +function sub_str(t, begin, end) = + is_undef(end) ? _sub_str(t, begin, len(t)) : _sub_str(t, begin, end); -function shape_path_extend(stroke_pts, path_pts, scale = 1.0, closed = false) = + +function __lines_from(pts, closed = false) = let( - leng_path_pts = len(path_pts), - scale_step = (scale - 1) / (leng_path_pts - 1), - strokes = _shape_path_extend_inner(stroke_pts, path_pts, leng_path_pts, scale_step, 1) + leng = len(pts), + endi = leng - 1 ) - closed && path_pts[0] == path_pts[leng_path_pts - 1] ? - __polytransversals(concat(strokes, [strokes[0]])) : - __polytransversals( - concat([_shape_path_first_stroke(stroke_pts, path_pts)], strokes) - ); - - - -/** -* box_extrude.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-box_extrude.html -* -**/ - -module box_extrude(height, shell_thickness, offset_mode = "delta", chamfer = false) { - linear_extrude(shell_thickness) - children(); - - linear_extrude(height) - difference() { - children(); - if(offset_mode == "delta") { - offset(delta = -shell_thickness, chamfer = chamfer) - children(); - } else { - offset(r = -shell_thickness) - children(); - } - } -} - - - -/** -* triangulate.scad -* -* @copyright Justin Lin, 2019 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-triangulate.html -* -**/ - -function _triangulate_in_triangle(p0, p1, p2, p) = - let( - v0 = p0 - p, - v1 = p1 - p, - v2 = p2 - p, - c0 = cross(v0, v1), - c1 = cross(v1, v2), - c2 = cross(v2, v0) - ) - (c0 > 0 && c1 > 0 && c2 > 0) || (c0 < 0 && c1 < 0 && c2 < 0); - -function _triangulate_snipable(shape_pts, u, v, w, n, indices, epsilon = 0.0001) = - let( - a = shape_pts[indices[u]], - b = shape_pts[indices[v]], - c = shape_pts[indices[w]], - ax = a[0], - ay = a[1], - bx = b[0], - by = b[1], - cx = c[0], - cy = c[1] - ) - epsilon > (((bx - ax) * (cy - ay)) - ((by - ay) * (cx - ax))) ? - false : _triangulate_snipable_sub(shape_pts, n, u, v, w, a, b, c, indices); - -function _triangulate_snipable_sub(shape_pts, n, u, v, w, a, b, c, indices, p = 0) = - p == n ? true : ( - ((p == u) || (p == v) || (p == w)) ? _triangulate_snipable_sub(shape_pts, n, u, v, w, a, b, c, indices, p + 1) : ( - _triangulate_in_triangle(a, b, c, shape_pts[indices[p]]) ? - false : _triangulate_snipable_sub(shape_pts, n, u, v, w, a, b, c, indices, p + 1) - ) - ); - -// remove the elem at idx v from indices -function _triangulate_remove_v(indices, v, num_of_vertices) = - let( - nv_minuns_one = num_of_vertices - 1 - ) - v == 0 ? [for(i = [1:nv_minuns_one]) indices[i]] : ( - v == nv_minuns_one ? [for(i = [0:v - 1]) indices[i]] : concat( - [for(i = [0:v - 1]) indices[i]], - [for(i = [v + 1:nv_minuns_one]) indices[i]] - ) - ); - -function _triangulate_zero_or_value(num_of_vertices, value) = - num_of_vertices <= value ? 0 : value; - - -function _triangulate_real_triangulate_sub(shape_pts, collector, indices, v, num_of_vertices, count, epsilon) = - let( - // idxes of three consecutive vertices - u = _triangulate_zero_or_value(num_of_vertices, v), - vi = _triangulate_zero_or_value(num_of_vertices, u + 1), - w = _triangulate_zero_or_value(num_of_vertices, vi + 1) - ) - _triangulate_snipable(shape_pts, u, vi, w, num_of_vertices, indices, epsilon) ? - _triangulate_snip(shape_pts, collector, indices, u, vi, w, num_of_vertices, count, epsilon) : - _triangulate_real_triangulate(shape_pts, collector, indices, vi, num_of_vertices, count, epsilon); - -function _triangulate_snip(shape_pts, collector, indices, u, v, w, num_of_vertices, count, epsilon) = - let( - a = indices[u], - b = indices[v], - c = indices[w], - new_nv = num_of_vertices - 1 - ) - _triangulate_real_triangulate( - shape_pts, - concat(collector, [[a, b, c]]), - _triangulate_remove_v(indices, v, num_of_vertices), - v, - new_nv, - 2 * new_nv, - epsilon - ); - -function _triangulate_real_triangulate(shape_pts, collector, indices, v, num_of_vertices, count, epsilon) = - count <= 0 ? [] : ( - num_of_vertices == 2 ? - collector : _triangulate_real_triangulate_sub(shape_pts, collector, indices, v, num_of_vertices, count - 1, epsilon) - ); - -function triangulate(shape_pts, epsilon = 0.0001) = - let( - num_of_vertices = len(shape_pts), - v = num_of_vertices - 1, - indices = [for(vi = [0:v]) vi], - count = 2 * num_of_vertices - ) - num_of_vertices < 3 ? [] : _triangulate_real_triangulate(shape_pts, [], indices, v, num_of_vertices, count, epsilon); - - -/** -* line2d.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-line2d.html -* -**/ - - -module line2d(p1, p2, width, p1Style = "CAP_SQUARE", p2Style = "CAP_SQUARE") { - half_width = 0.5 * width; - - atan_angle = atan2(p2[1] - p1[1], p2[0] - p1[0]); - leng = sqrt(pow(p2[0] - p1[0], 2) + pow(p2[1] - p1[1], 2)); - - frags = __nearest_multiple_of_4(__frags(half_width)); - - module square_end(point) { - translate(point) - rotate(atan_angle) - square(width, center = true); - - // hook for testing - test_line2d_cap(point, "CAP_SQUARE"); - } - - module round_end(point) { - translate(point) - rotate(atan_angle) - circle(half_width, $fn = frags); - - // hook for testing - test_line2d_cap(point, "CAP_ROUND"); - } - - if(p1Style == "CAP_SQUARE") { - square_end(p1); - } else if(p1Style == "CAP_ROUND") { - round_end(p1); - } - - translate(p1) - rotate(atan_angle) - translate([0, -width / 2]) - square([leng, width]); - - if(p2Style == "CAP_SQUARE") { - square_end(p2); - } else if(p2Style == "CAP_ROUND") { - round_end(p2); - } - - // hook for testing - test_line2d_line(atan_angle, leng, width, frags); -} - -// override them to test -module test_line2d_cap(point, style) { -} - -module test_line2d_line(angle, length, width, frags) { -} - - - -/** -* hull_polyline2d.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/hull_polyline2d.html -* -**/ - -module hull_polyline2d(points, width) { - half_width = width / 2; - leng = len(points); - - module hull_line2d(index) { - point1 = points[index - 1]; - point2 = points[index]; - - hull() { - translate(point1) - circle(half_width); - translate(point2) - circle(half_width); - } - - // hook for testing - test_line_segment(index, point1, point2, half_width); - } - - module polyline2d_inner(index) { - if(index < leng) { - hull_line2d(index); - polyline2d_inner(index + 1); - } - } - - polyline2d_inner(1); -} - -// override it to test -module test_line_segment(index, point1, point2, radius) { - -} - -/** -* circle_path.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-circle_path.html -* -**/ - - -function circle_path(radius, n) = - let( - _frags = __frags(radius), - step_a = 360 / _frags, - end_a = 360 - step_a * ((n == undef || n > _frags) ? 1 : _frags - n + 1) - ) - [ - for(a = [0 : step_a : end_a]) - [radius * cos(a), radius * sin(a)] - ]; - - -/** -* m_rotation.scad -* -* @copyright Justin Lin, 2019 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-m_rotation.html -* -**/ - - -function _q_rotation(a, v) = - let( - half_a = a / 2, - axis = v / norm(v), - s = sin(half_a), - x = s * axis[0], - y = s * axis[1], - z = s * axis[2], - w = cos(half_a), - - x2 = x + x, - y2 = y + y, - z2 = z + z, - - xx = x * x2, - yx = y * x2, - yy = y * y2, - zx = z * x2, - zy = z * y2, - zz = z * z2, - wx = w * x2, - wy = w * y2, - wz = w * z2 - ) - [ - [1 - yy - zz, yx - wz, zx + wy, 0], - [yx + wz, 1 - xx - zz, zy - wx, 0], - [zx - wy, zy + wx, 1 - xx - yy, 0], - [0, 0, 0, 1] - ]; - -function _m_xRotation(a) = - let(c = cos(a), s = sin(a)) - [ - [1, 0, 0, 0], - [0, c, -s, 0], - [0, s, c, 0], - [0, 0, 0, 1] - ]; - -function _m_yRotation(a) = - let(c = cos(a), s = sin(a)) - [ - [c, 0, s, 0], - [0, 1, 0, 0], - [-s, 0, c, 0], - [0, 0, 0, 1] - ]; - -function _m_zRotation(a) = - let(c = cos(a), s = sin(a)) - [ - [c, -s, 0, 0], - [s, c, 0, 0], - [0, 0, 1, 0], - [0, 0, 0, 1] - ]; - -function _xyz_rotation(a) = - let(ang = __to_ang_vect(a)) - _m_zRotation(ang[2]) * _m_yRotation(ang[1]) * _m_xRotation(ang[0]); - -function m_rotation(a, v) = - (a == 0 || a == [0, 0, 0] || a == [0] || a == [0, 0]) ? [ - [1, 0, 0, 0], - [0, 1, 0, 0], - [0, 0, 1, 0], - [0, 0, 0, 1] - ] : (v == undef ? _xyz_rotation(a) : _q_rotation(a, v)); - -function __tr__corner_t_leng_lt_zero(frags, t_sector_angle, l1, l2, h, round_r) = - let(t_height = tan(t_sector_angle) * l1 - round_r / sin(90 - t_sector_angle) - h / 2) - [ - for(pt = __pie_for_rounding(round_r, 90 - t_sector_angle, 90, frags * t_sector_angle / 180)) - [pt[0], pt[1] + t_height] - ]; - -function __tr_corner_t_leng_gt_or_eq_zero(frags, t_sector_angle, t_leng, h, round_r) = - let(offset_y = h / 2 - round_r) - [ - for(pt = __pie_for_rounding(round_r, 90 - t_sector_angle, 90, frags * t_sector_angle / 360)) - [pt[0] + t_leng, pt[1] + offset_y] - ]; - -function __tr_corner(frags, b_ang, l1, l2, h, round_r) = - let(t_leng = l2 - round_r * tan(b_ang / 2)) - t_leng >= 0 ? - __tr_corner_t_leng_gt_or_eq_zero(frags, b_ang, t_leng, h, round_r) : - __tr__corner_t_leng_lt_zero(frags, b_ang, l1, l2, h, round_r); - -function __tr__corner_b_leng_lt_zero(frags, b_sector_angle, l1, l2, h, round_r) = - let( - reversed = __tr__corner_t_leng_lt_zero(frags, b_sector_angle, l2, l1, h, round_r), - leng = len(reversed) - ) - [ - for(i = [0:leng - 1]) - let(pt = reversed[leng - 1 - i]) - [pt[0], -pt[1]] - ]; - -function __br_corner_b_leng_gt_or_eq_zero(frags, b_sector_angle, l1, l2, b_leng, h, round_r) = - let(half_h = h / 2) - [ - for(pt = __pie_for_rounding(round_r, -90, -90 + b_sector_angle, frags * b_sector_angle / 360)) - [pt[0] + b_leng, pt[1] + round_r - half_h] - ]; - -function __br_corner(frags, b_ang, l1, l2, h, round_r) = - let(b_leng = l1 - round_r / tan(b_ang / 2)) - b_leng >= 0 ? - __br_corner_b_leng_gt_or_eq_zero(frags, 180 - b_ang, l1, l2, b_leng, h, round_r) : - __tr__corner_b_leng_lt_zero(frags, 180 - b_ang, l1, l2, h, round_r); - -function __half_trapezium(length, h, round_r) = - let( - is_flt = __is_float(length), - l1 = is_flt ? length : length[0], - l2 = is_flt ? length : length[1], - frags = __frags(round_r), - b_ang = atan2(h, l1 - l2), - br_corner = __br_corner(frags, b_ang, l1, l2, h, round_r), - tr_corner = __tr_corner(frags, b_ang, l1, l2, h, round_r) - ) concat( - br_corner, - tr_corner + [for(i = 0; i < endi; i = i + 1) [pts[i], pts[i + 1]]], + closed ? [[pts[len(pts) - 1], pts[0]]] : [] ); - -/** -* rounded_cube.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-rounded_cube.html -* -**/ - - -module rounded_cube(size, corner_r, center = false) { - is_flt = __is_float(size); - x = is_flt ? size : size[0]; - y = is_flt ? size : size[1]; - z = is_flt ? size : size[2]; - - corner_frags = __nearest_multiple_of_4(__frags(corner_r)); - edge_d = corner_r * cos(180 / corner_frags); - - half_x = x / 2; - half_y = y / 2; - half_z = z / 2; - half_l = half_x - edge_d; - half_w = half_y - edge_d; - half_h = half_z - edge_d; - - half_cube_leng = size / 2; - half_leng = half_cube_leng - edge_d; - - corners = [ - for(z = [1, -1]) - for(y = [1, -1]) - for(x = [1, -1]) - [half_l * x, half_w * y, half_h * z] - ]; - - module corner(i) { - translate(corners[i]) - sphere(corner_r, $fn = corner_frags); - } - - center_pts = center ? [0, 0, 0] : [half_x, half_y, half_z]; - - // Don't use `hull() for(...) {...}` because it's slow. - translate(center_pts) hull() { - corner(0); - corner(1); - corner(2); - corner(3); - corner(4); - corner(5); - corner(6); - corner(7); - } - - // hook for testing - test_rounded_edge_corner_center(corner_frags, corners, center_pts); -} - -// override it to test -module test_rounded_edge_corner_center(corner_frags, corners, center_pts) { - -} - -/** -* shape_pie.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-shape_pie.html -* -**/ - - -function shape_pie(radius, angle) = - __shape_pie(radius, angle); diff --git a/src/ellipse_extrude.scad b/src/ellipse_extrude.scad index 8d81b297..e449038e 100644 --- a/src/ellipse_extrude.scad +++ b/src/ellipse_extrude.scad @@ -9,47 +9,40 @@ **/ module ellipse_extrude(semi_minor_axis, height, center = false, convexity = 10, twist = 0, slices = 20) { - h = height == undef ? semi_minor_axis : ( + h = is_undef(height) ? semi_minor_axis : ( // `semi_minor_axis` is always equal to or greater than `height`. height > semi_minor_axis ? semi_minor_axis : height ); angle = asin(h / semi_minor_axis) / slices; - function f_extrude(i = 1) = - i <= slices ? - concat( - [ - [ - cos(angle * i) / cos(angle * (i - 1)), - semi_minor_axis * sin(angle * i) - ] - ], - f_extrude(i + 1) - ) : []; + f_extrude = [ + for(i = 1; i <= slices; i = i + 1) + [ + cos(angle * i) / cos(angle * (i - 1)), + semi_minor_axis * sin(angle * i) + ] + ]; + len_f_extrude = len(f_extrude); - fzs = f_extrude(); - len_fzs = len(fzs); + accm_fs = + [ + for(i = 0, pre_f = 1; i < len_f_extrude; pre_f = pre_f * f_extrude[i][0], i = i + 1) + pre_f * f_extrude[i][0] + ]; - function accm_fs(pre_f = 1, i = 0) = - i < len_fzs ? - concat( - [pre_f * fzs[i][0]], - accm_fs(pre_f * fzs[i][0], i + 1) - ) : []; - - child_fs = concat([1], accm_fs()); + child_fs = concat([1], accm_fs); pre_zs = concat( [0], [ - for(i = [0:len_fzs - 1]) - fzs[i][1] + for(i = 0; i < len_f_extrude; i = i + 1) + f_extrude[i][1] ] ); module extrude() { - for(i = [0:len_fzs - 1]) { - f = fzs[i][0]; - z = fzs[i][1]; + for(i = [0:len_f_extrude - 1]) { + f = f_extrude[i][0]; + z = f_extrude[i][1]; translate([0, 0, pre_zs[i]]) rotate(-twist / slices * i) diff --git a/src/function_grapher.scad b/src/function_grapher.scad index 46c58870..8cbd5c00 100644 --- a/src/function_grapher.scad +++ b/src/function_grapher.scad @@ -8,13 +8,16 @@ * **/ -include <__private__/__reverse.scad>; +include ; module function_grapher(points, thickness, style = "FACES", slicing = "SLASH") { rows = len(points); columns = len(points[0]); + yi_range = [0:rows - 2]; + xi_range = [0:columns - 2]; + // Increasing $fn will be slow when you use "LINES", "HULL_FACES" or "HULL_LINES". module faces() { @@ -34,16 +37,16 @@ module function_grapher(points, thickness, style = "FACES", slicing = "SLASH") { leng_pts = len(top_pts); top_tri_faces1 = slicing == "SLASH" ? [ - for(yi = [0:rows - 2]) - for(xi = [0:columns - 2]) + for(yi = yi_range) + for(xi = xi_range) [ xy_to_index(xi, yi, columns), xy_to_index(xi + 1, yi + 1, columns), xy_to_index(xi + 1, yi, columns) ] ] : [ - for(yi = [0:rows - 2]) - for(xi = [0:columns - 2]) + for(yi = yi_range) + for(xi = xi_range) [ xy_to_index(xi, yi, columns), xy_to_index(xi, yi + 1, columns), @@ -52,16 +55,16 @@ module function_grapher(points, thickness, style = "FACES", slicing = "SLASH") { ]; top_tri_faces2 = slicing == "SLASH" ? [ - for(yi = [0:rows - 2]) - for(xi = [0:columns - 2]) + for(yi = yi_range) + for(xi = xi_range) [ xy_to_index(xi, yi, columns), xy_to_index(xi, yi + 1, columns), xy_to_index(xi + 1, yi + 1, columns) ] ] : [ - for(yi = [0:rows - 2]) - for(xi = [0:columns - 2]) + for(yi = yi_range) + for(xi = xi_range) [ xy_to_index(xi, yi + 1, columns), xy_to_index(xi + 1, yi + 1, columns), @@ -80,7 +83,7 @@ module function_grapher(points, thickness, style = "FACES", slicing = "SLASH") { ]; side_faces1 = [ - for(xi = [0:columns - 2]) + for(xi = xi_range) let( idx1 = xy_to_index(xi, 0, columns), idx2 = xy_to_index(xi + 1, 0, columns) @@ -94,7 +97,7 @@ module function_grapher(points, thickness, style = "FACES", slicing = "SLASH") { ]; side_faces2 = [ - for(yi = [0:rows - 2]) + for(yi = yi_range) let( xi = columns - 1, idx1 = xy_to_index(xi, yi, columns), @@ -109,7 +112,7 @@ module function_grapher(points, thickness, style = "FACES", slicing = "SLASH") { ]; side_faces3 = [ - for(xi = [0:columns - 2]) + for(xi = xi_range) let( yi = rows - 1, idx1 = xy_to_index(xi, yi, columns), @@ -124,7 +127,7 @@ module function_grapher(points, thickness, style = "FACES", slicing = "SLASH") { ]; side_faces4 = [ - for(yi = [0:rows - 2]) + for(yi = yi_range) let( idx1 = xy_to_index(0, yi, columns), idx2 = xy_to_index(0, yi + 1, columns) @@ -193,8 +196,8 @@ module function_grapher(points, thickness, style = "FACES", slicing = "SLASH") { if(style == "FACES") { faces(); } else { - for(yi = [0:rows - 2]) { - for(xi = [0:columns - 2]) { + for(yi = yi_range) { + for(xi = xi_range) { if(slicing == "SLASH") { tri_to_graph([ points[yi][xi], diff --git a/src/golden_spiral.scad b/src/golden_spiral.scad index 5277c3b8..28aa20cc 100644 --- a/src/golden_spiral.scad +++ b/src/golden_spiral.scad @@ -26,7 +26,7 @@ function _fast_fibonacci(nth) = function _remove_same_pts(pts1, pts2) = pts1[len(pts1) - 1] == pts2[0] ? - concat(pts1, [for(i = [1:len(pts2) - 1]) pts2[i]]) : + concat(pts1, [for(i = 1; i < len(pts2); i = i + 1) pts2[i]]) : concat(pts1, pts2); function _golden_spiral_from_ls_or_eql_to(from, to, point_distance, rt_dir) = @@ -38,11 +38,12 @@ function _golden_spiral_from_ls_or_eql_to(from, to, point_distance, rt_dir) = circle_pts = circle_path(radius = f1, n = $fn / 4 + 1), len_pts = len(circle_pts), a_step = 360 / $fn * rt_dir, + range_i = [0:len_pts - 1], arc_points_angles = (rt_dir == 1 ? [ - for(i = [0:len_pts - 1]) + for(i = range_i) [circle_pts[i], a_step * i] ] : [ - for(i = [0:len_pts - 1]) let(idx = len_pts - i - 1) + for(i = range_i) let(idx = len_pts - i - 1) [circle_pts[idx], a_step * i] ]), offset = f2 - f1 diff --git a/src/helix.scad b/src/helix.scad index a51a3319..b54650e7 100644 --- a/src/helix.scad +++ b/src/helix.scad @@ -8,12 +8,11 @@ * **/ -include <__private__/__is_float.scad>; -include <__private__/__frags.scad>; +include <__comm__/__frags.scad>; function helix(radius, levels, level_dist, vt_dir = "SPI_DOWN", rt_dir = "CT_CLK") = let( - is_flt = __is_float(radius), + is_flt = is_num(radius), r1 = is_flt ? radius : radius[0], r2 = is_flt ? radius : radius[1], init_r = vt_dir == "SPI_DOWN" ? r2 : r1, @@ -26,10 +25,11 @@ function helix(radius, levels, level_dist, vt_dir = "SPI_DOWN", rt_dir = "CT_CLK r_step = r_diff / (levels * _frags), a_step = 360 / _frags * rt_d, begin_r = vt_dir == "SPI_DOWN" ? r2 : r1, - begin_h = vt_dir == "SPI_DOWN" ? h : 0 + begin_h = vt_dir == "SPI_DOWN" ? h : 0, + end_i = _frags * levels ) [ - for(i = [0:_frags * levels]) + for(i = 0; i <= end_i; i = i + 1) let(r = begin_r + r_step * i, a = a_step * i) [r * cos(a), r * sin(a), begin_h - h_step * i] ]; \ No newline at end of file diff --git a/src/helix_extrude.scad b/src/helix_extrude.scad index 1417e135..e8a1efcc 100644 --- a/src/helix_extrude.scad +++ b/src/helix_extrude.scad @@ -8,8 +8,7 @@ * **/ -include <__private__/__is_float.scad>; -include <__private__/__frags.scad>; +include <__comm__/__frags.scad>; module helix_extrude(shape_pts, radius, levels, level_dist, vt_dir = "SPI_DOWN", rt_dir = "CT_CLK", @@ -18,11 +17,11 @@ module helix_extrude(shape_pts, radius, levels, level_dist, function reverse(vt) = let(leng = len(vt)) [ - for(i = [0:leng - 1]) + for(i = 0; i < leng; i = i + 1) vt[leng - 1 - i] ]; - is_flt = __is_float(radius); + is_flt = is_num(radius); r1 = is_flt ? radius : radius[0]; r2 = is_flt ? radius : radius[1]; @@ -34,7 +33,7 @@ module helix_extrude(shape_pts, radius, levels, level_dist, r_dir = rt_dir == "CT_CLK" ? 1 : -1; angle_step = 360 / frags * r_dir; - initial_angle = atan2(level_dist / frags, 6.28318 * init_r / frags) * v_dir * r_dir; + initial_angle = atan2(level_dist / frags, PI * 2 * init_r / frags) * v_dir * r_dir; path_points = helix( radius = radius, @@ -45,7 +44,7 @@ module helix_extrude(shape_pts, radius, levels, level_dist, ); clk_a = r_dir == 1 ? 0 : 180; - angles = [for(i = [0:len(path_points) - 1]) [90 + initial_angle, 0, clk_a + angle_step * i]]; + angles = [for(i = 0; i < len(path_points); i = i + 1) [90 + initial_angle, 0, clk_a + angle_step * i]]; sections = cross_sections(shape_pts, path_points, angles, twist, scale); diff --git a/src/hexagons.scad b/src/hexagons.scad index c51c8888..a2ab1c51 100644 --- a/src/hexagons.scad +++ b/src/hexagons.scad @@ -26,7 +26,7 @@ module hexagons(radius, spacing, levels) { tx = hex_datum[0][0], ty = hex_datum[0][1], n = hex_datum[1], - offset_xs = [for(i = [0:n - 1]) i * offset_step + center_offset] + offset_xs = [for(i = 0; i < n; i = i + 1) i * offset_step + center_offset] ) [ for(x = offset_xs) [x + tx, ty] @@ -37,7 +37,7 @@ module hexagons(radius, spacing, levels) { ty = hex_datum[0][1]; n = hex_datum[1]; - offset_xs = [for(i = [0:n - 1]) i * offset_step + center_offset]; + offset_xs = [for(i = 0; i < n; i = i + 1) i * offset_step + center_offset]; for(x = offset_xs) { p = [x + tx, ty, 0]; translate(p) diff --git a/src/in_polyline.scad b/src/in_polyline.scad index f0b093a2..41ce4eba 100644 --- a/src/in_polyline.scad +++ b/src/in_polyline.scad @@ -8,15 +8,14 @@ * **/ -include <__private__/__to3d.scad>; -include <__private__/__in_line.scad>; - -function _in_polyline_sub(pts, pt, epsilon, iend, i = 0) = - i == iend ? false : ( - __in_line([pts[i], pts[i + 1]], pt, epsilon) ? true : - _in_polyline_sub(pts, pt, epsilon, iend, i + 1) - ); +include <__comm__/__to3d.scad>; +include <__comm__/__in_line.scad>; function in_polyline(line_pts, pt, epsilon = 0.0001) = - _in_polyline_sub(line_pts, pt, epsilon, len(line_pts) - 1); + let( + leng = len(line_pts), + iend = leng - 1, + maybe_last = [for(i = 0; i < iend && !__in_line([line_pts[i], line_pts[i + 1]], pt, epsilon); i = i + 1) i][leng - 2] + ) + is_undef(maybe_last); \ No newline at end of file diff --git a/src/in_shape.scad b/src/in_shape.scad index e104e883..307e423c 100644 --- a/src/in_shape.scad +++ b/src/in_shape.scad @@ -8,9 +8,9 @@ * **/ -include <__private__/__to3d.scad>; -include <__private__/__lines_from.scad>; -include <__private__/__in_line.scad>; +include <__comm__/__to3d.scad>; +include <__comm__/__lines_from.scad>; +include <__comm__/__in_line.scad>; function _in_shape_in_line_equation(edge, pt) = let( @@ -23,13 +23,13 @@ function _in_shape_in_line_equation(edge, pt) = ) (pt[1] == a * pt[0] + b); -function _in_shape_in_any_edges_sub(edges, leng, pt, i, epsilon) = - leng == i ? false : ( - __in_line(edges[i], pt, epsilon) ? true : _in_shape_in_any_edges_sub(edges, leng, pt, i + 1, epsilon) - ); +function _in_shape_in_any_edges(edges, pt, epsilon) = + let( + leng = len(edges), + maybe_last = [for(i = 0; i < leng && !__in_line(edges[i], pt, epsilon); i = i + 1) i][leng - 1] + ) + is_undef(maybe_last); -function _in_shape_in_any_edges(edges, pt, epsilon) = _in_shape_in_any_edges_sub(edges, len(edges), pt, 0, epsilon); - function _in_shape_interpolate_x(y, p1, p2) = p1[1] == p2[1] ? p1[0] : ( p1[0] + (p2[0] - p1[0]) * (y - p1[1]) / (p2[1] - p1[1]) diff --git a/src/line2d.scad b/src/line2d.scad index f8035459..654d09c1 100644 --- a/src/line2d.scad +++ b/src/line2d.scad @@ -8,8 +8,8 @@ * **/ -include <__private__/__frags.scad>; -include <__private__/__nearest_multiple_of_4.scad>; +include <__comm__/__frags.scad>; +include <__comm__/__nearest_multiple_of_4.scad>; module line2d(p1, p2, width, p1Style = "CAP_SQUARE", p2Style = "CAP_SQUARE") { half_width = 0.5 * width; diff --git a/src/line3d.scad b/src/line3d.scad index dc295ca5..ae5f9cbf 100644 --- a/src/line3d.scad +++ b/src/line3d.scad @@ -8,8 +8,8 @@ * **/ -include <__private__/__frags.scad>; -include <__private__/__nearest_multiple_of_4.scad>; +include <__comm__/__frags.scad>; +include <__comm__/__nearest_multiple_of_4.scad>; module line3d(p1, p2, thickness, p1Style = "CAP_CIRCLE", p2Style = "CAP_CIRCLE") { r = thickness / 2; diff --git a/src/log.scad b/src/log.scad deleted file mode 100644 index 84a6067c..00000000 --- a/src/log.scad +++ /dev/null @@ -1,70 +0,0 @@ -/** -* log.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-log.html -* -**/ - -/* - The accepted values are "OFF" (-1), "INFO" (20), - "WARNING" (30), "ERROR" (40) or positive integers. -*/ -$log_level = "INFO"; - -module log(level = "INFO", level_color) { - default_level_ints = [ - ["OFF", -1], - ["INFO", 20], - ["WARNING", 30], - ["ERROR", 40] - ]; - - default_level_colors = [ - ["INFO", "green"], - ["WARNING", "orange"], - ["ERROR", "red"] - ]; - - /* - The built-in lookup function require integer keys. - I overwrite it so that using string keys is ok. - */ - function lookup(key, mappings, i = 0) = - i == len(mappings) ? key : ( - key == mappings[i][0] ? - mappings[i][1] : - lookup(key, mappings, i + 1) - ); - - if($log_level != "OFF") { - argu_level = lookup(level, default_level_ints); - golbal_level = lookup( - $log_level == undef ? "INFO" : $log_level, - default_level_ints - ); - - if(argu_level >= golbal_level) { - c = level_color == undef ? lookup(level, default_level_colors) : level_color; - lv = str(len(level) == undef ? "LEVEL " : "", level); - - // level text - echo( - str( - "", - "", - lv, - "", - "" - ) - ); - - // echo - for(i = [0:$children - 1]) { - children(i); - } - } - } -} \ No newline at end of file diff --git a/src/m_scaling.scad b/src/m_scaling.scad deleted file mode 100644 index 0c4dfd74..00000000 --- a/src/m_scaling.scad +++ /dev/null @@ -1,28 +0,0 @@ -/** -* m_scaling.scad -* -* @copyright Justin Lin, 2019 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-m_scaling.html -* -**/ - -include <__private__/__is_float.scad>; - -function _to_3_elems_scaling_vect(s) = - let(leng = len(s)) - leng == 3 ? s : ( - leng == 2 ? [s[0], s[1], 1] : [s[0], 1, 1] - ); - -function _to_scaling_vect(s) = __is_float(s) ? [s, s, s] : _to_3_elems_scaling_vect(s); - -function m_scaling(s) = - let(v = _to_scaling_vect(s)) - [ - [v[0], 0, 0, 0], - [0, v[1], 0, 0], - [0, 0, v[2], 0], - [0, 0, 0, 1] - ]; \ No newline at end of file diff --git a/src/m_rotation.scad b/src/matrix/__comm__/__m_rotation.scad similarity index 68% rename from src/m_rotation.scad rename to src/matrix/__comm__/__m_rotation.scad index c532bcc5..4ce85d6a 100644 --- a/src/m_rotation.scad +++ b/src/matrix/__comm__/__m_rotation.scad @@ -1,17 +1,4 @@ -/** -* m_rotation.scad -* -* @copyright Justin Lin, 2019 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-m_rotation.html -* -**/ - -include <__private__/__is_float.scad>; -include <__private__/__to_ang_vect.scad>; - -function _q_rotation(a, v) = +function __m_rotation_q_rotation(a, v) = let( half_a = a / 2, axis = v / norm(v), @@ -42,7 +29,7 @@ function _q_rotation(a, v) = [0, 0, 0, 1] ]; -function _m_xRotation(a) = +function __m_rotation_xRotation(a) = let(c = cos(a), s = sin(a)) [ [1, 0, 0, 0], @@ -51,7 +38,7 @@ function _m_xRotation(a) = [0, 0, 0, 1] ]; -function _m_yRotation(a) = +function __m_rotation_yRotation(a) = let(c = cos(a), s = sin(a)) [ [c, 0, s, 0], @@ -60,7 +47,7 @@ function _m_yRotation(a) = [0, 0, 0, 1] ]; -function _m_zRotation(a) = +function __m_rotation_zRotation(a) = let(c = cos(a), s = sin(a)) [ [c, -s, 0, 0], @@ -69,14 +56,14 @@ function _m_zRotation(a) = [0, 0, 0, 1] ]; -function _xyz_rotation(a) = +function __m_rotation_xyz_rotation(a) = let(ang = __to_ang_vect(a)) - _m_zRotation(ang[2]) * _m_yRotation(ang[1]) * _m_xRotation(ang[0]); + __m_rotation_zRotation(ang[2]) * __m_rotation_yRotation(ang[1]) * __m_rotation_xRotation(ang[0]); -function m_rotation(a, v) = +function __m_rotation(a, v) = (a == 0 || a == [0, 0, 0] || a == [0] || a == [0, 0]) ? [ [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1] - ] : (v == undef ? _xyz_rotation(a) : _q_rotation(a, v)); \ No newline at end of file + ] : (is_undef(v) ? __m_rotation_xyz_rotation(a) : __m_rotation_q_rotation(a, v)); \ No newline at end of file diff --git a/src/matrix/__comm__/__m_scaling.scad b/src/matrix/__comm__/__m_scaling.scad new file mode 100644 index 00000000..cd07fcce --- /dev/null +++ b/src/matrix/__comm__/__m_scaling.scad @@ -0,0 +1,16 @@ +function __m_scaling_to_3_elems_scaling_vect(s) = + let(leng = len(s)) + leng == 3 ? s : ( + leng == 2 ? [s[0], s[1], 1] : [s[0], 1, 1] + ); + +function __m_scaling_to_scaling_vect(s) = is_num(s) ? [s, s, s] : __m_scaling_to_3_elems_scaling_vect(s); + +function __m_scaling(s) = + let(v = __m_scaling_to_scaling_vect(s)) + [ + [v[0], 0, 0, 0], + [0, v[1], 0, 0], + [0, 0, v[2], 0], + [0, 0, 0, 1] + ]; \ No newline at end of file diff --git a/src/__private__/__m_shearing.scad b/src/matrix/__comm__/__m_shearing.scad similarity index 100% rename from src/__private__/__m_shearing.scad rename to src/matrix/__comm__/__m_shearing.scad diff --git a/src/m_cumulate.scad b/src/matrix/m_cumulate.scad similarity index 85% rename from src/m_cumulate.scad rename to src/matrix/m_cumulate.scad index ae511501..57f6c87f 100644 --- a/src/m_cumulate.scad +++ b/src/matrix/m_cumulate.scad @@ -4,7 +4,7 @@ * @copyright Justin Lin, 2019 * @license https://opensource.org/licenses/lgpl-3.0.html * -* @see https://openhome.cc/eGossip/OpenSCAD/lib-m_cumulate.html +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-m_cumulate.html * **/ diff --git a/src/m_mirror.scad b/src/matrix/m_mirror.scad similarity index 88% rename from src/m_mirror.scad rename to src/matrix/m_mirror.scad index 11ec7fed..b9502e2d 100644 --- a/src/m_mirror.scad +++ b/src/matrix/m_mirror.scad @@ -4,7 +4,7 @@ * @copyright Justin Lin, 2019 * @license https://opensource.org/licenses/lgpl-3.0.html * -* @see https://openhome.cc/eGossip/OpenSCAD/lib-m_mirror.html +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-m_mirror.html * **/ diff --git a/src/matrix/m_rotation.scad b/src/matrix/m_rotation.scad new file mode 100644 index 00000000..c40a554b --- /dev/null +++ b/src/matrix/m_rotation.scad @@ -0,0 +1,14 @@ +/** +* m_rotation.scad +* +* @copyright Justin Lin, 2019 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-m_rotation.html +* +**/ + +include <__comm__/__to_ang_vect.scad>; +include ; + +function m_rotation(a, v) = __m_rotation(a, v); \ No newline at end of file diff --git a/src/matrix/m_scaling.scad b/src/matrix/m_scaling.scad new file mode 100644 index 00000000..f4d1f292 --- /dev/null +++ b/src/matrix/m_scaling.scad @@ -0,0 +1,13 @@ +/** +* m_scaling.scad +* +* @copyright Justin Lin, 2019 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-m_scaling.html +* +**/ + +include ; + +function m_scaling(s) = __m_scaling(s); \ No newline at end of file diff --git a/src/m_shearing.scad b/src/matrix/m_shearing.scad similarity index 65% rename from src/m_shearing.scad rename to src/matrix/m_shearing.scad index 84b20db2..3602715d 100644 --- a/src/m_shearing.scad +++ b/src/matrix/m_shearing.scad @@ -4,10 +4,10 @@ * @copyright Justin Lin, 2019 * @license https://opensource.org/licenses/lgpl-3.0.html * -* @see https://openhome.cc/eGossip/OpenSCAD/lib-m_shearing.html +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-m_shearing.html * **/ -include <__private__/__m_shearing.scad>; +include ; function m_shearing(sx = [0, 0], sy = [0, 0], sz = [0, 0]) = __m_shearing(sx, sy, sz); \ No newline at end of file diff --git a/src/m_translation.scad b/src/matrix/m_translation.scad similarity index 69% rename from src/m_translation.scad rename to src/matrix/m_translation.scad index 04f19335..9ca23a83 100644 --- a/src/m_translation.scad +++ b/src/matrix/m_translation.scad @@ -4,19 +4,17 @@ * @copyright Justin Lin, 2019 * @license https://opensource.org/licenses/lgpl-3.0.html * -* @see https://openhome.cc/eGossip/OpenSCAD/lib-m_translation.html +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-m_translation.html * **/ -include <__private__/__is_float.scad>; - function _to_3_elems_translation_vect(v) = let(leng = len(v)) leng == 3 ? v : ( leng == 2 ? [v[0], v[1], 0] : [v[0], 0, 0] ); -function _to_translation_vect(v) = __is_float(v) ? [v, 0, 0] : _to_3_elems_translation_vect(v); +function _to_translation_vect(v) = is_num(v) ? [v, 0, 0] : _to_3_elems_translation_vect(v); function m_translation(v) = let(vt = _to_translation_vect(v)) diff --git a/src/midpt_smooth.scad b/src/midpt_smooth.scad index ac816c12..ffefd922 100644 --- a/src/midpt_smooth.scad +++ b/src/midpt_smooth.scad @@ -8,14 +8,17 @@ * **/ -function _midpt_smooth_sub(points, iend, i, closed = false) = - i == iend ? ( - closed ? [(points[i] + points[0]) / 2] - : [] - ) : concat([(points[i] + points[i + 1]) / 2], _midpt_smooth_sub(points, iend, i + 1, closed)); +function _midpt_smooth_sub(points, iend, closed = false) = + concat( + [ + for(i = 0; i < iend; i = i + 1) + (points[i] + points[i + 1]) / 2 + ], + closed ? [(points[iend] + points[0]) / 2] : [] + ); function midpt_smooth(points, n, closed = false) = let( - smoothed = _midpt_smooth_sub(points, len(points) - 1, 0, closed) + smoothed = _midpt_smooth_sub(points, len(points) - 1, closed) ) n == 1 ? smoothed : midpt_smooth(smoothed, n - 1, closed); \ No newline at end of file diff --git a/src/path_extrude.scad b/src/path_extrude.scad index 61303d33..90fefdbe 100644 --- a/src/path_extrude.scad +++ b/src/path_extrude.scad @@ -8,13 +8,9 @@ * **/ -include <__private__/__is_float.scad>; -include <__private__/__to3d.scad>; -include <__private__/__angy_angz.scad>; - -// Becuase of improving the performance, this module requires m_rotation.scad which doesn't require in dotSCAD 1.0. -// For backward compatibility, I directly include m_rotation here. -include ; +include <__comm__/__to3d.scad>; +include <__comm__/__angy_angz.scad>; +include ; module path_extrude(shape_pts, path_pts, triangles = "SOLID", twist = 0, scale = 1.0, closed = false, method = "AXIS_ANGLE") { sh_pts = len(shape_pts[0]) == 3 ? shape_pts : [for(p = shape_pts) __to3d(p)]; @@ -23,7 +19,6 @@ module path_extrude(shape_pts, path_pts, triangles = "SOLID", twist = 0, scale = len_path_pts = len(pth_pts); len_path_pts_minus_one = len_path_pts - 1; - module axis_angle_path_extrude() { twist_step_a = twist / len_path_pts; @@ -36,36 +31,32 @@ module path_extrude(shape_pts, path_pts, triangles = "SOLID", twist = 0, scale = ]; function rotate_pts(pts, a, v) = [for(p = pts) rotate_p(p, a, v)]; - - function scale_step() = - let(s = (scale - 1) / len_path_pts_minus_one) - [s, s, s]; - scale_step_vt = __is_float(scale) ? - scale_step() : + scale_step_vt = is_num(scale) ? + let(s = (scale - 1) / len_path_pts_minus_one) [s, s, s] : [ (scale[0] - 1) / len_path_pts_minus_one, (scale[1] - 1) / len_path_pts_minus_one, - scale[2] == undef ? 0 : (scale[2] - 1) / len_path_pts_minus_one + is_undef(scale[2]) ? 0 : (scale[2] - 1) / len_path_pts_minus_one ]; // get rotation matrice for sections function local_ang_vects(j) = - j == 0 ? [] : local_ang_vects_sub(j); - - function local_ang_vects_sub(j) = - let( - vt0 = pth_pts[j] - pth_pts[j - 1], - vt1 = pth_pts[j + 1] - pth_pts[j], - a = acos((vt0 * vt1) / (norm(vt0) * norm(vt1))), - v = cross(vt0, vt1) - ) - concat([[a, v]], local_ang_vects(j - 1)); + [ + for(i = j; i > 0; i = i - 1) + let( + vt0 = pth_pts[i] - pth_pts[i - 1], + vt1 = pth_pts[i + 1] - pth_pts[i], + a = acos((vt0 * vt1) / (norm(vt0) * norm(vt1))), + v = cross(vt0, vt1) + ) + [a, v] + ]; rot_matrice = [ for(ang_vect = local_ang_vects(len_path_pts - 2)) - m_rotation(ang_vect[0], ang_vect[1]) + __m_rotation(ang_vect[0], ang_vect[1]) ]; leng_rot_matrice = len(rot_matrice); @@ -133,40 +124,36 @@ module path_extrude(shape_pts, path_pts, triangles = "SOLID", twist = 0, scale = ] ]; - function sections() = + sections = let( fst_section = translate_pts(local_rotate_section(0, 0, [1, 1, 1]), pth_pts[0]), + end_i = len_path_pts - 1, remain_sections = [ - for(i = [0:len_path_pts - 2]) - + for(i = 0; i < end_i; i = i + 1) translate_pts( local_rotate_section(i, i * twist_step_a, [1, 1, 1] + scale_step_vt * i), pth_pts[i + 1] ) - - ] ) concat([fst_section], remain_sections); - - sects = sections(); - function calculated_sections() = + calculated_sections = closed && pth_pts[0] == pth_pts[len_path_pts_minus_one] ? - concat(sects, [sects[0]]) : // round-robin - sects; + concat(sections, [sections[0]]) : // round-robin + sections; polysections( - calculated_sections(), + calculated_sections, triangles = triangles ); // hook for testing - test_path_extrude(sects); + test_path_extrude(sections); } module euler_angle_path_extrude() { - scale_step_vt = __is_float(scale) ? + scale_step_vt = is_num(scale) ? [(scale - 1) / len_path_pts_minus_one, (scale - 1) / len_path_pts_minus_one] : [(scale[0] - 1) / len_path_pts_minus_one, (scale[1] - 1) / len_path_pts_minus_one]; @@ -192,28 +179,24 @@ module path_extrude(shape_pts, path_pts, triangles = "SOLID", twist = 0, scale = ) + p1 ]; - function path_extrude_inner(index) = - index == len_path_pts ? [] : - concat( - [section(pth_pts[index - 1], pth_pts[index], index)], - path_extrude_inner(index + 1) - ); + path_extrude_inner = + [ + for(i = 1; i < len_path_pts; i = i + 1) + section(pth_pts[i - 1], pth_pts[i], i) + ]; - function calculated_sections() = - let(sections = path_extrude_inner(1)) + calculated_sections = closed && pth_pts[0] == pth_pts[len_path_pts_minus_one] ? - concat(sections, [sections[0]]) : // round-robin - concat([section(pth_pts[0], pth_pts[1], 0)], sections); - - sections = calculated_sections(); + concat(path_extrude_inner, [path_extrude_inner[0]]) : // round-robin + concat([section(pth_pts[0], pth_pts[1], 0)], path_extrude_inner); polysections( - sections, + calculated_sections, triangles = triangles ); // hook for testing - test_path_extrude(sections); + test_path_extrude(calculated_sections); } if(method == "AXIS_ANGLE") { @@ -224,7 +207,6 @@ module path_extrude(shape_pts, path_pts, triangles = "SOLID", twist = 0, scale = } } - // override to test module test_path_extrude(sections) { diff --git a/src/path_scaling_sections.scad b/src/path_scaling_sections.scad index 7a903367..a3cdabde 100644 --- a/src/path_scaling_sections.scad +++ b/src/path_scaling_sections.scad @@ -8,7 +8,8 @@ * **/ -include <__private__/__reverse.scad>; +include ; +include ; function path_scaling_sections(shape_pts, edge_path) = let( @@ -17,11 +18,12 @@ function path_scaling_sections(shape_pts, edge_path) = scaling_matrice = [ for(p = edge_path) let(s = norm([p[0], p[1], 0]) / base_leng) - m_scaling([s, s, 1]) - ] + __m_scaling([s, s, 1]) + ], + leng_edge_path = len(edge_path) ) __reverse([ - for(i = [0:len(edge_path) - 1]) + for(i = 0; i < leng_edge_path; i = i + 1) [ for(p = shape_pts) let(scaled_p = scaling_matrice[i] * [p[0], p[1], edge_path[i][2], 1]) diff --git a/src/paths2sections.scad b/src/paths2sections.scad index c7eb55b2..56b3b562 100644 --- a/src/paths2sections.scad +++ b/src/paths2sections.scad @@ -14,9 +14,9 @@ function paths2sections(paths) = leng_paths = len(paths) ) [ - for(i = [0:leng_path - 1]) + for(i = 0; i < leng_path; i = i + 1) [ - for(j = [0:leng_paths - 1]) + for(j = 0; j < leng_paths; j = j + 1) paths[j][i] ] ]; \ No newline at end of file diff --git a/src/pie.scad b/src/pie.scad index c8f735ae..37364c08 100644 --- a/src/pie.scad +++ b/src/pie.scad @@ -8,10 +8,9 @@ * **/ -include <__private__/__frags.scad>; -include <__private__/__is_float.scad>; -include <__private__/__ra_to_xy.scad>; -include <__private__/__shape_pie.scad>; +include <__comm__/__frags.scad>; +include <__comm__/__ra_to_xy.scad>; +include <__comm__/__shape_pie.scad>; module pie(radius, angle) { polygon(__shape_pie(radius, angle)); diff --git a/src/pixel/px_circle.scad b/src/pixel/px_circle.scad new file mode 100644 index 00000000..45982054 --- /dev/null +++ b/src/pixel/px_circle.scad @@ -0,0 +1,64 @@ +/** +* px_circle.scad +* +* @copyright Justin Lin, 2019 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-px_circle.html +* +**/ + +function _px_circle_y(f, y) = f >= 0 ? y - 1 : y; +function _px_circle_ddf_y(f, ddf_y) = f >= 0 ? ddf_y + 2 : ddf_y; +function _px_circle_f(f, ddf_y) = f >= 0 ? f + ddf_y : f; + +function _px_circle(f, ddf_x, ddf_y, x, y, filled) = + x >= y ? [] : + let( + ny = _px_circle_y(f, y), + nddf_y = _px_circle_ddf_y(f, ddf_y), + nx = x + 1, + nddf_x = ddf_x + 2, + nf = _px_circle_f(f, ddf_y) + nddf_x + ) + concat( + filled ? + concat( + [for(xi = -nx; xi <= nx; xi = xi + 1) [xi, -ny]], + [for(xi = -ny; xi <= ny; xi = xi + 1) [xi, -nx]], + [for(xi = -ny; xi <= ny; xi = xi + 1) [xi, nx]], + [for(xi = -nx; xi <= nx; xi = xi + 1) [xi, ny]] + ) + : + [ + [-nx, -ny], [nx, -ny], + [-ny, -nx], [ny, -nx], + [-ny, nx], [ny, nx], + [-nx, ny], [nx, ny] + ], + _px_circle(nf, nddf_x, nddf_y, nx, ny, filled) + ); + +function px_circle(radius, filled = false) = + let( + f = 1 - radius, + ddf_x = 1, + ddf_y = -2 * radius, + x = 0, + y = radius + ) + concat( + filled ? + concat( + [[0, radius], [0, -radius]], + [for(xi = -radius; xi <= radius; xi = xi + 1) [xi, 0]] + ) + : + [ + [0, -radius], + [-radius, 0], + [radius, 0], + [0, radius] + ], + _px_circle(f, ddf_x, ddf_y, x, y, filled) + ); \ No newline at end of file diff --git a/src/pixel/px_cylinder.scad b/src/pixel/px_cylinder.scad new file mode 100644 index 00000000..7f7309fd --- /dev/null +++ b/src/pixel/px_cylinder.scad @@ -0,0 +1,59 @@ +/** +* px_cylinder.scad +* +* @copyright Justin Lin, 2019 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-px_cylinder.html +* +**/ + +function _px_cylinder_px_circle(radius, filled, thickness) = + let(range = [-radius: radius - 1]) + filled ? [ + for(y = range) + for(x = range) + let(v = [x, y]) + if(norm(v) < radius) v + ] : + let(ishell = radius * radius - 2 * thickness * radius) + [ + for(y = range) + for(x = range) + let( + v = [x, y], + leng = norm(v) + ) + if(leng < radius && (leng * leng) > ishell) v + ]; + +function _px_cylinder_diff_r(r, h, filled, thickness) = + let( + r1 = r[0], + r2 = r[1] + ) + r1 == r2 ? _px_cylinder_same_r(r1, h, filled, thickness) : + let(dr = (r2 - r1) / (h - 1)) + [ + for(i = 0; i < h; i = i + 1) + let(r = round(r1 + dr * i)) + each [ + for(pt = _px_cylinder_px_circle(r, filled, thickness)) + [pt[0], pt[1], i] + ] + ]; + +function _px_cylinder_same_r(r, h, filled, thickness) = + let(c = _px_cylinder_px_circle(r, filled, thickness)) + [ + for(i = 0; i < h; i = i + 1) + each [ + for(pt = c) + [pt[0], pt[1], i] + ] + ]; + +function px_cylinder(r, h, filled = false, thickness = 1) = + is_num(r) ? + _px_cylinder_same_r(r, h, filled, thickness) : + _px_cylinder_diff_r(r, h, filled, thickness); \ No newline at end of file diff --git a/src/pixel/px_line.scad b/src/pixel/px_line.scad new file mode 100644 index 00000000..ccb5cb36 --- /dev/null +++ b/src/pixel/px_line.scad @@ -0,0 +1,211 @@ +/** +* px_line.scad +* +* @copyright Justin Lin, 2019 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-px_line.html +* +**/ + +include <__comm__/__to3d.scad>; +include <__comm__/__to2d.scad>; + +function _px_line_zsgn(a) = a == 0 ? a : a / abs(a); + +// x-dominant +function _px_line_xdominant_y(y, yd, sy) = yd >= 0 ? y + sy : y; +function _px_line_xdominant_yd(yd, ax, ay) = (yd >= 0 ? yd - ax : yd) + ay; +function _px_line_xdominant_z(z, zd, sz) = zd >= 0 ? z + sz : z; +function _px_line_xdominant_zd(zd, ax, az) = (zd >= 0 ? zd - ax : zd) + az; + +function _px_line_xdominant(start, end, a, s) = + let( + x = start[0], + y = start[1], + z = start[2], + ax = a[0], + ay = a[1], + az = a[2], + sx = s[0], + sy = s[1], + sz = s[2], + shrx = floor(ax / 2), + yd = ay - shrx, + zd = az - shrx, + endx = end[0] + ) + concat( + [start], + _px_line_xdominant_sub( + x + sx, + _px_line_xdominant_y(y, yd, sy), + _px_line_xdominant_z(z, zd, sz), + endx, + a, + s, + _px_line_xdominant_yd(yd, ax, ay), + _px_line_xdominant_zd(zd, ax, az) + ) + ); + +function _px_line_xdominant_sub(x, y, z, endx, a, s, yd, zd) = + let( + ax = a[0], + ay = a[1], + az = a[2], + sx = s[0], + sy = s[1], + sz = s[2] + ) + x == endx ? [] : + concat([[x, y, z]], + _px_line_xdominant_sub( + x + sx, + _px_line_xdominant_y(y, yd, sy), + _px_line_xdominant_z(z, zd, sz), + endx, + a, + s, + _px_line_xdominant_yd(yd, ax, ay), + _px_line_xdominant_zd(zd, ax, az) + ) + ); + +// y-dominant +function _px_line_ydominant_x(x, xd, sx) = xd >= 0 ? x + sx : x; +function _px_line_ydominant_xd(xd, ax, ay) = (xd >= 0 ? xd - ay : xd) + ax; +function _px_line_ydominant_z(z, zd, sz) = zd >= 0 ? z + sz : z; +function _px_line_ydominant_zd(zd, ay, az) = (zd >= 0 ? zd - ay : zd) + az; + +function _px_line_ydominant(start, end, a, s) = + let( + x = start[0], + y = start[1], + z = start[2], + ax = a[0], + ay = a[1], + az = a[2], + sx = s[0], + sy = s[1], + sz = s[2], + shry = floor(ay / 2), + xd = ax - shry, + zd = az - shry, + endy = end[1] + ) + concat( + [start], + _px_line_ydominant_sub( + _px_line_ydominant_x(x, xd, sx), + y + sy, + _px_line_ydominant_z(z, zd, sz), + endy, + a, + s, + _px_line_ydominant_xd(xd, ax, ay), + _px_line_ydominant_zd(zd, ay, az) + ) + ); + +function _px_line_ydominant_sub(x, y, z, endy, a, s, xd, zd) = + let( + ax = a[0], + ay = a[1], + az = a[2], + sx = s[0], + sy = s[1], + sz = s[2] + ) + y == endy ? [] : + concat([[x, y, z]], + _px_line_ydominant_sub( + _px_line_ydominant_x(x, xd, sx), + y + sy, + _px_line_ydominant_z(z, zd, sz), + endy, + a, + s, + _px_line_ydominant_xd(xd, ax, ay), + _px_line_ydominant_zd(zd, ay, az) + ) + ); + +// z-dominant +function _px_line_zdominant_x(x, xd, sx) = xd >= 0 ? x + sx : x; +function _px_line_zdominant_xd(xd, ax, az) = (xd >= 0 ? xd - az : xd) + ax; + +function _px_line_zdominant_y(y, yd, sy) = yd >= 0 ? y + sy : y; +function _px_line_zdominant_yd(yd, ay, az) = (yd >= 0 ? yd - az : yd) + ay; + +function _px_line_zdominant(start, end, a, s) = + let( + x = start[0], + y = start[1], + z = start[2], + ax = a[0], + ay = a[1], + az = a[2], + sx = s[0], + sy = s[1], + sz = s[2], + shrz = floor(az / 2), + xd = ax - shrz, + yd = ay - shrz, + endz = end[2] + ) + concat( + [start], + _px_line_zdominant_sub( + _px_line_zdominant_x(x, xd, sx), + _px_line_zdominant_y(y, yd, sy), + z + sz, + endz, + a, + s, + _px_line_zdominant_xd(xd, ax, az), + _px_line_zdominant_yd(yd, ay, az) + ) + ); + +function _px_line_zdominant_sub(x, y, z, endz, a, s, xd, yd) = + let( + ax = a[0], + ay = a[1], + az = a[2], + sx = s[0], + sy = s[1], + sz = s[2] + ) + z == endz ? [] : + concat([[x, y, z]], + _px_line_zdominant_sub( + _px_line_zdominant_x(x, xd, sx), + _px_line_zdominant_y(y, yd, sy), + z + sz, + endz, + a, + s, + _px_line_zdominant_xd(xd, ax, az), + _px_line_zdominant_yd(yd, ay, az) + ) + ); + +function px_line(p1, p2) = + let( + is_2d = len(p1) == 2, + start_pt = is_2d ? __to3d(p1) : p1, + end_pt = is_2d ? __to3d(p2) : p2, + dt = end_pt - start_pt, + ax = floor(abs(dt[0]) * 2), + ay = floor(abs(dt[1]) * 2), + az = floor(abs(dt[2]) * 2), + sx = _px_line_zsgn(dt[0]), + sy = _px_line_zsgn(dt[1]), + sz = _px_line_zsgn(dt[2]), + points = ax >= max(ay, az) ? _px_line_xdominant(start_pt, end_pt, [ax, ay, az], [sx, sy, sz]) : ( + ay >= max(ax, az) ? _px_line_ydominant(start_pt, end_pt, [ax, ay, az], [sx, sy, sz]) : + _px_line_zdominant(start_pt, end_pt, [ax, ay, az], [sx, sy, sz]) + ) + ) + is_2d ? [for(pt = points) __to2d(pt)] : points; \ No newline at end of file diff --git a/src/pixel/px_polygon.scad b/src/pixel/px_polygon.scad new file mode 100644 index 00000000..60b04452 --- /dev/null +++ b/src/pixel/px_polygon.scad @@ -0,0 +1,31 @@ +/** +* px_polygon.scad +* +* @copyright Justin Lin, 2019 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-px_polygon.html +* +**/ + +function px_polygon(points, filled = false) = + filled ? + let( + xs = [for(pt = points) pt[0]], + ys = [for(pt = points) pt[1]], + max_x = max(xs), + min_x = min(xs), + max_y = max(ys), + min_y = min(ys) + ) + [ + for(y = min_y; y <= max_y; y = y + 1) + for(x = min_x; x <= max_x; x = x + 1) + let(pt = [x, y]) + if(in_shape(points, pt, true)) pt + ] + : + px_polyline( + concat(points, [points[len(points) - 1], points[0]]) + ); + \ No newline at end of file diff --git a/src/pixel/px_polyline.scad b/src/pixel/px_polyline.scad new file mode 100644 index 00000000..4ce16efb --- /dev/null +++ b/src/pixel/px_polyline.scad @@ -0,0 +1,21 @@ +/** +* px_polyline.scad +* +* @copyright Justin Lin, 2019 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-px_polyline.html +* +**/ + +include <__comm__/__to3d.scad>; +include <__comm__/__to2d.scad>; +include <__comm__/__lines_from.scad>; + +function px_polyline(points) = + let( + is_2d = len(points[0]) == 2, + pts = is_2d ? [for(pt = points) __to3d(pt)] : points, + polyline = [for(line = __lines_from(pts)) each px_line(line[0], line[1])] + ) + is_2d ? [for(pt = polyline) __to2d(pt)] : polyline; \ No newline at end of file diff --git a/src/pixel/px_sphere.scad b/src/pixel/px_sphere.scad new file mode 100644 index 00000000..de62b2e6 --- /dev/null +++ b/src/pixel/px_sphere.scad @@ -0,0 +1,31 @@ +/** +* px_sphere.scad +* +* @copyright Justin Lin, 2019 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-px_sphere.html +* +**/ + +function px_sphere(radius, filled = false, thickness = 1) = + let(range = [-radius: radius - 1]) + filled ? [ + for(z = range) + for(y = range) + for(x = range) + let(v = [x, y, z]) + if(norm(v) < radius) v + ] : + let(ishell = radius * radius - 2 * thickness * radius) + [ + for(z = range) + for(y = range) + for(x = range) + let( + v = [x, y, z], + leng = norm(v) + ) + if(leng < radius && (leng * leng) > ishell) v + ]; + \ No newline at end of file diff --git a/src/polysections.scad b/src/polysections.scad index 6625959f..23ed3cbb 100644 --- a/src/polysections.scad +++ b/src/polysections.scad @@ -8,19 +8,21 @@ * **/ -include <__private__/__reverse.scad>; +include ; module polysections(sections, triangles = "SOLID") { function side_indexes(sects, begin_idx = 0) = let( leng_sects = len(sects), - leng_pts_sect = len(sects[0]) + leng_pts_sect = len(sects[0]), + range_j = [begin_idx:leng_pts_sect:begin_idx + (leng_sects - 2) * leng_pts_sect], + range_i = [0:leng_pts_sect - 1] ) concat( [ - for(j = [begin_idx:leng_pts_sect:begin_idx + (leng_sects - 2) * leng_pts_sect]) - for(i = [0:leng_pts_sect - 1]) + for(j = range_j) + for(i = range_i) [ j + i, j + (i + 1) % leng_pts_sect, @@ -28,8 +30,8 @@ module polysections(sections, triangles = "SOLID") { ] ], [ - for(j = [begin_idx:leng_pts_sect:begin_idx + (leng_sects - 2) * leng_pts_sect]) - for(i = [0:leng_pts_sect - 1]) + for(j = range_j) + for(i = range_i) [ j + i, j + (i + 1) % leng_pts_sect + leng_pts_sect , @@ -38,7 +40,7 @@ module polysections(sections, triangles = "SOLID") { ] ); - function search_at(f_sect, p, leng_pts_sect, i = 0) = + function search_at(f_sect, p, leng_pts_sect, i = 0) = i < leng_pts_sect ? (p == f_sect[i] ? i : search_at(f_sect, p, leng_pts_sect, i + 1)) : -1; @@ -48,8 +50,8 @@ module polysections(sections, triangles = "SOLID") { ) found_at_i <= 0 ? false : l_sect == concat( - [for(i = [found_at_i:leng_pts_sect-1]) f_sect[i]], - [for(i = [0:found_at_i - 1]) f_sect[i]] + [for(i = found_at_i; i < leng_pts_sect; i = i + 1) f_sect[i]], + [for(i = 0; i < found_at_i; i = i + 1) f_sect[i]] ); function to_v_pts(sects) = @@ -72,11 +74,11 @@ module polysections(sections, triangles = "SOLID") { pt ]; - function begin_end_the_same() = + begin_end_the_same = first_sect == last_sect || the_same_after_twisting(first_sect, last_sect, leng_pts_sect); - if(begin_end_the_same()) { + if(begin_end_the_same) { f_idxes = side_indexes(sects); polyhedron( @@ -87,9 +89,10 @@ module polysections(sections, triangles = "SOLID") { // hook for testing test_polysections_solid(v_pts, f_idxes); } else { - first_idxes = [for(i = [0:leng_pts_sect - 1]) leng_pts_sect - 1 - i]; + range_i = [0:leng_pts_sect - 1]; + first_idxes = [for(i = range_i) leng_pts_sect - 1 - i]; last_idxes = [ - for(i = [0:leng_pts_sect - 1]) + for(i = range_i) i + leng_pts_sect * (leng_sects - 1) ]; @@ -113,16 +116,16 @@ module polysections(sections, triangles = "SOLID") { function strip_sects(begin_idx, end_idx) = [ - for(i = [0:leng_sects - 1]) + for(i = 0; i < leng_sects; i = i + 1) [ - for(j = [begin_idx:end_idx]) + for(j = begin_idx; j <= end_idx; j = j + 1) sects[i][j] ] ]; function first_idxes() = [ - for(i = [0:half_leng_sect - 1]) + for(i = 0; i < half_leng_sect; i = i + 1) [ i, i + half_leng_v_pts, @@ -133,7 +136,7 @@ module polysections(sections, triangles = "SOLID") { function last_idxes(begin_idx) = [ - for(i = [0:half_leng_sect - 1]) + for(i = 0; i < half_leng_sect; i = i + 1) [ begin_idx + i, begin_idx + (i + 1) % half_leng_sect, @@ -161,7 +164,7 @@ module polysections(sections, triangles = "SOLID") { leng_pts_sect = len(first_outer_sect); - function begin_end_the_same() = + begin_end_the_same = (first_outer_sect == last_outer_sect && first_inner_sect == last_inner_sect) || ( the_same_after_twisting(first_outer_sect, last_outer_sect, leng_pts_sect) && @@ -170,7 +173,7 @@ module polysections(sections, triangles = "SOLID") { v_pts = concat(outer_v_pts, inner_v_pts); - if(begin_end_the_same()) { + if(begin_end_the_same) { f_idxes = concat(outer_idxes, inner_idxes); polyhedron( diff --git a/src/polytransversals.scad b/src/polytransversals.scad index 6022d2e8..68dd00d1 100644 --- a/src/polytransversals.scad +++ b/src/polytransversals.scad @@ -8,8 +8,8 @@ * **/ -include <__private__/__reverse.scad>; -include <__private__/__polytransversals.scad>; +include ; +include <__comm__/__polytransversals.scad>; module polytransversals(transversals) { polygon( diff --git a/src/ring_extrude.scad b/src/ring_extrude.scad index 9d92ab66..5af1e557 100644 --- a/src/ring_extrude.scad +++ b/src/ring_extrude.scad @@ -8,18 +8,18 @@ * **/ -include <__private__/__frags.scad>; -include <__private__/__ra_to_xy.scad>; +include <__comm__/__frags.scad>; +include <__comm__/__ra_to_xy.scad>; module ring_extrude(shape_pts, radius, angle = 360, twist = 0, scale = 1.0, triangles = "SOLID") { - if(angle == 360 && twist == 0 && scale == 1.0) { - rotate_extrude() + if(twist == 0 && scale == 1.0) { + rotate_extrude(angle = angle) translate([radius, 0, 0]) polygon(shape_pts); } else { a_step = 360 / __frags(radius); - angles = __is_float(angle) ? [0, angle] : angle; + angles = is_num(angle) ? [0, angle] : angle; m = floor(angles[0] / a_step) + 1; n = floor(angles[1] / a_step); diff --git a/src/rotate_p.scad b/src/rotate_p.scad index fb3b9cf8..b49f965f 100644 --- a/src/rotate_p.scad +++ b/src/rotate_p.scad @@ -8,10 +8,9 @@ * **/ -include <__private__/__to2d.scad>; -include <__private__/__to3d.scad>; -include <__private__/__is_float.scad>; -include <__private__/__to_ang_vect.scad>; +include <__comm__/__to2d.scad>; +include <__comm__/__to3d.scad>; +include <__comm__/__to_ang_vect.scad>; function _q_rotate_p_3d(p, a, v) = let( @@ -87,4 +86,4 @@ function _q_rotate_p(p, a, v) = ); function rotate_p(point, a, v) = - v == undef ? _rotate_p(point, a) : _q_rotate_p(point, a, v); + is_undef(v) ? _rotate_p(point, a) : _q_rotate_p(point, a, v); diff --git a/src/rounded_cube.scad b/src/rounded_cube.scad index 2c80bb74..f3be8d2d 100644 --- a/src/rounded_cube.scad +++ b/src/rounded_cube.scad @@ -8,12 +8,11 @@ * **/ -include <__private__/__is_float.scad>; -include <__private__/__frags.scad>; -include <__private__/__nearest_multiple_of_4.scad>; +include <__comm__/__frags.scad>; +include <__comm__/__nearest_multiple_of_4.scad>; module rounded_cube(size, corner_r, center = false) { - is_flt = __is_float(size); + is_flt = is_num(size); x = is_flt ? size : size[0]; y = is_flt ? size : size[1]; z = is_flt ? size : size[2]; diff --git a/src/rounded_cylinder.scad b/src/rounded_cylinder.scad index 124d0dd7..6d062f5c 100644 --- a/src/rounded_cylinder.scad +++ b/src/rounded_cylinder.scad @@ -8,10 +8,9 @@ * **/ -include <__private__/__is_float.scad>; -include <__private__/__frags.scad>; -include <__private__/__pie_for_rounding.scad>; -include <__private__/__half_trapezium.scad>; +include <__comm__/__frags.scad>; +include <__comm__/__pie_for_rounding.scad>; +include <__comm__/__half_trapezium.scad>; module rounded_cylinder(radius, h, round_r, convexity = 2, center = false) { r_corners = __half_trapezium(radius, h, round_r); diff --git a/src/rounded_extrude.scad b/src/rounded_extrude.scad index badf6af9..a2aff45d 100644 --- a/src/rounded_extrude.scad +++ b/src/rounded_extrude.scad @@ -8,12 +8,11 @@ * **/ -include <__private__/__frags.scad>; -include <__private__/__is_float.scad>; +include <__comm__/__frags.scad>; module rounded_extrude(size, round_r, angle = 90, twist = 0, convexity = 10) { - is_flt = __is_float(size); + is_flt = is_num(size); x = is_flt ? size : size[0]; y = is_flt ? size : size[1]; diff --git a/src/rounded_square.scad b/src/rounded_square.scad index 3c8a1399..22bfce1e 100644 --- a/src/rounded_square.scad +++ b/src/rounded_square.scad @@ -8,14 +8,13 @@ * **/ -include <__private__/__is_float.scad>; -include <__private__/__frags.scad>; -include <__private__/__pie_for_rounding.scad>; -include <__private__/__half_trapezium.scad>; -include <__private__/__trapezium.scad>; +include <__comm__/__frags.scad>; +include <__comm__/__pie_for_rounding.scad>; +include <__comm__/__half_trapezium.scad>; +include <__comm__/__trapezium.scad>; module rounded_square(size, corner_r, center = false) { - is_flt = __is_float(size); + is_flt = is_num(size); x = is_flt ? size : size[0]; y = is_flt ? size : size[1]; diff --git a/src/shape_arc.scad b/src/shape_arc.scad index bcf0ceb1..4730620e 100644 --- a/src/shape_arc.scad +++ b/src/shape_arc.scad @@ -8,11 +8,10 @@ * **/ -include <__private__/__frags.scad>; -include <__private__/__is_float.scad>; -include <__private__/__ra_to_xy.scad>; -include <__private__/__shape_arc.scad>; -include <__private__/__edge_r.scad> +include <__comm__/__frags.scad>; +include <__comm__/__ra_to_xy.scad>; +include <__comm__/__shape_arc.scad>; +include <__comm__/__edge_r.scad> function shape_arc(radius, angle, width, width_mode = "LINE_CROSS") = __shape_arc(radius, angle, width, width_mode); \ No newline at end of file diff --git a/src/shape_cyclicpolygon.scad b/src/shape_cyclicpolygon.scad index d4a3be54..9798b5ec 100644 --- a/src/shape_cyclicpolygon.scad +++ b/src/shape_cyclicpolygon.scad @@ -8,8 +8,8 @@ * **/ -include <__private__/__frags.scad>; -include <__private__/__pie_for_rounding.scad>; +include <__comm__/__frags.scad>; +include <__comm__/__pie_for_rounding.scad>; function shape_cyclicpolygon(sides, circle_r, corner_r) = let( @@ -34,7 +34,7 @@ function shape_cyclicpolygon(sides, circle_r, corner_r) = concat( first_corner, [ - for(side = [1:sides - 1]) + for(side = 1; side < sides; side = side + 1) for(pt = first_corner) let( a = frag_a * side, diff --git a/src/shape_ellipse.scad b/src/shape_ellipse.scad index e7ed4548..1951ca4d 100644 --- a/src/shape_ellipse.scad +++ b/src/shape_ellipse.scad @@ -8,14 +8,15 @@ * **/ -include <__private__/__frags.scad>; +include <__comm__/__frags.scad>; function shape_ellipse(axes) = let( frags = __frags(axes[0]), step_a = 360 / frags, + a_end = 360 - step_a, shape_pts = [ - for(a = [0:step_a:360 - step_a]) + for(a = 0; a <= a_end; a = a + step_a) [axes[0] * cos(a), axes[1] * sin(a)] ] ) shape_pts; \ No newline at end of file diff --git a/src/shape_glued2circles.scad b/src/shape_glued2circles.scad index 73318d19..28446aa0 100644 --- a/src/shape_glued2circles.scad +++ b/src/shape_glued2circles.scad @@ -12,10 +12,11 @@ function _glued2circles_pie_curve(radius, centre_dist, tangent_angle) = let( begin_ang = 90 + tangent_angle, - shape_pts = shape_pie(radius, [-begin_ang, begin_ang]) + shape_pts = shape_pie(radius, [-begin_ang, begin_ang]), + leng = len(shape_pts) ) [ - for(i = [1:len(shape_pts) - 1]) + for(i = 1; i < leng; i = i + 1) shape_pts[i] + [centre_dist / 2, 0] ]; @@ -36,15 +37,12 @@ function _glued2circles_bezier(radius, centre_dist, tangent_angle, t_step, ctrl_ ] ); -function _glued2circles_lower_half_curve(curve_pts, leng, i = 0) = - i < leng ? ( - curve_pts[leng - 1 - i][0] >= 0 ? - concat( - [curve_pts[leng - 1 - i]], - _glued2circles_lower_half_curve(curve_pts, leng, i + 1) - ) : - _glued2circles_lower_half_curve(curve_pts, leng, i + 1) - ) : []; +function _glued2circles_lower_half_curve(curve_pts, leng) = + [ + for(i = 0; i < leng; i = i + 1) + let(p = curve_pts[leng - 1 - i]) + if(p[0] >= 0) p + ]; function _glued2circles_half_glued_circle(radius, centre_dist, tangent_angle, t_step) = let( @@ -53,7 +51,7 @@ function _glued2circles_half_glued_circle(radius, centre_dist, tangent_angle, t_ lower_curve_pts = _glued2circles_lower_half_curve(curve_pts, len(curve_pts)), leng_half_curve_pts = len(lower_curve_pts), upper_curve_pts = [ - for(i = [0:leng_half_curve_pts - 1]) + for(i = 0; i < leng_half_curve_pts; i = i + 1) let(pt = lower_curve_pts[leng_half_curve_pts - 1 - i]) [pt[0], -pt[1]] ] @@ -68,7 +66,7 @@ function shape_glued2circles(radius, centre_dist, tangent_angle = 30, t_step = 0 half_glued_circles = _glued2circles_half_glued_circle(radius, centre_dist, tangent_angle, t_step), leng_half_glued_circles = len(half_glued_circles), left_half_glued_circles = [ - for(i = [0:leng_half_glued_circles - 1]) + for(i = 0; i < leng_half_glued_circles; i = i + 1) let(pt = half_glued_circles[leng_half_glued_circles - 1 - i]) [-pt[0], pt[1]] ] diff --git a/src/shape_path_extend.scad b/src/shape_path_extend.scad index b21a2548..0eac7f2e 100644 --- a/src/shape_path_extend.scad +++ b/src/shape_path_extend.scad @@ -8,9 +8,9 @@ * **/ -include <__private__/__to3d.scad>; -include <__private__/__polytransversals.scad>; -include <__private__/__reverse.scad>; +include <__comm__/__to3d.scad>; +include <__comm__/__polytransversals.scad>; +include ; function _shape_path_extend_az(p1, p2) = let( @@ -41,32 +41,23 @@ function _shape_path_extend_stroke(stroke_pts, p1, p2, scale_step, i) = rotate_p(p * (1 + scale_step * i) + [0, leng], a) + p1 ]; -function _shape_path_extend_inner(stroke_pts, path_pts, leng_path_pts, scale_step, index) = - index == leng_path_pts ? [] : - concat( - [ - _shape_path_extend_stroke( - stroke_pts, - path_pts[index - 1], - path_pts[index], - scale_step, - index - ) - ], - _shape_path_extend_inner( +function _shape_path_extend_inner(stroke_pts, path_pts, leng_path_pts, scale_step) = + [ + for(i = 1; i < leng_path_pts; i = i + 1) + _shape_path_extend_stroke( stroke_pts, - path_pts, - leng_path_pts, + path_pts[i - 1], + path_pts[i ], scale_step, - index + 1 + i ) - ); + ]; function shape_path_extend(stroke_pts, path_pts, scale = 1.0, closed = false) = let( leng_path_pts = len(path_pts), scale_step = (scale - 1) / (leng_path_pts - 1), - strokes = _shape_path_extend_inner(stroke_pts, path_pts, leng_path_pts, scale_step, 1) + strokes = _shape_path_extend_inner(stroke_pts, path_pts, leng_path_pts, scale_step) ) closed && path_pts[0] == path_pts[leng_path_pts - 1] ? __polytransversals(concat(strokes, [strokes[0]])) : diff --git a/src/shape_pie.scad b/src/shape_pie.scad index 3285573f..5c91858b 100644 --- a/src/shape_pie.scad +++ b/src/shape_pie.scad @@ -8,10 +8,9 @@ * **/ -include <__private__/__frags.scad>; -include <__private__/__is_float.scad>; -include <__private__/__ra_to_xy.scad>; -include <__private__/__shape_pie.scad>; +include <__comm__/__frags.scad>; +include <__comm__/__ra_to_xy.scad>; +include <__comm__/__shape_pie.scad>; function shape_pie(radius, angle) = __shape_pie(radius, angle); \ No newline at end of file diff --git a/src/shape_square.scad b/src/shape_square.scad index edea534b..f5364c36 100644 --- a/src/shape_square.scad +++ b/src/shape_square.scad @@ -8,15 +8,14 @@ * **/ -include <__private__/__is_float.scad>; -include <__private__/__frags.scad>; -include <__private__/__pie_for_rounding.scad>; -include <__private__/__half_trapezium.scad>; -include <__private__/__trapezium.scad>; +include <__comm__/__frags.scad>; +include <__comm__/__pie_for_rounding.scad>; +include <__comm__/__half_trapezium.scad>; +include <__comm__/__trapezium.scad>; function shape_square(size, corner_r = 0) = let( - is_flt = __is_float(size), + is_flt = is_num(size), x = is_flt ? size : size[0], y = is_flt ? size : size[1] ) diff --git a/src/shape_starburst.scad b/src/shape_starburst.scad index 6cc15710..ae3ee319 100644 --- a/src/shape_starburst.scad +++ b/src/shape_starburst.scad @@ -12,18 +12,19 @@ function __outer_points_shape_starburst(r1, r2, n) = let( a = 360 / n ) - [for(i = [0:n-1]) [r1 * cos(a * i), r1 * sin(a * i)]]; + [for(i = 0; i < n; i = i + 1) [r1 * cos(a * i), r1 * sin(a * i)]]; + function __inner_points_shape_starburst(r1, r2, n) = let ( a = 360 / n, half_a = a / 2 ) - [for(i = [0:n-1]) [r2 * cos(a * i + half_a), r2 * sin(a * i + half_a)]]; + [for(i = 0; i < n; i = i + 1) [r2 * cos(a * i + half_a), r2 * sin(a * i + half_a)]]; -function __one_by_one_shape_starburst(outer_points, inner_points, i = 0) = - len(outer_points) == i ? [] : - concat([outer_points[i], inner_points[i]], __one_by_one_shape_starburst(outer_points, inner_points, i + 1)); - -function shape_starburst(r1, r2, n) = __one_by_one_shape_starburst( - __outer_points_shape_starburst(r1, r2, n), __inner_points_shape_starburst(r1, r2, n) -); \ No newline at end of file +function shape_starburst(r1, r2, n) = + let( + outer_points = __outer_points_shape_starburst(r1, r2, n), + inner_points = __inner_points_shape_starburst(r1, r2, n), + leng = len(outer_points) + ) + [for(i = 0; i < leng; i = i + 1) each [outer_points[i], inner_points[i]]]; \ No newline at end of file diff --git a/src/shape_superformula.scad b/src/shape_superformula.scad index 169d0129..1211416c 100644 --- a/src/shape_superformula.scad +++ b/src/shape_superformula.scad @@ -8,8 +8,8 @@ * **/ -include <__private__/__ra_to_xy.scad>; -include <__private__/__to_degree.scad>; +include <__comm__/__ra_to_xy.scad>; +include <__comm__/__to_degree.scad>; function _superformula_r(angle, m1, m2, n1, n2 = 1, n3 = 1, a = 1, b = 1) = pow( @@ -19,12 +19,12 @@ function _superformula_r(angle, m1, m2, n1, n2 = 1, n3 = 1, a = 1, b = 1) = ); function shape_superformula(phi_step, m1, m2, n1, n2 = 1, n3 = 1, a = 1, b = 1) = + let(tau = PI * 2) [ - for(phi = [0:phi_step:6.28318]) + for(phi = 0; phi <= tau; phi = phi + phi_step) let( angle = __to_degree(phi), r = _superformula_r(angle, m1, m2, n1, n2, n3, a, b) - ) __ra_to_xy(r, angle) ]; \ No newline at end of file diff --git a/src/shape_taiwan.scad b/src/shape_taiwan.scad index 1686c8cf..c38ce660 100644 --- a/src/shape_taiwan.scad +++ b/src/shape_taiwan.scad @@ -9,5 +9,8 @@ **/ function shape_taiwan(h, distance = 0) = - let(tw = [[3.85724, 6.24078], [3.7902, 6.25779], [3.73596, 6.26288], [3.62807, 6.24587], [3.59581, 6.2602], [3.55429, 6.32386], [3.51698, 6.4571], [3.50768, 6.5361], [3.51188, 6.58284], [3.53917, 6.63708], [3.48981, 6.66934], [2.78286, 6.83905], [2.7218, 6.86112], [2.68441, 6.90272], [2.61063, 6.96209], [2.64288, 7.05549], [2.61062, 7.06568], [2.56396, 7.06058], [2.50281, 7.04109], [2.44849, 7.15647], [2.29319, 7.37123], [2.22438, 7.42555], [2.05644, 7.44248], [1.88674, 7.40509], [1.73901, 7.32879], [1.63795, 7.238], [1.58868, 7.14974], [1.54463, 7.0555], [1.5149, 7.0411], [1.48526, 7.01895], [1.53658, 6.9725], [1.58825, 6.92909], [1.63096, 6.86281], [1.61348, 6.80387], [1.57757, 6.83721], [1.53949, 6.89116], [1.48525, 6.87393], [1.43851, 6.87393], [1.40381, 6.86623], [1.37408, 6.85174], [1.28068, 6.77282], [1.20682, 6.7457], [0.723984, 6.65659], [0.586451, 6.60741], [0.5152, 6.57094], [0.458435, 6.52167], [0.393838, 6.47922], [0.108666, 6.38843], [-0.002506, 6.2925], [-0.110307, 6.16693], [-0.278327, 5.89785], [-0.312266, 5.80452], [-0.319942, 5.74076], [-0.35978, 5.72804], [-0.398773, 5.69411], [-0.431113, 5.64921], [-0.443073, 5.60508], [-0.45317, 5.54563], [-0.477762, 5.51429], [-0.504966, 5.48196], [-0.527025, 5.4379], [-0.511683, 5.32413], [-0.544022, 5.28008], [-0.630518, 5.10523], [-0.652506, 5.02118], [-0.721317, 4.96517], [-0.751047, 4.87851], [-0.807895, 4.81922], [-0.849502, 4.76313], [-0.835106, 4.67916], [-0.94535, 4.70123], [-1.03193, 4.67664], [-1.10318, 4.62476], [-1.16685, 4.55856], [-1.18724, 4.52125], [-1.20679, 4.47981], [-1.23643, 4.44755], [-1.33927, 4.41782], [-1.36462, 4.37621], [-1.38844, 4.28037], [-1.47747, 4.11993], [-1.51477, 4.03419], [-1.52674, 3.93321], [-1.55638, 3.87122], [-1.87389, 3.52162], [-1.92308, 3.43757], [-1.96721, 3.28479], [-2.11055, 3.03862], [-2.15224, 2.84946], [-2.18703, 2.75092], [-2.23874, 2.70864], [-2.2481, 2.65676], [-2.43313, 2.44284], [-2.47482, 2.40393], [-2.48998, 2.36148], [-2.49681, 2.20617], [-2.51727, 2.15951], [-2.59526, 2.09828], [-2.61312, 2.05583], [-2.62237, 2.00926], [-2.64705, 1.98728], [-2.68183, 1.97279], [-2.71915, 1.94559], [-2.76589, 1.90137], [-2.80741, 1.82768], [-2.89576, 1.58074], [-2.9601, 1.46267], [-3.00171, 1.34223], [-3.03396, 1.29978], [-3.14261, 1.19451], [-3.16223, 1.14945], [-3.18683, 1.04173], [-3.21142, 0.994987], [-3.30988, 0.906048], [-3.32504, 0.864443], [-3.42105, 0.738702], [-3.43797, 0.692212], [-3.47452, 0.558807], [-3.54409, 0.411083], [-3.62553, 0.283068], [-3.69434, 0.142925], [-3.72407, -0.047077], [-3.71634, -0.135425], [-3.67474, -0.317847], [-3.65948, -0.475761], [-3.62302, -0.539348], [-3.61029, -0.588533], [-3.62554, -0.628538], [-3.65703, -0.687068], [-3.61029, -0.73878], [-3.64002, -0.795629], [-3.57542, -0.918676], [-3.67902, -1.14784], [-3.62553, -1.18944], [-3.59589, -1.2046], [-3.60515, -1.24376], [-3.6476, -1.28781], [-3.68162, -1.37186], [-3.72138, -1.38205], [-3.74597, -1.40925], [-3.79785, -1.54426], [-3.80458, -1.58157], [-3.81731, -1.61121], [-3.84956, -1.65526], [-3.87677, -1.70958], [-3.8665, -1.75893], [-3.84714, -1.80812], [-3.83434, -1.86665], [-3.85397, -1.90666], [-3.89633, -1.91845], [-3.93532, -1.94052], [-3.94552, -2.0025], [-3.90315, -2.05169], [-3.83687, -2.10846], [-3.91452, -2.12525], [-3.92486, -2.16746], [-3.8021, -2.21718], [-3.78004, -2.24169], [-3.79537, -2.28599], [-3.84194, -2.30292], [-3.9014, -2.31052], [-3.94553, -2.3325], [-3.90902, -2.38984], [-3.81228, -2.42599], [-3.7487, -2.45311], [-3.7359, -2.49042], [-3.61032, -2.51249], [-3.51439, -2.52698], [-3.49737, -2.60598], [-3.53645, -2.69921], [-3.61031, -2.75101], [-3.55085, -2.813], [-3.52197, -2.86732], [-3.47455, -3.17194], [-3.46268, -3.20175], [-3.42108, -3.27805], [-3.36173, -3.36723], [-3.3667, -3.40353], [-3.39137, -3.45802], [-3.39137, -3.50468], [-3.37605, -3.57332], [-3.3048, -3.72879], [-3.22849, -3.84755], [-3.18689, -3.9332], [-3.16473, -4.02239], [-3.18175, -4.08606], [-3.21401, -4.15723], [-3.18942, -4.22848], [-3.1377, -4.29316], [-2.99756, -4.4237], [-2.91612, -4.51458], [-2.85675, -4.62575], [-2.84478, -4.76572], [-2.64282, -4.92119], [-2.55624, -4.90831], [-2.51219, -4.92877], [-2.47733, -4.95075], [-2.40355, -5.01441], [-2.33222, -5.06116], [-2.17691, -5.13485], [-2.10053, -5.19944], [-2.05126, -5.27328], [-2.00199, -5.30293], [-1.87641, -5.40147], [-1.84416, -5.44552], [-1.77804, -5.59577], [-1.69399, -5.70181], [-1.66687, -5.74611], [-1.35963, -6.53694], [-1.36899, -6.58351], [-1.4063, -6.638], [-1.41556, -6.68466], [-1.41556, -6.84915], [-1.42322, -6.93076], [-1.41556, -6.96992], [-1.33, -7.11073], [-1.34945, -7.21845], [-1.34692, -7.25315], [-1.28999, -7.29989], [-1.23921, -7.31522], [-1.20181, -7.27783], [-1.19675, -7.17685], [-1.07362, -7.20658], [-0.953101, -7.2609], [-0.849593, -7.33982], [-0.778259, -7.44248], [-0.775729, -7.35413], [-0.795186, -7.21416], [-0.797786, -7.08606], [-0.736641, -7.02913], [-0.685014, -6.99014], [-0.645009, -6.89851], [-0.620417, -6.78565], [-0.637343, -5.77062], [-0.612751, -5.52192], [-0.590692, -5.43534], [-0.443136, -5.1799], [-0.371802, -4.92362], [-0.341989, -4.73344], [-0.29036, -4.64283], [-0.16723, -4.48735], [-0.128151, -4.41105], [-0.046711, -4.20395], [-0.014539, -4.16235], [0.027066, -4.14297], [0.191803, -3.96039], [0.441265, -3.79565], [0.515127, -3.72608], [0.588904, -3.63285], [0.62032, -3.58105], [0.640788, -3.5317], [0.643228, -3.48757], [0.633124, -3.39173], [0.640794, -3.35189], [0.689979, -3.29336], [0.9039, -3.11338], [0.923353, -3.07093], [1.08363, -2.84522], [1.11605, -2.75342], [1.16262, -2.55407], [1.23396, -2.42344], [1.26116, -2.33518], [1.27809, -2.30031], [1.31035, -2.26637], [1.38421, -2.21213], [1.41638, -2.17987], [1.49024, -2.02701], [1.50464, -1.87935], [1.50212, -1.72405], [1.52671, -1.54937], [1.55897, -1.45589], [1.59897, -1.37942], [1.70669, -1.23616], [1.74147, -1.16044], [1.98243, 0.226167], [2.05637, 0.376416], [2.18195, 0.989965], [2.27788, 1.25316], [2.32959, 1.50186], [2.33469, 1.60107], [2.34741, 1.65447], [2.40173, 1.74366], [2.42118, 1.79798], [2.38391, 1.88363], [2.36176, 1.9185], [2.33473, 1.99994], [2.33213, 2.07136], [2.3542, 2.13747], [2.46798, 2.30473], [2.51203, 2.49221], [2.55625, 2.58553], [2.59356, 2.62284], [2.71147, 2.72138], [2.69968, 2.75364], [2.72175, 2.78497], [2.793, 2.8419], [2.89145, 2.97513], [2.98064, 3.06078], [2.97805, 3.26778], [2.98485, 3.3638], [2.99757, 3.41297], [3.01702, 3.44775], [3.03412, 3.48936], [3.02732, 3.59547], [3.03152, 3.64474], [3.14008, 3.76771], [3.23348, 3.82464], [3.27332, 3.8611], [3.26572, 3.90356], [3.23852, 3.94517], [3.22673, 3.98929], [3.23343, 4.02904], [3.32515, 4.08085], [3.33955, 4.16659], [3.31748, 4.26758], [3.2784, 4.34405], [3.3056, 4.3635], [3.37526, 4.38649], [3.39869, 4.42513], [3.32514, 4.42541], [3.22669, 4.4874], [3.17237, 4.58324], [3.16977, 4.70636], [3.19192, 4.7675], [3.19432, 4.8294], [3.14261, 5.06624], [3.14001, 5.17909], [3.14781, 5.29709], [3.1724, 5.41583], [3.20634, 5.51943], [3.25384, 5.59329], [3.54153, 5.94036], [3.62558, 6.01431], [3.94553, 6.17215], [3.91327, 6.21106]] / 15 * h) - distance == 0 ? tw : [for(i = [0 : len(tw) - 1]) if(norm(tw[i] - tw[i + 1]) > distance) tw[i]]; + let( + tw = [[3.85724, 6.24078], [3.7902, 6.25779], [3.73596, 6.26288], [3.62807, 6.24587], [3.59581, 6.2602], [3.55429, 6.32386], [3.51698, 6.4571], [3.50768, 6.5361], [3.51188, 6.58284], [3.53917, 6.63708], [3.48981, 6.66934], [2.78286, 6.83905], [2.7218, 6.86112], [2.68441, 6.90272], [2.61063, 6.96209], [2.64288, 7.05549], [2.61062, 7.06568], [2.56396, 7.06058], [2.50281, 7.04109], [2.44849, 7.15647], [2.29319, 7.37123], [2.22438, 7.42555], [2.05644, 7.44248], [1.88674, 7.40509], [1.73901, 7.32879], [1.63795, 7.238], [1.58868, 7.14974], [1.54463, 7.0555], [1.5149, 7.0411], [1.48526, 7.01895], [1.53658, 6.9725], [1.58825, 6.92909], [1.63096, 6.86281], [1.61348, 6.80387], [1.57757, 6.83721], [1.53949, 6.89116], [1.48525, 6.87393], [1.43851, 6.87393], [1.40381, 6.86623], [1.37408, 6.85174], [1.28068, 6.77282], [1.20682, 6.7457], [0.723984, 6.65659], [0.586451, 6.60741], [0.5152, 6.57094], [0.458435, 6.52167], [0.393838, 6.47922], [0.108666, 6.38843], [-0.002506, 6.2925], [-0.110307, 6.16693], [-0.278327, 5.89785], [-0.312266, 5.80452], [-0.319942, 5.74076], [-0.35978, 5.72804], [-0.398773, 5.69411], [-0.431113, 5.64921], [-0.443073, 5.60508], [-0.45317, 5.54563], [-0.477762, 5.51429], [-0.504966, 5.48196], [-0.527025, 5.4379], [-0.511683, 5.32413], [-0.544022, 5.28008], [-0.630518, 5.10523], [-0.652506, 5.02118], [-0.721317, 4.96517], [-0.751047, 4.87851], [-0.807895, 4.81922], [-0.849502, 4.76313], [-0.835106, 4.67916], [-0.94535, 4.70123], [-1.03193, 4.67664], [-1.10318, 4.62476], [-1.16685, 4.55856], [-1.18724, 4.52125], [-1.20679, 4.47981], [-1.23643, 4.44755], [-1.33927, 4.41782], [-1.36462, 4.37621], [-1.38844, 4.28037], [-1.47747, 4.11993], [-1.51477, 4.03419], [-1.52674, 3.93321], [-1.55638, 3.87122], [-1.87389, 3.52162], [-1.92308, 3.43757], [-1.96721, 3.28479], [-2.11055, 3.03862], [-2.15224, 2.84946], [-2.18703, 2.75092], [-2.23874, 2.70864], [-2.2481, 2.65676], [-2.43313, 2.44284], [-2.47482, 2.40393], [-2.48998, 2.36148], [-2.49681, 2.20617], [-2.51727, 2.15951], [-2.59526, 2.09828], [-2.61312, 2.05583], [-2.62237, 2.00926], [-2.64705, 1.98728], [-2.68183, 1.97279], [-2.71915, 1.94559], [-2.76589, 1.90137], [-2.80741, 1.82768], [-2.89576, 1.58074], [-2.9601, 1.46267], [-3.00171, 1.34223], [-3.03396, 1.29978], [-3.14261, 1.19451], [-3.16223, 1.14945], [-3.18683, 1.04173], [-3.21142, 0.994987], [-3.30988, 0.906048], [-3.32504, 0.864443], [-3.42105, 0.738702], [-3.43797, 0.692212], [-3.47452, 0.558807], [-3.54409, 0.411083], [-3.62553, 0.283068], [-3.69434, 0.142925], [-3.72407, -0.047077], [-3.71634, -0.135425], [-3.67474, -0.317847], [-3.65948, -0.475761], [-3.62302, -0.539348], [-3.61029, -0.588533], [-3.62554, -0.628538], [-3.65703, -0.687068], [-3.61029, -0.73878], [-3.64002, -0.795629], [-3.57542, -0.918676], [-3.67902, -1.14784], [-3.62553, -1.18944], [-3.59589, -1.2046], [-3.60515, -1.24376], [-3.6476, -1.28781], [-3.68162, -1.37186], [-3.72138, -1.38205], [-3.74597, -1.40925], [-3.79785, -1.54426], [-3.80458, -1.58157], [-3.81731, -1.61121], [-3.84956, -1.65526], [-3.87677, -1.70958], [-3.8665, -1.75893], [-3.84714, -1.80812], [-3.83434, -1.86665], [-3.85397, -1.90666], [-3.89633, -1.91845], [-3.93532, -1.94052], [-3.94552, -2.0025], [-3.90315, -2.05169], [-3.83687, -2.10846], [-3.91452, -2.12525], [-3.92486, -2.16746], [-3.8021, -2.21718], [-3.78004, -2.24169], [-3.79537, -2.28599], [-3.84194, -2.30292], [-3.9014, -2.31052], [-3.94553, -2.3325], [-3.90902, -2.38984], [-3.81228, -2.42599], [-3.7487, -2.45311], [-3.7359, -2.49042], [-3.61032, -2.51249], [-3.51439, -2.52698], [-3.49737, -2.60598], [-3.53645, -2.69921], [-3.61031, -2.75101], [-3.55085, -2.813], [-3.52197, -2.86732], [-3.47455, -3.17194], [-3.46268, -3.20175], [-3.42108, -3.27805], [-3.36173, -3.36723], [-3.3667, -3.40353], [-3.39137, -3.45802], [-3.39137, -3.50468], [-3.37605, -3.57332], [-3.3048, -3.72879], [-3.22849, -3.84755], [-3.18689, -3.9332], [-3.16473, -4.02239], [-3.18175, -4.08606], [-3.21401, -4.15723], [-3.18942, -4.22848], [-3.1377, -4.29316], [-2.99756, -4.4237], [-2.91612, -4.51458], [-2.85675, -4.62575], [-2.84478, -4.76572], [-2.64282, -4.92119], [-2.55624, -4.90831], [-2.51219, -4.92877], [-2.47733, -4.95075], [-2.40355, -5.01441], [-2.33222, -5.06116], [-2.17691, -5.13485], [-2.10053, -5.19944], [-2.05126, -5.27328], [-2.00199, -5.30293], [-1.87641, -5.40147], [-1.84416, -5.44552], [-1.77804, -5.59577], [-1.69399, -5.70181], [-1.66687, -5.74611], [-1.35963, -6.53694], [-1.36899, -6.58351], [-1.4063, -6.638], [-1.41556, -6.68466], [-1.41556, -6.84915], [-1.42322, -6.93076], [-1.41556, -6.96992], [-1.33, -7.11073], [-1.34945, -7.21845], [-1.34692, -7.25315], [-1.28999, -7.29989], [-1.23921, -7.31522], [-1.20181, -7.27783], [-1.19675, -7.17685], [-1.07362, -7.20658], [-0.953101, -7.2609], [-0.849593, -7.33982], [-0.778259, -7.44248], [-0.775729, -7.35413], [-0.795186, -7.21416], [-0.797786, -7.08606], [-0.736641, -7.02913], [-0.685014, -6.99014], [-0.645009, -6.89851], [-0.620417, -6.78565], [-0.637343, -5.77062], [-0.612751, -5.52192], [-0.590692, -5.43534], [-0.443136, -5.1799], [-0.371802, -4.92362], [-0.341989, -4.73344], [-0.29036, -4.64283], [-0.16723, -4.48735], [-0.128151, -4.41105], [-0.046711, -4.20395], [-0.014539, -4.16235], [0.027066, -4.14297], [0.191803, -3.96039], [0.441265, -3.79565], [0.515127, -3.72608], [0.588904, -3.63285], [0.62032, -3.58105], [0.640788, -3.5317], [0.643228, -3.48757], [0.633124, -3.39173], [0.640794, -3.35189], [0.689979, -3.29336], [0.9039, -3.11338], [0.923353, -3.07093], [1.08363, -2.84522], [1.11605, -2.75342], [1.16262, -2.55407], [1.23396, -2.42344], [1.26116, -2.33518], [1.27809, -2.30031], [1.31035, -2.26637], [1.38421, -2.21213], [1.41638, -2.17987], [1.49024, -2.02701], [1.50464, -1.87935], [1.50212, -1.72405], [1.52671, -1.54937], [1.55897, -1.45589], [1.59897, -1.37942], [1.70669, -1.23616], [1.74147, -1.16044], [1.98243, 0.226167], [2.05637, 0.376416], [2.18195, 0.989965], [2.27788, 1.25316], [2.32959, 1.50186], [2.33469, 1.60107], [2.34741, 1.65447], [2.40173, 1.74366], [2.42118, 1.79798], [2.38391, 1.88363], [2.36176, 1.9185], [2.33473, 1.99994], [2.33213, 2.07136], [2.3542, 2.13747], [2.46798, 2.30473], [2.51203, 2.49221], [2.55625, 2.58553], [2.59356, 2.62284], [2.71147, 2.72138], [2.69968, 2.75364], [2.72175, 2.78497], [2.793, 2.8419], [2.89145, 2.97513], [2.98064, 3.06078], [2.97805, 3.26778], [2.98485, 3.3638], [2.99757, 3.41297], [3.01702, 3.44775], [3.03412, 3.48936], [3.02732, 3.59547], [3.03152, 3.64474], [3.14008, 3.76771], [3.23348, 3.82464], [3.27332, 3.8611], [3.26572, 3.90356], [3.23852, 3.94517], [3.22673, 3.98929], [3.23343, 4.02904], [3.32515, 4.08085], [3.33955, 4.16659], [3.31748, 4.26758], [3.2784, 4.34405], [3.3056, 4.3635], [3.37526, 4.38649], [3.39869, 4.42513], [3.32514, 4.42541], [3.22669, 4.4874], [3.17237, 4.58324], [3.16977, 4.70636], [3.19192, 4.7675], [3.19432, 4.8294], [3.14261, 5.06624], [3.14001, 5.17909], [3.14781, 5.29709], [3.1724, 5.41583], [3.20634, 5.51943], [3.25384, 5.59329], [3.54153, 5.94036], [3.62558, 6.01431], [3.94553, 6.17215], [3.91327, 6.21106]] / 15 * h, + leng = len(tw) + ) + distance == 0 ? tw : [for(i = 0; i < leng; i = i + 1) if(norm(tw[i] - tw[i + 1]) > distance) tw[i]]; diff --git a/src/shape_trapezium.scad b/src/shape_trapezium.scad index 867c5b3e..e9f1c0ec 100644 --- a/src/shape_trapezium.scad +++ b/src/shape_trapezium.scad @@ -8,11 +8,10 @@ * **/ -include <__private__/__is_float.scad>; -include <__private__/__frags.scad>; -include <__private__/__pie_for_rounding.scad>; -include <__private__/__half_trapezium.scad>; -include <__private__/__trapezium.scad>; +include <__comm__/__frags.scad>; +include <__comm__/__pie_for_rounding.scad>; +include <__comm__/__half_trapezium.scad>; +include <__comm__/__trapezium.scad>; function shape_trapezium(length, h, corner_r = 0) = __trapezium( diff --git a/src/shear.scad b/src/shear.scad index 41c2f089..19618257 100644 --- a/src/shear.scad +++ b/src/shear.scad @@ -8,7 +8,7 @@ * **/ -include <__private__/__m_shearing.scad>; +include ; module shear(sx = [0, 0], sy = [0, 0], sz = [0, 0]) { multmatrix(__m_shearing(sx, sy, sz)) children(); diff --git a/src/sphere_spiral.scad b/src/sphere_spiral.scad index 25858319..9fb211ba 100644 --- a/src/sphere_spiral.scad +++ b/src/sphere_spiral.scad @@ -9,8 +9,11 @@ **/ function sphere_spiral(radius, za_step, z_circles = 1, begin_angle = 0, end_angle = 0, vt_dir = "SPI_DOWN", rt_dir = "CT_CLK") = + let( + a_end = 90 * z_circles - end_angle + ) [ - for(a = [begin_angle:za_step:90 * z_circles - end_angle]) + for(a = begin_angle; a <= a_end; a = a + za_step) let( ya = vt_dir == "SPI_DOWN" ? (-90 + 2 * a / z_circles) : (90 + 2 * a / z_circles), za = (rt_dir == "CT_CLK" ? 1 : -1) * a, diff --git a/src/split_str.scad b/src/split_str.scad deleted file mode 100644 index c8f311da..00000000 --- a/src/split_str.scad +++ /dev/null @@ -1,19 +0,0 @@ -/** -* split_str.scad -* -* @copyright Justin Lin, 2017 -* @license https://opensource.org/licenses/lgpl-3.0.html -* -* @see https://openhome.cc/eGossip/OpenSCAD/lib-split_str.html -* -**/ - -function _split_t_by(idxs, t, ts = [], i = -1) = - i == -1 ? _split_t_by(idxs, t, [sub_str(t, 0, idxs[0])], i + 1) : ( - i == len(idxs) - 1 ? concat(ts, sub_str(t, idxs[i] + 1)) : - _split_t_by(idxs, t, concat(ts, sub_str(t, idxs[i] + 1, idxs[i + 1])), i + 1) - ); - -function split_str(t, delimiter) = - len(search(delimiter, t)) == 0 ? - [t] : _split_t_by(search(delimiter, t, 0)[0], t); \ No newline at end of file diff --git a/src/torus_knot.scad b/src/torus_knot.scad index 84803b84..607f22c0 100644 --- a/src/torus_knot.scad +++ b/src/torus_knot.scad @@ -8,14 +8,16 @@ * **/ -function torus_knot(p, q, phi_step) = [ - for(phi = [0:phi_step:6.28318]) - let( - degree = phi * 180 / 3.14159, - r = cos(q * degree) + 2, - x = r * cos(p * degree), - y = r * sin(p * degree), - z = -sin(q * degree) - ) - [x, y, z] -]; \ No newline at end of file +function torus_knot(p, q, phi_step) = + let(tau = PI * 2) + [ + for(phi = 0; phi < tau; phi = phi + phi_step) + let( + degree = phi * 180 / PI, + r = cos(q * degree) + 2, + x = r * cos(p * degree), + y = r * sin(p * degree), + z = -sin(q * degree) + ) + [x, y, z] + ]; \ No newline at end of file diff --git a/src/triangulate.scad b/src/triangulate.scad index 6aeec0c1..6af65524 100644 --- a/src/triangulate.scad +++ b/src/triangulate.scad @@ -47,17 +47,16 @@ function _triangulate_remove_v(indices, v, num_of_vertices) = let( nv_minuns_one = num_of_vertices - 1 ) - v == 0 ? [for(i = [1:nv_minuns_one]) indices[i]] : ( - v == nv_minuns_one ? [for(i = [0:v - 1]) indices[i]] : concat( - [for(i = [0:v - 1]) indices[i]], - [for(i = [v + 1:nv_minuns_one]) indices[i]] + v == 0 ? [for(i = 1; i <= nv_minuns_one; i = i + 1) indices[i]] : ( + v == nv_minuns_one ? [for(i = 0; i < v; i = i + 1) indices[i]] : concat( + [for(i = 0; i < v; i = i + 1) indices[i]], + [for(i = v + 1; i <= nv_minuns_one; i = i + 1) indices[i]] ) ); function _triangulate_zero_or_value(num_of_vertices, value) = num_of_vertices <= value ? 0 : value; - function _triangulate_real_triangulate_sub(shape_pts, collector, indices, v, num_of_vertices, count, epsilon) = let( // idxes of three consecutive vertices @@ -96,7 +95,7 @@ function triangulate(shape_pts, epsilon = 0.0001) = let( num_of_vertices = len(shape_pts), v = num_of_vertices - 1, - indices = [for(vi = [0:v]) vi], + indices = [for(vi = 0; vi <= v; vi = vi + 1) vi], count = 2 * num_of_vertices ) num_of_vertices < 3 ? [] : _triangulate_real_triangulate(shape_pts, [], indices, v, num_of_vertices, count, epsilon); diff --git a/src/trim_shape.scad b/src/trim_shape.scad index d1e175e6..c436abc0 100644 --- a/src/trim_shape.scad +++ b/src/trim_shape.scad @@ -8,10 +8,10 @@ * **/ -include <__private__/__to3d.scad>; -include <__private__/__line_intersection.scad>; -include <__private__/__in_line.scad>; -include <__private__/__lines_from.scad>; +include <__comm__/__to3d.scad>; +include <__comm__/__line_intersection.scad>; +include <__comm__/__in_line.scad>; +include <__comm__/__lines_from.scad>; function _trim_shape_any_intersection_sub(lines, line, lines_leng, i, epsilon) = let( @@ -27,8 +27,8 @@ function _trim_sub(lines, leng, epsilon) = let( current_line = lines[0], next_line = lines[1], - lines_from_next = [for(j = [1 : leng - 1]) lines[j]], - lines_from_next2 = [for(j = [2 : leng - 1]) lines[j]], + lines_from_next = [for(j = 1; j < leng; j = j + 1) lines[j]], + lines_from_next2 = [for(j = 2; j < leng; j = j + 1) lines[j]], current_p = current_line[0], leng_lines_from_next2 = len(lines_from_next2), inter_p = _trim_shape_any_intersection(lines_from_next2, current_line, leng_lines_from_next2, 0, epsilon) @@ -39,7 +39,7 @@ function _trim_sub(lines, leng, epsilon) = (leng == 3 || (inter_p[0] == (leng_lines_from_next2 - 1))) ? [current_p, inter_p[1], lines[leng - 1]] : ( // collect current_p, intersecting pt and trim remain lines concat([current_p, inter_p[1]], - _trim_shape_trim_lines([for(i = [inter_p[0] + 1 : leng_lines_from_next2 - 1]) lines_from_next2[i]], epsilon) + _trim_shape_trim_lines([for(i = inter_p[0] + 1; i < leng_lines_from_next2; i = i + 1) lines_from_next2[i]], epsilon) ) ) ); @@ -53,7 +53,7 @@ function _trim_shape_collect_pts_from(lines, leng) = function trim_shape(shape_pts, from, to, epsilon = 0.0001) = let( - pts = [for(i = [from:to]) shape_pts[i]], + pts = [for(i = from; i <= to; i = i + 1) shape_pts[i]], trimmed = _trim_shape_trim_lines(__lines_from(pts), epsilon) ) len(shape_pts) == len(trimmed) ? trimmed : trim_shape(trimmed, 0, len(trimmed) - 1, epsilon); diff --git a/src/turtle2d.scad b/src/turtle/turtle2d.scad similarity index 94% rename from src/turtle2d.scad rename to src/turtle/turtle2d.scad index 5ab77606..8c2716ab 100644 --- a/src/turtle2d.scad +++ b/src/turtle/turtle2d.scad @@ -4,7 +4,7 @@ * @copyright Justin Lin, 2017 * @license https://opensource.org/licenses/lgpl-3.0.html * -* @see https://openhome.cc/eGossip/OpenSCAD/lib-turtle2d.html +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-turtle2d.html * **/ @@ -34,7 +34,7 @@ function _turtle2d_three_args_command(cmd, arg1, arg2, arg3) = cmd == "create" ? _turtle2d_turtle(arg1, arg2, arg3) : _turtle2d_two_args_command(cmd, arg1, arg2); function _turtle2d_two_args_command(cmd, arg1, arg2) = - arg2 == undef ? _turtle2d_one_arg_command(cmd, arg1) : ( + is_undef(arg2) ? _turtle2d_one_arg_command(cmd, arg1) : ( cmd == "pt" ? _turtle2d_set_point(arg1, arg2) : ( cmd == "x" ? _turtle2d_set_x(arg1, arg2) : ( cmd == "y" ? _turtle2d_set_y(arg1, arg2) : ( diff --git a/src/turtle3d.scad b/src/turtle/turtle3d.scad similarity index 95% rename from src/turtle3d.scad rename to src/turtle/turtle3d.scad index c93448ed..10210683 100644 --- a/src/turtle3d.scad +++ b/src/turtle/turtle3d.scad @@ -4,7 +4,7 @@ * @copyright Justin Lin, 2017 * @license https://opensource.org/licenses/lgpl-3.0.html * -* @see https://openhome.cc/eGossip/OpenSCAD/lib-turtle3d.html +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-turtle3d.html * **/ @@ -122,8 +122,8 @@ function _turtle3d_zu_turn(turtle, a) = ); function _turtle3d_create_cmd(arg1, arg2) = - (arg1 == undef && arg2 == undef) ? _turtle3d_create_default() : ( - (arg1 != undef && arg2 != undef) ? _turtle3d_create(arg1, arg2) : undef + (is_undef(arg1) && is_undef(arg2)) ? _turtle3d_create_default() : ( + (!is_undef(arg1) && !is_undef(arg2)) ? _turtle3d_create(arg1, arg2) : undef ); function _turtle3d_chain_move(cmd, arg1, arg2) = diff --git a/src/unittest.scad b/src/unittest.scad index 4102a497..c6bea457 100644 --- a/src/unittest.scad +++ b/src/unittest.scad @@ -1,128 +1,38 @@ -include <__private__/__is_float.scad>; +module assertEqualPoint(expected, actual, epsilon = 0.0001) { + leng_expected = len(expected); + leng_actual = len(actual); -module fail(title, message) { - echo( - str( - "", - "", - "FAIL: ", title, - "", - "" - ) + assert( + leng_expected == leng_actual, + str("expected length: ", leng_expected, ", but: ", leng_actual) + ); + + v_diff = expected - actual; + v3d = len(v_diff) == 2 ? [v_diff[0], v_diff[1], 0] : v_diff; + + assert( + abs(v3d[0]) <= epsilon && abs(v3d[1]) <= epsilon && abs(v3d[2]) <= epsilon, + str("expected: ", expected, ", but: ", actual) ); - if(message != undef) { - echo( - str( - "", - "　", - message, - "", - "" - ) - ); - } } -function round_n(number, float_digits = 4) = - let(n = pow(10, float_digits)) - round(number * n) / n; - -function mul_round_pt(point, n) = - let(pt = point * n) - len(pt) == 2 ? - [round(pt[0]), round(pt[1])] : - [round(pt[0]), round(pt[1]), round(pt[2])]; - -function round_pts(points, float_digits = 4) = - let(n = pow(10, float_digits)) - [for(pt = points) mul_round_pt(pt, n) / n]; - -module assertEqualPoint(expected, actual, float_digits = 4) { +module assertEqualPoints(expected, actual, epsilon = 0.0001) { leng_expected = len(expected); leng_actual = len(actual); - if(leng_expected != leng_actual) { - fail( - "Point", - str("expected length: ", leng_expected, - ", but: ", leng_actual) - ); - } else { - n = pow(10, float_digits); + assert( + leng_expected == leng_actual, + str("expected length: ", leng_expected, ", but: ", leng_actual) + ); - shifted_expected = mul_round_pt( - expected, n - ); - - shifted_actual = mul_round_pt( - actual, n - ); - - if(shifted_expected != shifted_actual) { - fail( - "Point", - str("expected: ", shifted_expected / n, - ", but: ", shifted_actual / n) - ); - } + for(i = [0:len(actual) - 1]) { + assertEqualPoint(expected[i], actual[i], epsilon); } } -module assertEqualPoints(expected, actual, float_digits = 4) { - leng_expected = len(expected); - leng_actual = len(actual); - - if(leng_expected != leng_actual) { - fail( - "Points", - str("expected length: ", leng_expected, - ", but: ", leng_actual) - ); - } else { - for(i = [0:len(actual) - 1]) { - assertEqualPoint(expected[i], actual[i], float_digits); - } - } +module assertEqualNum(expected, actual, epsilon = 0.0001) { + assert( + abs(expected - actual) <= epsilon, + str("expected: ", expected, ", but: ", actual) + ); } - -module assertEqual(expected, actual, float_digits = 4) { - r_expected = __is_float(expected) ? round_n(expected, float_digits) : expected; - r_actual = __is_float(actual) ? round_n(actual, float_digits) : actual; - - if(r_expected != r_actual) { - fail( - "Equality", - str("expected: ", r_expected, - ", but: ", r_actual) - ); - } -} - -module assertTrue(truth) { - if(!truth) { - fail( - "Truth", - "expected: true, but: false" - ); - } -} - -module round_echo_pts(points, float_digits = 4) { - echo(round_pts(points, float_digits)); -} - -module round_echo_n(number, float_digits = 4) { - echo(round_n(number, float_digits)); -} - -function mul_round_vector(vector, n) = - let(vt = vector * n) - [for(v = vt) round(v)]; - -function round_vectors(vectors, float_digits = 4) = - let(n = pow(10, float_digits)) - [for(vt = vectors) mul_round_vector(vt, n) / n]; - -module round_echo_vectors(vectors, float_digits = 4) { - echo(round_vectors(vectors, float_digits = 4)); -} \ No newline at end of file diff --git a/src/util/__comm__/__reverse.scad b/src/util/__comm__/__reverse.scad new file mode 100644 index 00000000..a09b6b1b --- /dev/null +++ b/src/util/__comm__/__reverse.scad @@ -0,0 +1 @@ +function __reverse(vt) = [for(i = len(vt) - 1; i >= 0; i = i - 1) vt[i]]; \ No newline at end of file diff --git a/src/parse_number.scad b/src/util/parse_number.scad similarity index 100% rename from src/parse_number.scad rename to src/util/parse_number.scad diff --git a/src/util/reverse.scad b/src/util/reverse.scad new file mode 100644 index 00000000..d2696b02 --- /dev/null +++ b/src/util/reverse.scad @@ -0,0 +1,13 @@ +/** +* reverse.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-reverse.html +* +**/ + +include ; + +function reverse(lt) = __reverse(lt); \ No newline at end of file diff --git a/src/util/slice.scad b/src/util/slice.scad new file mode 100644 index 00000000..0eb9c0c5 --- /dev/null +++ b/src/util/slice.scad @@ -0,0 +1,14 @@ +/** +* slice.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-slice.html +* +**/ + +function slice(lt, begin, end) = + let(ed = is_undef(end) ? len(lt) : end) + [for(i = begin; i < ed; i = i + 1) lt[i]]; + \ No newline at end of file diff --git a/src/util/sort.scad b/src/util/sort.scad new file mode 100644 index 00000000..0c51290a --- /dev/null +++ b/src/util/sort.scad @@ -0,0 +1,26 @@ +/** +* sort.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-sort.html +* +**/ + +function _sort(lt, i) = + let(leng = len(lt)) + leng <= 1 ? lt : + let( + pivot = lt[0], + before = [for(j = 1; j < leng; j = j + 1) if(lt[j][i] < pivot[i]) lt[j]], + after = [for(j = 1; j < leng; j = j + 1) if(lt[j][i] >= pivot[i]) lt[j]] + ) + concat(_sort(before, i), [pivot], _sort(after, i)); + +function sort(lt, by = "idx", idx = 0) = + let( + dict = [["x", 0], ["y", 1], ["z", 0], ["idx", idx]], + i = dict[search(by, dict)[0]][1] + ) + _sort(lt, i); \ No newline at end of file diff --git a/src/util/split_str.scad b/src/util/split_str.scad new file mode 100644 index 00000000..9cf4196f --- /dev/null +++ b/src/util/split_str.scad @@ -0,0 +1,23 @@ +/** +* split_str.scad +* +* @copyright Justin Lin, 2017 +* @license https://opensource.org/licenses/lgpl-3.0.html +* +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-split_str.html +* +**/ + +function _split_t_by(idxs, t) = + let(leng = len(idxs)) + concat( + [sub_str(t, 0, idxs[0])], + [ + for(i = 0; i < leng; i = i + 1) + sub_str(t, idxs[i] + 1, idxs[i + 1]) + ] + ); + +function split_str(t, delimiter) = + len(search(delimiter, t)) == 0 ? + [t] : _split_t_by(search(delimiter, t, 0)[0], t); \ No newline at end of file diff --git a/src/sub_str.scad b/src/util/sub_str.scad similarity index 65% rename from src/sub_str.scad rename to src/util/sub_str.scad index 61cf2413..e692c62c 100644 --- a/src/sub_str.scad +++ b/src/util/sub_str.scad @@ -4,7 +4,7 @@ * @copyright Justin Lin, 2017 * @license https://opensource.org/licenses/lgpl-3.0.html * -* @see https://openhome.cc/eGossip/OpenSCAD/lib-sub_str.html +* @see https://openhome.cc/eGossip/OpenSCAD/lib2-sub_str.html * **/ @@ -12,5 +12,4 @@ function _sub_str(t, begin, end) = begin == end ? "" : str(t[begin], sub_str(t, begin + 1, end)); function sub_str(t, begin, end) = - end == undef ? _sub_str(t, begin, len(t)) : _sub_str(t, begin, end); - \ No newline at end of file + is_undef(end) ? _sub_str(t, begin, len(t)) : _sub_str(t, begin, end); diff --git a/src/voronoi3d.scad b/src/voronoi3d.scad index 072c34d7..214c2a87 100644 --- a/src/voronoi3d.scad +++ b/src/voronoi3d.scad @@ -8,7 +8,7 @@ * **/ -include <__private__/__angy_angz.scad>; +include <__comm__/__angy_angz.scad>; // slow but workable diff --git a/test/matrix/test_m_cumulate.scad b/test/matrix/test_m_cumulate.scad new file mode 100644 index 00000000..52ffbd3d --- /dev/null +++ b/test/matrix/test_m_cumulate.scad @@ -0,0 +1,19 @@ + +module test_m_cumulate() { + echo("==== test_m_cumulate ===="); + + include ; + include ; + include ; + include ; + include ; + + expected = [[1, -1.73205, 0, 10], [1.73205, 1, 0, 20], [0, 0, 2, 10], [0, 0, 0, 1]]; + actual = m_cumulate([ + m_translation([10, 20, 10]), m_scaling(2), m_rotation(60)] + ); + + assertEqualPoints(expected, actual); +} + +test_m_cumulate(); \ No newline at end of file diff --git a/test/pixel/test_px_circle.scad b/test/pixel/test_px_circle.scad new file mode 100644 index 00000000..a800318d --- /dev/null +++ b/test/pixel/test_px_circle.scad @@ -0,0 +1,13 @@ + +module test_px_circle() { + echo("==== test_px_circle ===="); + + include ; + include ; + expected = [[0, 10], [0, -10], [-10, 0], [-9, 0], [-8, 0], [-7, 0], [-6, 0], [-5, 0], [-4, 0], [-3, 0], [-2, 0], [-1, 0], [0, 0], [1, 0], [2, 0], [3, 0], [4, 0], [5, 0], [6, 0], [7, 0], [8, 0], [9, 0], [10, 0], [-1, -10], [0, -10], [1, -10], [-10, -1], [-9, -1], [-8, -1], [-7, -1], [-6, -1], [-5, -1], [-4, -1], [-3, -1], [-2, -1], [-1, -1], [0, -1], [1, -1], [2, -1], [3, -1], [4, -1], [5, -1], [6, -1], [7, -1], [8, -1], [9, -1], [10, -1], [-10, 1], [-9, 1], [-8, 1], [-7, 1], [-6, 1], [-5, 1], [-4, 1], [-3, 1], [-2, 1], [-1, 1], [0, 1], [1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1], [9, 1], [10, 1], [-1, 10], [0, 10], [1, 10], [-2, -10], [-1, -10], [0, -10], [1, -10], [2, -10], [-10, -2], [-9, -2], [-8, -2], [-7, -2], [-6, -2], [-5, -2], [-4, -2], [-3, -2], [-2, -2], [-1, -2], [0, -2], [1, -2], [2, -2], [3, -2], [4, -2], [5, -2], [6, -2], [7, -2], [8, -2], [9, -2], [10, -2], [-10, 2], [-9, 2], [-8, 2], [-7, 2], [-6, 2], [-5, 2], [-4, 2], [-3, 2], [-2, 2], [-1, 2], [0, 2], [1, 2], [2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [10, 2], [-2, 10], [-1, 10], [0, 10], [1, 10], [2, 10], [-3, -10], [-2, -10], [-1, -10], [0, -10], [1, -10], [2, -10], [3, -10], [-10, -3], [-9, -3], [-8, -3], [-7, -3], [-6, -3], [-5, -3], [-4, -3], [-3, -3], [-2, -3], [-1, -3], [0, -3], [1, -3], [2, -3], [3, -3], [4, -3], [5, -3], [6, -3], [7, -3], [8, -3], [9, -3], [10, -3], [-10, 3], [-9, 3], [-8, 3], [-7, 3], [-6, 3], [-5, 3], [-4, 3], [-3, 3], [-2, 3], [-1, 3], [0, 3], [1, 3], [2, 3], [3, 3], [4, 3], [5, 3], [6, 3], [7, 3], [8, 3], [9, 3], [10, 3], [-3, 10], [-2, 10], [-1, 10], [0, 10], [1, 10], [2, 10], [3, 10], [-4, -9], [-3, -9], [-2, -9], [-1, -9], [0, -9], [1, -9], [2, -9], [3, -9], [4, -9], [-9, -4], [-8, -4], [-7, -4], [-6, -4], [-5, -4], [-4, -4], [-3, -4], [-2, -4], [-1, -4], [0, -4], [1, -4], [2, -4], [3, -4], [4, -4], [5, -4], [6, -4], [7, -4], [8, -4], [9, -4], [-9, 4], [-8, 4], [-7, 4], [-6, 4], [-5, 4], [-4, 4], [-3, 4], [-2, 4], [-1, 4], [0, 4], [1, 4], [2, 4], [3, 4], [4, 4], [5, 4], [6, 4], [7, 4], [8, 4], [9, 4], [-4, 9], [-3, 9], [-2, 9], [-1, 9], [0, 9], [1, 9], [2, 9], [3, 9], [4, 9], [-5, -9], [-4, -9], [-3, -9], [-2, -9], [-1, -9], [0, -9], [1, -9], [2, -9], [3, -9], [4, -9], [5, -9], [-9, -5], [-8, -5], [-7, -5], [-6, -5], [-5, -5], [-4, -5], [-3, -5], [-2, -5], [-1, -5], [0, -5], [1, -5], [2, -5], [3, -5], [4, -5], [5, -5], [6, -5], [7, -5], [8, -5], [9, -5], [-9, 5], [-8, 5], [-7, 5], [-6, 5], [-5, 5], [-4, 5], [-3, 5], [-2, 5], [-1, 5], [0, 5], [1, 5], [2, 5], [3, 5], [4, 5], [5, 5], [6, 5], [7, 5], [8, 5], [9, 5], [-5, 9], [-4, 9], [-3, 9], [-2, 9], [-1, 9], [0, 9], [1, 9], [2, 9], [3, 9], [4, 9], [5, 9], [-6, -8], [-5, -8], [-4, -8], [-3, -8], [-2, -8], [-1, -8], [0, -8], [1, -8], [2, -8], [3, -8], [4, -8], [5, -8], [6, -8], [-8, -6], [-7, -6], [-6, -6], [-5, -6], [-4, -6], [-3, -6], [-2, -6], [-1, -6], [0, -6], [1, -6], [2, -6], [3, -6], [4, -6], [5, -6], [6, -6], [7, -6], [8, -6], [-8, 6], [-7, 6], [-6, 6], [-5, 6], [-4, 6], [-3, 6], [-2, 6], [-1, 6], [0, 6], [1, 6], [2, 6], [3, 6], [4, 6], [5, 6], [6, 6], [7, 6], [8, 6], [-6, 8], [-5, 8], [-4, 8], [-3, 8], [-2, 8], [-1, 8], [0, 8], [1, 8], [2, 8], [3, 8], [4, 8], [5, 8], [6, 8], [-7, -7], [-6, -7], [-5, -7], [-4, -7], [-3, -7], [-2, -7], [-1, -7], [0, -7], [1, -7], [2, -7], [3, -7], [4, -7], [5, -7], [6, -7], [7, -7], [-7, -7], [-6, -7], [-5, -7], [-4, -7], [-3, -7], [-2, -7], [-1, -7], [0, -7], [1, -7], [2, -7], [3, -7], [4, -7], [5, -7], [6, -7], [7, -7], [-7, 7], [-6, 7], [-5, 7], [-4, 7], [-3, 7], [-2, 7], [-1, 7], [0, 7], [1, 7], [2, 7], [3, 7], [4, 7], [5, 7], [6, 7], [7, 7], [-7, 7], [-6, 7], [-5, 7], [-4, 7], [-3, 7], [-2, 7], [-1, 7], [0, 7], [1, 7], [2, 7], [3, 7], [4, 7], [5, 7], [6, 7], [7, 7]]; + actual = px_circle(10, true); + + assertEqualPoints(expected, actual); +} + +test_px_circle(); \ No newline at end of file diff --git a/test/pixel/test_px_cylinder.scad b/test/pixel/test_px_cylinder.scad new file mode 100644 index 00000000..a359db4c --- /dev/null +++ b/test/pixel/test_px_cylinder.scad @@ -0,0 +1,23 @@ + +module test_px_cylinder() { + echo("==== test_px_cylinder ===="); + + include ; + include ; + + r1 = 10; + r2 = 5; + h = 3; + + expected = [[-4, -9, 0], [-3, -9, 0], [-2, -9, 0], [-1, -9, 0], [0, -9, 0], [1, -9, 0], [2, -9, 0], [3, -9, 0], [4, -9, 0], [-5, -8, 0], [-4, -8, 0], [-3, -8, 0], [-2, -8, 0], [-1, -8, 0], [0, -8, 0], [1, -8, 0], [2, -8, 0], [3, -8, 0], [4, -8, 0], [5, -8, 0], [-7, -7, 0], [-6, -7, 0], [-5, -7, 0], [-4, -7, 0], [-3, -7, 0], [-2, -7, 0], [-1, -7, 0], [0, -7, 0], [1, -7, 0], [2, -7, 0], [3, -7, 0], [4, -7, 0], [5, -7, 0], [6, -7, 0], [7, -7, 0], [-7, -6, 0], [-6, -6, 0], [-5, -6, 0], [-4, -6, 0], [-3, -6, 0], [-2, -6, 0], [-1, -6, 0], [0, -6, 0], [1, -6, 0], [2, -6, 0], [3, -6, 0], [4, -6, 0], [5, -6, 0], [6, -6, 0], [7, -6, 0], [-8, -5, 0], [-7, -5, 0], [-6, -5, 0], [-5, -5, 0], [-4, -5, 0], [-3, -5, 0], [-2, -5, 0], [-1, -5, 0], [0, -5, 0], [1, -5, 0], [2, -5, 0], [3, -5, 0], [4, -5, 0], [5, -5, 0], [6, -5, 0], [7, -5, 0], [8, -5, 0], [-9, -4, 0], [-8, -4, 0], [-7, -4, 0], [-6, -4, 0], [-5, -4, 0], [-4, -4, 0], [-3, -4, 0], [-2, -4, 0], [-1, -4, 0], [0, -4, 0], [1, -4, 0], [2, -4, 0], [3, -4, 0], [4, -4, 0], [5, -4, 0], [6, -4, 0], [7, -4, 0], [8, -4, 0], [9, -4, 0], [-9, -3, 0], [-8, -3, 0], [-7, -3, 0], [-6, -3, 0], [-5, -3, 0], [-4, -3, 0], [-3, -3, 0], [-2, -3, 0], [-1, -3, 0], [0, -3, 0], [1, -3, 0], [2, -3, 0], [3, -3, 0], [4, -3, 0], [5, -3, 0], [6, -3, 0], [7, -3, 0], [8, -3, 0], [9, -3, 0], [-9, -2, 0], [-8, -2, 0], [-7, -2, 0], [-6, -2, 0], [-5, -2, 0], [-4, -2, 0], [-3, -2, 0], [-2, -2, 0], [-1, -2, 0], [0, -2, 0], [1, -2, 0], [2, -2, 0], [3, -2, 0], [4, -2, 0], [5, -2, 0], [6, -2, 0], [7, -2, 0], [8, -2, 0], [9, -2, 0], [-9, -1, 0], [-8, -1, 0], [-7, -1, 0], [-6, -1, 0], [-5, -1, 0], [-4, -1, 0], [-3, -1, 0], [-2, -1, 0], [-1, -1, 0], [0, -1, 0], [1, -1, 0], [2, -1, 0], [3, -1, 0], [4, -1, 0], [5, -1, 0], [6, -1, 0], [7, -1, 0], [8, -1, 0], [9, -1, 0], [-9, 0, 0], [-8, 0, 0], [-7, 0, 0], [-6, 0, 0], [-5, 0, 0], [-4, 0, 0], [-3, 0, 0], [-2, 0, 0], [-1, 0, 0], [0, 0, 0], [1, 0, 0], [2, 0, 0], [3, 0, 0], [4, 0, 0], [5, 0, 0], [6, 0, 0], [7, 0, 0], [8, 0, 0], [9, 0, 0], [-9, 1, 0], [-8, 1, 0], [-7, 1, 0], [-6, 1, 0], [-5, 1, 0], [-4, 1, 0], [-3, 1, 0], [-2, 1, 0], [-1, 1, 0], [0, 1, 0], [1, 1, 0], [2, 1, 0], [3, 1, 0], [4, 1, 0], [5, 1, 0], [6, 1, 0], [7, 1, 0], [8, 1, 0], [9, 1, 0], [-9, 2, 0], [-8, 2, 0], [-7, 2, 0], [-6, 2, 0], [-5, 2, 0], [-4, 2, 0], [-3, 2, 0], [-2, 2, 0], [-1, 2, 0], [0, 2, 0], [1, 2, 0], [2, 2, 0], [3, 2, 0], [4, 2, 0], [5, 2, 0], [6, 2, 0], [7, 2, 0], [8, 2, 0], [9, 2, 0], [-9, 3, 0], [-8, 3, 0], [-7, 3, 0], [-6, 3, 0], [-5, 3, 0], [-4, 3, 0], [-3, 3, 0], [-2, 3, 0], [-1, 3, 0], [0, 3, 0], [1, 3, 0], [2, 3, 0], [3, 3, 0], [4, 3, 0], [5, 3, 0], [6, 3, 0], [7, 3, 0], [8, 3, 0], [9, 3, 0], [-9, 4, 0], [-8, 4, 0], [-7, 4, 0], [-6, 4, 0], [-5, 4, 0], [-4, 4, 0], [-3, 4, 0], [-2, 4, 0], [-1, 4, 0], [0, 4, 0], [1, 4, 0], [2, 4, 0], [3, 4, 0], [4, 4, 0], [5, 4, 0], [6, 4, 0], [7, 4, 0], [8, 4, 0], [9, 4, 0], [-8, 5, 0], [-7, 5, 0], [-6, 5, 0], [-5, 5, 0], [-4, 5, 0], [-3, 5, 0], [-2, 5, 0], [-1, 5, 0], [0, 5, 0], [1, 5, 0], [2, 5, 0], [3, 5, 0], [4, 5, 0], [5, 5, 0], [6, 5, 0], [7, 5, 0], [8, 5, 0], [-7, 6, 0], [-6, 6, 0], [-5, 6, 0], [-4, 6, 0], [-3, 6, 0], [-2, 6, 0], [-1, 6, 0], [0, 6, 0], [1, 6, 0], [2, 6, 0], [3, 6, 0], [4, 6, 0], [5, 6, 0], [6, 6, 0], [7, 6, 0], [-7, 7, 0], [-6, 7, 0], [-5, 7, 0], [-4, 7, 0], [-3, 7, 0], [-2, 7, 0], [-1, 7, 0], [0, 7, 0], [1, 7, 0], [2, 7, 0], [3, 7, 0], [4, 7, 0], [5, 7, 0], [6, 7, 0], [7, 7, 0], [-5, 8, 0], [-4, 8, 0], [-3, 8, 0], [-2, 8, 0], [-1, 8, 0], [0, 8, 0], [1, 8, 0], [2, 8, 0], [3, 8, 0], [4, 8, 0], [5, 8, 0], [-4, 9, 0], [-3, 9, 0], [-2, 9, 0], [-1, 9, 0], [0, 9, 0], [1, 9, 0], [2, 9, 0], [3, 9, 0], [4, 9, 0], [-3, -7, 1], [-2, -7, 1], [-1, -7, 1], [0, -7, 1], [1, -7, 1], [2, -7, 1], [3, -7, 1], [-5, -6, 1], [-4, -6, 1], [-3, -6, 1], [-2, -6, 1], [-1, -6, 1], [0, -6, 1], [1, -6, 1], [2, -6, 1], [3, -6, 1], [4, -6, 1], [5, -6, 1], [-6, -5, 1], [-5, -5, 1], [-4, -5, 1], [-3, -5, 1], [-2, -5, 1], [-1, -5, 1], [0, -5, 1], [1, -5, 1], [2, -5, 1], [3, -5, 1], [4, -5, 1], [5, -5, 1], [6, -5, 1], [-6, -4, 1], [-5, -4, 1], [-4, -4, 1], [-3, -4, 1], [-2, -4, 1], [-1, -4, 1], [0, -4, 1], [1, -4, 1], [2, -4, 1], [3, -4, 1], [4, -4, 1], [5, -4, 1], [6, -4, 1], [-7, -3, 1], [-6, -3, 1], [-5, -3, 1], [-4, -3, 1], [-3, -3, 1], [-2, -3, 1], [-1, -3, 1], [0, -3, 1], [1, -3, 1], [2, -3, 1], [3, -3, 1], [4, -3, 1], [5, -3, 1], [6, -3, 1], [7, -3, 1], [-7, -2, 1], [-6, -2, 1], [-5, -2, 1], [-4, -2, 1], [-3, -2, 1], [-2, -2, 1], [-1, -2, 1], [0, -2, 1], [1, -2, 1], [2, -2, 1], [3, -2, 1], [4, -2, 1], [5, -2, 1], [6, -2, 1], [7, -2, 1], [-7, -1, 1], [-6, -1, 1], [-5, -1, 1], [-4, -1, 1], [-3, -1, 1], [-2, -1, 1], [-1, -1, 1], [0, -1, 1], [1, -1, 1], [2, -1, 1], [3, -1, 1], [4, -1, 1], [5, -1, 1], [6, -1, 1], [7, -1, 1], [-7, 0, 1], [-6, 0, 1], [-5, 0, 1], [-4, 0, 1], [-3, 0, 1], [-2, 0, 1], [-1, 0, 1], [0, 0, 1], [1, 0, 1], [2, 0, 1], [3, 0, 1], [4, 0, 1], [5, 0, 1], [6, 0, 1], [7, 0, 1], [-7, 1, 1], [-6, 1, 1], [-5, 1, 1], [-4, 1, 1], [-3, 1, 1], [-2, 1, 1], [-1, 1, 1], [0, 1, 1], [1, 1, 1], [2, 1, 1], [3, 1, 1], [4, 1, 1], [5, 1, 1], [6, 1, 1], [7, 1, 1], [-7, 2, 1], [-6, 2, 1], [-5, 2, 1], [-4, 2, 1], [-3, 2, 1], [-2, 2, 1], [-1, 2, 1], [0, 2, 1], [1, 2, 1], [2, 2, 1], [3, 2, 1], [4, 2, 1], [5, 2, 1], [6, 2, 1], [7, 2, 1], [-7, 3, 1], [-6, 3, 1], [-5, 3, 1], [-4, 3, 1], [-3, 3, 1], [-2, 3, 1], [-1, 3, 1], [0, 3, 1], [1, 3, 1], [2, 3, 1], [3, 3, 1], [4, 3, 1], [5, 3, 1], [6, 3, 1], [7, 3, 1], [-6, 4, 1], [-5, 4, 1], [-4, 4, 1], [-3, 4, 1], [-2, 4, 1], [-1, 4, 1], [0, 4, 1], [1, 4, 1], [2, 4, 1], [3, 4, 1], [4, 4, 1], [5, 4, 1], [6, 4, 1], [-6, 5, 1], [-5, 5, 1], [-4, 5, 1], [-3, 5, 1], [-2, 5, 1], [-1, 5, 1], [0, 5, 1], [1, 5, 1], [2, 5, 1], [3, 5, 1], [4, 5, 1], [5, 5, 1], [6, 5, 1], [-5, 6, 1], [-4, 6, 1], [-3, 6, 1], [-2, 6, 1], [-1, 6, 1], [0, 6, 1], [1, 6, 1], [2, 6, 1], [3, 6, 1], [4, 6, 1], [5, 6, 1], [-3, 7, 1], [-2, 7, 1], [-1, 7, 1], [0, 7, 1], [1, 7, 1], [2, 7, 1], [3, 7, 1], [-2, -4, 2], [-1, -4, 2], [0, -4, 2], [1, -4, 2], [2, -4, 2], [-3, -3, 2], [-2, -3, 2], [-1, -3, 2], [0, -3, 2], [1, -3, 2], [2, -3, 2], [3, -3, 2], [-4, -2, 2], [-3, -2, 2], [-2, -2, 2], [-1, -2, 2], [0, -2, 2], [1, -2, 2], [2, -2, 2], [3, -2, 2], [4, -2, 2], [-4, -1, 2], [-3, -1, 2], [-2, -1, 2], [-1, -1, 2], [0, -1, 2], [1, -1, 2], [2, -1, 2], [3, -1, 2], [4, -1, 2], [-4, 0, 2], [-3, 0, 2], [-2, 0, 2], [-1, 0, 2], [0, 0, 2], [1, 0, 2], [2, 0, 2], [3, 0, 2], [4, 0, 2], [-4, 1, 2], [-3, 1, 2], [-2, 1, 2], [-1, 1, 2], [0, 1, 2], [1, 1, 2], [2, 1, 2], [3, 1, 2], [4, 1, 2], [-4, 2, 2], [-3, 2, 2], [-2, 2, 2], [-1, 2, 2], [0, 2, 2], [1, 2, 2], [2, 2, 2], [3, 2, 2], [4, 2, 2], [-3, 3, 2], [-2, 3, 2], [-1, 3, 2], [0, 3, 2], [1, 3, 2], [2, 3, 2], [3, 3, 2], [-2, 4, 2], [-1, 4, 2], [0, 4, 2], [1, 4, 2], [2, 4, 2]]; + + actual = px_cylinder([r1, r2], h, true); + assertEqualPoints(expected, actual); + + expected2 = [[-4, -9, 0], [-3, -9, 0], [-2, -9, 0], [-1, -9, 0], [0, -9, 0], [1, -9, 0], [2, -9, 0], [3, -9, 0], [4, -9, 0], [-5, -8, 0], [-4, -8, 0], [-3, -8, 0], [-2, -8, 0], [-1, -8, 0], [0, -8, 0], [1, -8, 0], [2, -8, 0], [3, -8, 0], [4, -8, 0], [5, -8, 0], [-7, -7, 0], [-6, -7, 0], [-5, -7, 0], [-4, -7, 0], [-3, -7, 0], [-2, -7, 0], [-1, -7, 0], [0, -7, 0], [1, -7, 0], [2, -7, 0], [3, -7, 0], [4, -7, 0], [5, -7, 0], [6, -7, 0], [7, -7, 0], [-7, -6, 0], [-6, -6, 0], [-5, -6, 0], [-4, -6, 0], [-3, -6, 0], [-2, -6, 0], [-1, -6, 0], [0, -6, 0], [1, -6, 0], [2, -6, 0], [3, -6, 0], [4, -6, 0], [5, -6, 0], [6, -6, 0], [7, -6, 0], [-8, -5, 0], [-7, -5, 0], [-6, -5, 0], [-5, -5, 0], [-4, -5, 0], [-3, -5, 0], [-2, -5, 0], [-1, -5, 0], [0, -5, 0], [1, -5, 0], [2, -5, 0], [3, -5, 0], [4, -5, 0], [5, -5, 0], [6, -5, 0], [7, -5, 0], [8, -5, 0], [-9, -4, 0], [-8, -4, 0], [-7, -4, 0], [-6, -4, 0], [-5, -4, 0], [-4, -4, 0], [-3, -4, 0], [-2, -4, 0], [-1, -4, 0], [0, -4, 0], [1, -4, 0], [2, -4, 0], [3, -4, 0], [4, -4, 0], [5, -4, 0], [6, -4, 0], [7, -4, 0], [8, -4, 0], [9, -4, 0], [-9, -3, 0], [-8, -3, 0], [-7, -3, 0], [-6, -3, 0], [-5, -3, 0], [-4, -3, 0], [-3, -3, 0], [-2, -3, 0], [-1, -3, 0], [0, -3, 0], [1, -3, 0], [2, -3, 0], [3, -3, 0], [4, -3, 0], [5, -3, 0], [6, -3, 0], [7, -3, 0], [8, -3, 0], [9, -3, 0], [-9, -2, 0], [-8, -2, 0], [-7, -2, 0], [-6, -2, 0], [-5, -2, 0], [-4, -2, 0], [-3, -2, 0], [-2, -2, 0], [-1, -2, 0], [0, -2, 0], [1, -2, 0], [2, -2, 0], [3, -2, 0], [4, -2, 0], [5, -2, 0], 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6, 2], [6, 6, 2], [7, 6, 2], [-7, 7, 2], [-6, 7, 2], [-5, 7, 2], [-4, 7, 2], [-3, 7, 2], [-2, 7, 2], [-1, 7, 2], [0, 7, 2], [1, 7, 2], [2, 7, 2], [3, 7, 2], [4, 7, 2], [5, 7, 2], [6, 7, 2], [7, 7, 2], [-5, 8, 2], [-4, 8, 2], [-3, 8, 2], [-2, 8, 2], [-1, 8, 2], [0, 8, 2], [1, 8, 2], [2, 8, 2], [3, 8, 2], [4, 8, 2], [5, 8, 2], [-4, 9, 2], [-3, 9, 2], [-2, 9, 2], [-1, 9, 2], [0, 9, 2], [1, 9, 2], [2, 9, 2], [3, 9, 2], [4, 9, 2]]; + + actual2 = px_cylinder(r1, h, true); + assertEqualPoints(expected2, actual2); +} + +test_px_cylinder(); \ No newline at end of file diff --git a/test/pixel/test_px_line.scad b/test/pixel/test_px_line.scad new file mode 100644 index 00000000..6dbfd515 --- /dev/null +++ b/test/pixel/test_px_line.scad @@ -0,0 +1,13 @@ + +module test_px_line() { + echo("==== test_px_line ===="); + + include ; + include ; + expected = [[-10, 0, -10], [-9, 1, -10], [-9, 2, -9], [-8, 3, -9], [-8, 4, -8], [-7, 5, -8], [-6, 6, -8], [-6, 7, -7], [-5, 8, -7], [-5, 9, -6], [-4, 10, -6], [-3, 11, -6], [-3, 12, -5], [-2, 13, -5], [-2, 14, -4], [-1, 15, -4], [0, 16, -4], [0, 17, -3], [1, 18, -3], [1, 19, -2], [2, 20, -2], [3, 21, -2], [3, 22, -1], [4, 23, -1], [4, 24, 0], [5, 25, 0], [6, 26, 0], [6, 27, 1], [7, 28, 1], [7, 29, 2], [8, 30, 2], [9, 31, 2], [9, 32, 3], [10, 33, 3], [10, 34, 4], [11, 35, 4], [12, 36, 4], [12, 37, 5], [13, 38, 5], [13, 39, 6], [14, 40, 6], [15, 41, 6], [15, 42, 7], [16, 43, 7], [16, 44, 8], [17, 45, 8], [18, 46, 8], [18, 47, 9], [19, 48, 9], [19, 49, 10]]; + actual = px_line([-10, 0, -10], [20, 50, 10]); + + assertEqualPoints(expected, actual); +} + +test_px_line(); \ No newline at end of file diff --git a/test/pixel/test_px_polygon.scad b/test/pixel/test_px_polygon.scad new file mode 100644 index 00000000..c67cce05 --- /dev/null +++ b/test/pixel/test_px_polygon.scad @@ -0,0 +1,21 @@ + +module test_px_polygon() { + echo("==== test_px_polygon ===="); + + include ; + include ; + include ; + include ; + include ; + + expected = [[5, 10], [4, 10], [3, 9], [2, 9], [1, 9], [0, 8], [-1, 8], [-2, 8], [-3, 7], [-4, 7], [-5, 7], [-6, 6], [-7, 6], [-8, 6], [-9, 5], [-10, 5], [-10, 4], [-9, 3], [-9, 2], [-9, 1], [-8, 0], [-8, -1], [-8, -2], [-7, -3], [-7, -4], [-7, -5], [-6, -6], [-6, -7], [-6, -8], [-5, -9], [-5, -10], [-5, -10], [-4, -9], [-4, -8], [-3, -7], [-3, -6], [-2, -5], [-2, -4], [-1, -3], [-1, -2], [0, -1], [0, 0], [1, 1], [1, 2], [2, 3], [2, 4], [3, 5], [3, 6], [4, 7], [4, 8], [5, 9]]; + actual = px_polygon([[5, 10], [-10, 5], [-5, -10]], false); + + + assertEqualPoints(expected, actual); + + expected2 = [[-10, 5], [-9, 2], [-9, 3], [-9, 4], [-9, 5], [-8, -1], [-8, 0], [-8, 1], [-8, 2], [-8, 3], [-8, 4], [-8, 5], [-7, -4], [-7, -3], [-7, -2], [-7, -1], [-7, 0], [-7, 1], [-7, 2], [-7, 3], [-7, 4], [-7, 5], [-7, 6], [-6, -7], [-6, -6], [-6, -5], [-6, -4], [-6, -3], [-6, -2], [-6, -1], [-6, 0], [-6, 1], [-6, 2], [-6, 3], [-6, 4], [-6, 5], [-6, 6], [-5, -10], [-5, -9], [-5, -8], [-5, -7], [-5, -6], [-5, -5], [-5, -4], [-5, -3], [-5, -2], [-5, -1], [-5, 0], [-5, 1], [-5, 2], [-5, 3], [-5, 4], [-5, 5], [-5, 6], [-4, -8], [-4, -7], [-4, -6], [-4, -5], [-4, -4], [-4, -3], [-4, -2], [-4, -1], [-4, 0], [-4, 1], [-4, 2], [-4, 3], [-4, 4], [-4, 5], [-4, 6], [-4, 7], [-3, -6], [-3, -5], [-3, -4], [-3, -3], [-3, -2], [-3, -1], [-3, 0], [-3, 1], [-3, 2], [-3, 3], [-3, 4], [-3, 5], [-3, 6], [-3, 7], [-2, -4], [-2, -3], [-2, -2], [-2, -1], [-2, 0], [-2, 1], [-2, 2], [-2, 3], [-2, 4], [-2, 5], [-2, 6], [-2, 7], [-1, -2], [-1, -1], [-1, 0], [-1, 1], [-1, 2], [-1, 3], [-1, 4], [-1, 5], [-1, 6], [-1, 7], [-1, 8], [0, 0], [0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [3, 6], [3, 7], [3, 8], [3, 9], [4, 8], [4, 9], [5, 10]]; + actual2 = px_polygon([[5, 10], [-10, 5], [-5, -10]], true); +} + +test_px_polygon(); \ No newline at end of file diff --git a/test/pixel/test_px_polyline.scad b/test/pixel/test_px_polyline.scad new file mode 100644 index 00000000..66584b36 --- /dev/null +++ b/test/pixel/test_px_polyline.scad @@ -0,0 +1,14 @@ + +module test_px_polyline() { + echo("==== test_px_polyline ===="); + + include ; + include ; + include ; + expected = [[5, 10, 5], [4, 9, 5], [3, 8, 5], [2, 7, 6], [1, 6, 6], [0, 5, 6], [-1, 4, 6], [-2, 3, 6], [-3, 2, 6], [-4, 1, 7], [-5, 0, 7], [-6, -1, 7], [-7, -2, 7], [-8, -3, 7], [-9, -4, 7], [-10, -5, 8], [-11, -6, 8], [-12, -7, 8], [-13, -8, 8], [-14, -9, 8], [-15, -10, 8], [-16, -11, 9], [-17, -12, 9], [-18, -13, 9], [-19, -14, 9], [-20, -15, 9], [-21, -16, 9], [-22, -17, 10], [-23, -18, 10], [-24, -19, 10], [-25, -20, 10], [-25, -19, 10], [-25, -18, 10], [-25, -17, 10], [-25, -16, 11], [-25, -15, 11], [-25, -14, 11], [-25, -13, 11], [-25, -12, 11], [-25, -11, 11], [-25, -10, 11], [-25, -9, 12], [-25, -8, 12], [-25, -7, 12], [-25, -6, 12], [-25, -5, 12], [-25, -4, 12], [-25, -3, 12], [-25, -2, 13], [-25, -1, 13], [-25, 0, 13], [-25, 1, 13], [-25, 2, 13], [-25, 3, 13], [-25, 4, 13], [-25, 5, 14], [-25, 6, 14], [-25, 7, 14], [-25, 8, 14], [-25, 9, 14], [-25, 10, 14], [-25, 11, 14], [-25, 12, 15], [-25, 13, 15], [-25, 14, 15], [-25, 15, 15], [-24, 15, 15], [-23, 15, 15], [-22, 16, 15], [-21, 16, 15], [-20, 16, 16], [-19, 16, 16], [-18, 16, 16], [-17, 17, 16], [-16, 17, 16], [-15, 17, 16], [-14, 17, 16], [-13, 17, 16], [-12, 18, 16], [-11, 18, 16], [-10, 18, 17], [-9, 18, 17], [-8, 18, 17], [-7, 19, 17], [-6, 19, 17], [-5, 19, 17], [-4, 19, 17], [-3, 19, 17], [-2, 20, 17], [-1, 20, 17], [0, 20, 18], [1, 20, 18], [2, 20, 18], [3, 21, 18], [4, 21, 18], [5, 21, 18], [6, 21, 18], [7, 21, 18], [8, 22, 18], [9, 22, 18], [10, 22, 19], [11, 22, 19], [12, 22, 19], [13, 23, 19], [14, 23, 19], [15, 23, 19], [16, 23, 19], [17, 23, 19], [18, 24, 19], [19, 24, 19], [20, 24, 20], [21, 24, 20], [22, 24, 20], [23, 25, 20], [24, 25, 20]]; + actual = px_polyline([[5, 10, 5], [-25, -20, 10], [-25, 15, 15], [25, 25, 20]]); + + assertEqualPoints(expected, actual); +} + +test_px_polyline(); \ No newline at end of file diff --git a/test/pixel/test_px_sphere.scad b/test/pixel/test_px_sphere.scad new file mode 100644 index 00000000..d0c4708f --- /dev/null +++ b/test/pixel/test_px_sphere.scad @@ -0,0 +1,13 @@ + +module test_px_sphere() { + echo("==== test_px_sphere ===="); + + include ; + include ; + expected = [[-2, -2, -4], [-1, -2, -4], [0, -2, -4], [1, -2, -4], [2, -2, -4], [-2, -1, -4], [-1, -1, -4], [0, -1, -4], [1, -1, -4], [2, -1, -4], [-2, 0, -4], [-1, 0, -4], [0, 0, -4], [1, 0, -4], [2, 0, -4], [-2, 1, -4], [-1, 1, -4], [0, 1, -4], [1, 1, -4], [2, 1, -4], [-2, 2, -4], [-1, 2, -4], [0, 2, -4], [1, 2, -4], [2, 2, -4], [-2, -3, -3], [-1, -3, -3], [0, -3, -3], [1, -3, -3], [2, -3, -3], [-3, -2, -3], [-2, -2, -3], [2, -2, -3], [3, -2, -3], [-3, -1, -3], [3, -1, -3], [-3, 0, -3], [3, 0, -3], [-3, 1, -3], [3, 1, -3], [-3, 2, -3], [-2, 2, -3], [2, 2, -3], [3, 2, -3], [-2, 3, -3], [-1, 3, -3], [0, 3, -3], [1, 3, -3], [2, 3, -3], [-2, -4, -2], [-1, -4, -2], [0, -4, -2], [1, -4, -2], [2, -4, -2], [-3, -3, -2], [-2, -3, -2], [2, -3, -2], [3, -3, -2], [-4, -2, -2], [-3, -2, -2], [3, -2, -2], [4, -2, -2], [-4, -1, -2], [4, -1, -2], [-4, 0, -2], [4, 0, -2], [-4, 1, -2], [4, 1, -2], [-4, 2, -2], [-3, 2, -2], [3, 2, -2], [4, 2, -2], [-3, 3, -2], [-2, 3, -2], [2, 3, -2], [3, 3, -2], [-2, 4, -2], [-1, 4, -2], [0, 4, -2], [1, 4, -2], [2, 4, -2], [-2, -4, -1], [-1, -4, -1], [0, -4, -1], [1, -4, -1], [2, -4, -1], [-3, -3, -1], [3, -3, -1], [-4, -2, -1], [4, -2, -1], [-4, -1, -1], [4, -1, -1], [-4, 0, -1], [4, 0, -1], [-4, 1, -1], [4, 1, -1], [-4, 2, -1], [4, 2, -1], [-3, 3, -1], [3, 3, -1], [-2, 4, -1], [-1, 4, -1], [0, 4, -1], [1, 4, -1], [2, 4, -1], [-2, -4, 0], [-1, -4, 0], [0, -4, 0], [1, -4, 0], [2, -4, 0], [-3, -3, 0], [3, -3, 0], [-4, -2, 0], [4, -2, 0], [-4, -1, 0], [4, -1, 0], [-4, 0, 0], [4, 0, 0], [-4, 1, 0], [4, 1, 0], [-4, 2, 0], [4, 2, 0], [-3, 3, 0], [3, 3, 0], [-2, 4, 0], [-1, 4, 0], [0, 4, 0], [1, 4, 0], [2, 4, 0], [-2, -4, 1], [-1, -4, 1], [0, -4, 1], [1, -4, 1], [2, -4, 1], [-3, -3, 1], [3, -3, 1], [-4, -2, 1], [4, -2, 1], [-4, -1, 1], [4, -1, 1], [-4, 0, 1], [4, 0, 1], [-4, 1, 1], [4, 1, 1], [-4, 2, 1], [4, 2, 1], [-3, 3, 1], [3, 3, 1], [-2, 4, 1], [-1, 4, 1], [0, 4, 1], [1, 4, 1], [2, 4, 1], [-2, -4, 2], [-1, -4, 2], [0, -4, 2], [1, -4, 2], [2, -4, 2], [-3, -3, 2], [-2, -3, 2], [2, -3, 2], [3, -3, 2], [-4, -2, 2], [-3, -2, 2], [3, -2, 2], [4, -2, 2], [-4, -1, 2], [4, -1, 2], [-4, 0, 2], [4, 0, 2], [-4, 1, 2], [4, 1, 2], [-4, 2, 2], [-3, 2, 2], [3, 2, 2], [4, 2, 2], [-3, 3, 2], [-2, 3, 2], [2, 3, 2], [3, 3, 2], [-2, 4, 2], [-1, 4, 2], [0, 4, 2], [1, 4, 2], [2, 4, 2], [-2, -3, 3], [-1, -3, 3], [0, -3, 3], [1, -3, 3], [2, -3, 3], [-3, -2, 3], [-2, -2, 3], [2, -2, 3], [3, -2, 3], [-3, -1, 3], [3, -1, 3], [-3, 0, 3], [3, 0, 3], [-3, 1, 3], [3, 1, 3], [-3, 2, 3], [-2, 2, 3], [2, 2, 3], [3, 2, 3], [-2, 3, 3], [-1, 3, 3], [0, 3, 3], [1, 3, 3], [2, 3, 3], [-2, -2, 4], [-1, -2, 4], [0, -2, 4], [1, -2, 4], [2, -2, 4], [-2, -1, 4], [-1, -1, 4], [0, -1, 4], [1, -1, 4], [2, -1, 4], [-2, 0, 4], [-1, 0, 4], [0, 0, 4], [1, 0, 4], [2, 0, 4], [-2, 1, 4], [-1, 1, 4], [0, 1, 4], [1, 1, 4], [2, 1, 4], [-2, 2, 4], [-1, 2, 4], [0, 2, 4], [1, 2, 4], [2, 2, 4]]; + actual = px_sphere(5, false); + + assertEqualPoints(expected, actual); +} + +test_px_sphere(); \ No newline at end of file diff --git a/test/test_all.scad b/test/test_all.scad index fe4e1e76..2d66a739 100644 --- a/test/test_all.scad +++ b/test/test_all.scad @@ -17,14 +17,16 @@ include ; // Transformation include ; +include ; // Function include ; -include ; -include ; -include ; include ; include ; +include ; +include ; +include ; +include ; // Path include ; @@ -35,17 +37,21 @@ include ; include ; include ; include ; +include ; // Extrude include ; include ; // 2D Shape +include ; include ; include ; +include ; include ; include ; include ; +include ; include ; include ; @@ -54,4 +60,23 @@ include ; include ; include ; include ; -include ; \ No newline at end of file +include ; +include ; + +// Utilities +include ; +include ; +include ; +include ; +include ; + +// Pixel +include ; +include ; +include ; +include ; +include ; +include ; + +// Matrix +include ; \ No newline at end of file diff --git a/test/test_along_with.scad b/test/test_along_with.scad new file mode 100644 index 00000000..7016a52f --- /dev/null +++ b/test/test_along_with.scad @@ -0,0 +1,55 @@ +include ; + +module test_along_with_default_angles() { + echo("==== test_along_with_default_angles ===="); + + include ; + include ; + + $fn = 24; + + points = circle_path(radius = 50); + + module test_along_with_angles(angles) { + expected_angles = [[0, 0, 97.5], [0, 0, 97.5], [0, 0, 112.5], [0, 0, 127.5], [0, 0, 142.5], [0, 0, 157.5], [0, 0, 172.5], [0, 0, -172.5], [0, 0, -157.5], [0, 0, -142.5], [0, 0, -127.5], [0, 0, -112.5], [0, 0, -97.5], [0, 0, -82.5], [0, 0, -67.5], [0, 0, -52.5], [0, 0, -37.5], [0, 0, -22.5], [0, 0, -7.5], [0, 0, 7.5], [0, 0, 22.5], [0, 0, 37.5], [0, 0, 52.5], [0, 0, 67.5]]; + assert($fn == len(angles)); + assertEqualPoints(expected_angles, angles); + } + + along_with(points, method = "EULER_ANGLE") + sphere(5); + +} + +module test_along_with_children() { + echo("==== test_along_with_children ===="); + + include ; + include ; + + $fn = 24; + + points = circle_path(radius = 50); + + module test_along_with_angles(angles) { + expected_angles = [[0, 0, 97.5], [0, 0, 97.5], [0, 0, 112.5], [0, 0, 127.5], [0, 0, 142.5], [0, 0, 157.5], [0, 0, 172.5], [0, 0, -172.5]]; + + assert(8 == len(angles)); + assertEqualPoints(expected_angles, angles); + } + + along_with(points, method = "EULER_ANGLE") { + linear_extrude(10, center = true) text("A", valign = "center", halign = "center"); + linear_extrude(5, center = true) circle(2); + sphere(1); + cube(5); + linear_extrude(10, center = true) text("A", valign = "center", halign = "center"); + linear_extrude(5, center = true) circle(2); + sphere(1); + cube(5); + } + +} + +test_along_with_default_angles(); +test_along_with_children(); \ No newline at end of file diff --git a/test/test_archimedean_spiral.scad b/test/test_archimedean_spiral.scad index bb37fd13..cee26083 100644 --- a/test/test_archimedean_spiral.scad +++ b/test/test_archimedean_spiral.scad @@ -12,18 +12,16 @@ module test_archimedean_spiral() { ); - expected_points = [[-5, 0], [-3.3333, -5.7735], [1.9153, -7.6542], [6.9287, -5.6121], [9.7591, -1.1017], [9.7906, 4.1666], [7.2895, 8.7588], [3.0136, 11.7181], [-2.0901, 12.5895], [-7.0994, 11.3524], [-11.25, 8.3116], [-14.0047, 3.9802], [-15.0734, -1.03], [-14.3991, -6.0996], [-12.1214, -10.6703], [-8.5301, -14.2915], [-4.013, -16.6466], [0.9931, -17.5619], [6.0464, -17.0006], [10.7367, -15.0488], [14.7127, -11.8925], [17.7005, -7.7927], [19.5144, -3.0584], [20.0591, 1.9792], [19.327, 6.9904], [17.3894, 11.6667], [14.385, 15.7377], [10.5054, 18.9824], [5.9805, 21.2371], [1.0622, 22.3994], [-3.9897, 22.4281], [-8.9216, 21.3404], [-13.4974, 19.2066], [-17.5086, 16.1426], [-20.7812, 12.3017], [-23.1817, 7.8645], [-24.6193, 3.0301], [-25.0472, -1.9943], [-24.4614, -7.0016], [-22.8983, -11.7935], [-20.4309, -16.1876], [-17.1632, -20.0228], [-13.2255, -23.1648], [-8.7672, -25.5085], [-3.9513, -26.9808], [1.0527, -27.5407], [6.0742, -27.1795], [10.9476, -25.9189], [15.5171, -23.8091], [19.6415, -20.9256], [23.1974, -17.3655], [26.0825, -13.2437], [28.2172, -8.6885], [29.5463, -3.8373], [30.0392, 1.168], [29.6895, 6.1848], [28.5147, 11.0741], [26.5539, 15.704], [23.8664, 19.9529], [20.5291, 23.7124], [16.6337, 26.8894], [12.2839, 29.4078], [7.5924, 31.21], [2.6774, 32.2573], [-2.3402, 32.5302], [-7.3397, 32.0283], [-12.2036, 30.7692], [-16.8203, 28.7878], [-21.0862, 26.1347], [-24.9077, 22.8745], [-28.2033, 19.084], [-30.9046, 14.8497], [-32.9575, 10.2661], [-34.3228, 5.4333], [-34.9764, 0.4543], [-34.9096, -4.5667], [-34.1286, -9.5267], [-32.6536, -14.326], [-30.5187, -18.8701], [-27.77, -23.0711], [-24.4648, -26.8496], [-20.67, -30.1356], [-16.4604, -32.8699], [-11.9176, -35.0046], [-7.1276, -36.5038], [-2.1794, -37.3437], [2.8365, -37.513], [7.83, -37.0127], [12.713, -35.8552], [17.4007, -34.0647], [21.8134, -31.6755], [25.8769, -28.7318], [29.5245, -25.2864], [32.6974, -21.3997], [35.3456, -17.1384], [37.4285, -12.5742], [38.9152, -7.7828], [39.7851, -2.8422], [40.0275, 2.1685], [39.6416, 7.1699]]; - - expected_angles = [180, 240, 285, 321, 354, 384, 411, 436, 460, 483, 504, 525, 544, 563, 582, 600, 617, 634, 650, 666, 682, 697, 712, 726, 740, 754, 768, 782, 795, 808, 821, 833, 846, 858, 870, 882, 893, 905, 916, 928, 939, 950, 961, 972, 982, 993, 1003, 1013, 1024, 1034, 1044, 1054, 1063, 1073, 1083, 1092, 1102, 1111, 1120, 1130, 1139, 1148, 1157, 1166, 1175, 1183, 1192, 1201, 1209, 1218, 1226, 1235, 1243, 1252, 1260, 1268, 1276, 1284, 1292, 1300, 1308, 1316, 1324, 1332, 1339, 1347, 1355, 1362, 1370, 1378, 1385, 1393, 1400, 1407, 1415, 1422, 1429, 1436, 1444, 1451]; + expected_points = [[-5, -5.6166e-6], [-3.33332, -5.77351], [1.91533, -7.65424], [6.92877, -5.61211], [9.7591, -1.1017], [9.79062, 4.16668], [7.28945, 8.75883], [3.01356, 11.7181], [-2.09019, 12.5895], [-7.09946, 11.3523], [-11.25, 8.31153], [-14.0047, 3.9801], [-15.0734, -1.03017], [-14.399, -6.09976], [-12.1214, -10.6704], [-8.52998, -14.2915], [-4.01284, -16.6467], [0.993248, -17.5618], [6.04659, -17.0006], [10.7369, -15.0487], [14.7128, -11.8923], [17.7006, -7.79251], [19.5144, -3.05819], [20.0591, 1.97944], [19.327, 6.99059], [17.3893, 11.6669], [14.3848, 15.7379], [10.5052, 18.9825], [5.98025, 21.2372], [1.06198, 22.3994], [-3.98996, 22.4281], [-8.92185, 21.3403], [-13.4977, 19.2064], [-17.5088, 16.1424], [-20.7814, 12.3014], [-23.1818, 7.86423], [-24.6194, 3.02975], [-25.0472, -1.9946], [-24.4613, -7.0019], [-22.8982, -11.7938], [-20.4306, -16.1878], [-17.163, -20.0231], [-13.2252, -23.165], [-8.76686, -25.5087], [-3.95086, -26.9808], [1.05313, -27.5407], [6.07462, -27.1794], [10.948, -25.9187], [15.5175, -23.8089], [19.6418, -20.9253], [23.1977, -17.3652], [26.0827, -13.2433], [28.2174, -8.68809], [29.5464, -3.8368], [30.0391, 1.16851], [29.6894, 6.18531], [28.5145, 11.0746], [26.5536, 15.7045], [23.866, 19.9533], [20.5287, 23.7128], [16.6332, 26.8897], [12.2835, 29.408], [7.59187, 31.2101], [2.6768, 32.2573], [-2.34079, 32.5302], [-7.34027, 32.0282], [-12.2042, 30.769], [-16.8208, 28.7875], [-21.0866, 26.1344], [-24.9081, 22.8741], [-28.2036, 19.0834], [-30.9049, 14.8491], [-32.9577, 10.2655], [-34.3229, 5.43264], [-34.9764, 0.453654], [-34.9095, -4.56731], [-34.1284, -9.52732], [-32.6534, -14.3266], [-30.5184, -18.8707], [-27.7696, -23.0716], [-24.4643, -26.8501], [-20.6694, -30.136], [-16.4598, -32.8703], [-11.9169, -35.0049], [-7.12684, -36.5039], [-2.17866, -37.3437], [2.83721, -37.513], [7.83071, -37.0125], [12.7137, -35.855], [17.4014, -34.0643], [21.814, -31.675], [25.8775, -28.7313], [29.525, -25.2858], [32.6978, -21.399], [35.3459, -17.1377], [37.4287, -12.5734], [38.9154, -7.78198], [39.7852, -2.84131], [40.0274, 2.16931], [39.6415, 7.17075]]; + expected_angles = [180, 240, 284.049, 320.993, 353.559, 383.054, 410.231, 435.578, 459.427, 482.021, 503.543, 524.135, 543.91, 562.959, 581.357, 599.169, 616.447, 633.237, 649.579, 665.507, 681.051, 696.239, 711.093, 725.636, 739.885, 753.859, 767.572, 781.039, 794.273, 807.286, 820.087, 832.689, 845.098, 857.325, 869.377, 881.261, 892.984, 904.553, 915.973, 927.251, 938.391, 949.398, 960.277, 971.033, 981.669, 992.19, 1002.6, 1012.9, 1023.09, 1033.19, 1043.18, 1053.08, 1062.89, 1072.6, 1082.23, 1091.77, 1101.23, 1110.6, 1119.9, 1129.12, 1138.26, 1147.33, 1156.33, 1165.26, 1174.12, 1182.91, 1191.64, 1200.3, 1208.9, 1217.44, 1225.92, 1234.34, 1242.7, 1251.01, 1259.26, 1267.45, 1275.6, 1283.69, 1291.73, 1299.72, 1307.66, 1315.55, 1323.4, 1331.2, 1338.95, 1346.66, 1354.33, 1361.95, 1369.52, 1377.06, 1384.55, 1392.01, 1399.42, 1406.8, 1414.13, 1421.43, 1428.69, 1435.92, 1443.1, 1450.25]; actual_points = [for(pa = points_angles) pa[0]]; - // ceil for annoying float errors when echoing...XD - actual_angles = [for(pa = points_angles) ceil(pa[1])]; - + actual_angles = [for(pa = points_angles) pa[1]]; + assertEqualPoints(expected_points, actual_points); for(i = [0:0]) { - assertEqual(expected_angles[i], actual_angles[i]); + assertEqualNum(expected_angles[i], actual_angles[i]); } } diff --git a/test/test_archimedean_spiral_extrude.scad b/test/test_archimedean_spiral_extrude.scad index 96de41f9..af44fbbd 100644 --- a/test/test_archimedean_spiral_extrude.scad +++ b/test/test_archimedean_spiral_extrude.scad @@ -11,111 +11,10 @@ module test_archimedean_spiral_extrude_slide() { include ; module test_archimedean_spiral_extrude(sections) { - expected = [ - [[-12.5, 0, 0], [-12.5, 0, 4], [-11.5, 0, 4], [-11.5, 0, 2], [-3.5, 0, 2], [-3.5, 0, 4], [-2.5, 0, 4], [-2.5, 0, 0]] - , [[-10.984, -8.877, 0], [-10.984, -8.877, 4.162], [-10.206, -8.248, 4.162], [-10.206, -8.248, 2.081], [-3.984, -3.22, 2.081], [-3.984, -3.22, 4.162], [-3.206, -2.591, 4.162], [-3.206, -2.591, 0]] - , [[-5.092, -14.585, 0], [-5.092, -14.585, 4.323], [-4.763, -13.64, 4.323], [-4.763, -13.64, 2.162], [-2.126, -6.088, 2.162], [-2.126, -6.088, 4.323], [-1.796, -5.143, 4.323], [-1.796, -5.143, 0]] - , [[2.437, -16.422, 0], [2.437, -16.422, 4.485], [2.29, -15.433, 4.485], [2.29, -15.433, 2.242], [1.116, -7.519, 2.242], [1.116, -7.519, 4.485], [0.969, -6.53, 4.485], [0.969, -6.53, 0]] - , [[9.691, -14.738, 0], [9.691, -14.738, 4.646], [9.142, -13.902, 4.646], [9.142, -13.902, 2.323], [4.746, -7.218, 2.323], [4.746, -7.218, 4.646], [4.197, -6.382, 4.646], [4.197, -6.382, 0]] - , [[15.438, -10.356, 0], [15.438, -10.356, 4.808], [14.607, -9.799, 4.808], [14.607, -9.799, 2.404], [7.964, -5.342, 2.404], [7.964, -5.342, 4.808], [7.133, -4.785, 4.808], [7.133, -4.785, 0]] - , [[19, -4.265, 0], [19, -4.265, 4.97], [18.024, -4.046, 4.97], [18.024, -4.046, 2.485], [10.219, -2.294, 2.485], [10.219, -2.294, 4.97], [9.243, -2.075, 4.97], [9.243, -2.075, 0]] - , [[20.14, 2.559, 0], [20.14, 2.559, 5.131], [19.148, 2.433, 5.131], [19.148, 2.433, 2.566], [11.212, 1.425, 2.566], [11.212, 1.425, 5.131], [10.22, 1.299, 5.131], [10.22, 1.299, 0]] - , [[18.944, 9.259, 0], [18.944, 9.259, 5.293], [18.045, 8.82, 5.293], [18.045, 8.82, 2.646], [10.858, 5.307, 2.646], [10.858, 5.307, 5.293], [9.959, 4.868, 5.293], [9.959, 4.868, 0]] - , [[15.722, 15.146, 0], [15.722, 15.146, 5.455], [15.002, 14.452, 5.455], [15.002, 14.452, 2.727], [9.24, 8.902, 2.727], [9.24, 8.902, 5.455], [8.52, 8.208, 5.455], [8.52, 8.208, 0]] - , [[10.924, 19.719, 0], [10.924, 19.719, 5.616], [10.439, 18.844, 5.616], [10.439, 18.844, 2.808], [6.562, 11.846, 2.808], [6.562, 11.846, 5.616], [6.078, 10.971, 5.616], [6.078, 10.971, 0]] - , [[5.066, 22.666, 0], [5.066, 22.666, 5.778], [4.848, 21.69, 5.778], [4.848, 21.69, 2.889], [3.103, 13.883, 2.889], [3.103, 13.883, 5.778], [2.885, 12.907, 5.778], [2.885, 12.907, 0]] - , [[-1.321, 23.846, 0], [-1.321, 23.846, 5.939], [-1.265, 22.847, 5.939], [-1.265, 22.847, 2.97], [-0.823, 14.859, 2.97], [-0.823, 14.859, 5.939], [-0.768, 13.861, 5.939], [-0.768, 13.861, 0]] - , [[-7.733, 23.265, 0], [-7.733, 23.265, 6.101], [-7.418, 22.316, 6.101], [-7.418, 22.316, 3.051], [-4.894, 14.724, 3.051], [-4.894, 14.724, 6.101], [-4.579, 13.775, 6.101], [-4.579, 13.775, 0]] - , [[-13.726, 21.05, 0], [-13.726, 21.05, 6.263], [-13.179, 20.212, 6.263], [-13.179, 20.212, 3.131], [-8.81, 13.511, 3.131], [-8.81, 13.511, 6.263], [-8.264, 12.673, 6.263], [-8.264, 12.673, 0]] - , [[-18.928, 17.42, 0], [-18.928, 17.42, 6.424], [-18.192, 16.743, 6.424], [-18.192, 16.743, 3.212], [-12.306, 11.325, 3.212], [-12.306, 11.325, 6.424], [-11.57, 10.648, 6.424], [-11.57, 10.648, 0]] - , [[-23.055, 12.658, 0], [-23.055, 12.658, 6.586], [-22.179, 12.176, 6.586], [-22.179, 12.176, 3.293], [-15.166, 8.326, 3.293], [-15.166, 8.326, 6.586], [-14.289, 7.845, 6.586], [-14.289, 7.845, 0]] - , [[-25.912, 7.083, 0], [-25.912, 7.083, 6.747], [-24.948, 6.819, 6.747], [-24.948, 6.819, 3.374], [-17.231, 4.71, 3.374], [-17.231, 4.71, 6.747], [-16.266, 4.446, 6.747], [-16.266, 4.446, 0]] - , [[-27.391, 1.031, 0], [-27.391, 1.031, 6.909], [-26.392, 0.993, 6.909], [-26.392, 0.993, 3.455], [-18.397, 0.692, 3.455], [-18.397, 0.692, 6.909], [-17.398, 0.655, 6.909], [-17.398, 0.655, 0]] - , [[-27.462, -5.166, 0], [-27.462, -5.166, 7.071], [-26.479, -4.982, 7.071], [-26.479, -4.982, 3.535], [-18.617, -3.502, 3.535], [-18.617, -3.502, 7.071], [-17.635, -3.318, 7.071], [-17.635, -3.318, 0]] - , [[-26.17, -11.198, 0], [-26.17, -11.198, 7.232], [-25.251, -10.804, 7.232], [-25.251, -10.804, 3.616], [-17.896, -7.657, 3.616], [-17.896, -7.657, 7.232], [-16.976, -7.264, 7.232], [-16.976, -7.264, 0]] - , [[-23.619, -16.783, 0], [-23.619, -16.783, 7.394], [-22.804, -16.204, 7.394], [-22.804, -16.204, 3.697], [-16.283, -11.57, 3.697], [-16.283, -11.57, 7.394], [-15.468, -10.991, 7.394], [-15.468, -10.991, 0]] - , [[-19.962, -21.684, 0], [-19.962, -21.684, 7.556], [-19.285, -20.949, 7.556], [-19.285, -20.949, 3.778], [-13.867, -15.063, 3.778], [-13.867, -15.063, 7.556], [-13.189, -14.327, 7.556], [-13.189, -14.327, 0]] - , [[-15.39, -25.708, 0], [-15.39, -25.708, 7.717], [-14.876, -24.85, 7.717], [-14.876, -24.85, 3.859], [-10.767, -17.986, 3.859], [-10.767, -17.986, 7.717], [-10.253, -17.128, 7.717], [-10.253, -17.128, 0]] - , [[-10.116, -28.711, 0], [-10.116, -28.711, 7.879], [-9.784, -27.768, 7.879], [-9.784, -27.768, 3.939], [-7.126, -20.223, 3.939], [-7.126, -20.223, 7.879], [-6.793, -19.279, 7.879], [-6.793, -19.279, 0]] - , [[-4.372, -30.6, 0], [-4.372, -30.6, 8.04], [-4.231, -29.61, 8.04], [-4.231, -29.61, 4.02], [-3.099, -21.691, 4.02], [-3.099, -21.691, 8.04], [-2.958, -20.701, 8.04], [-2.958, -20.701, 0]] - , [[1.61, -31.331, 0], [1.61, -31.331, 8.202], [1.559, -30.333, 8.202], [1.559, -30.333, 4.101], [1.148, -22.343, 4.101], [1.148, -22.343, 8.202], [1.097, -21.344, 8.202], [1.097, -21.344, 0]] - , [[7.603, -30.904, 0], [7.603, -30.904, 8.364], [7.364, -29.933, 8.364], [7.364, -29.933, 4.182], [5.453, -22.165, 4.182], [5.453, -22.165, 8.364], [5.214, -21.194, 8.364], [5.214, -21.194, 0]] - , [[13.391, -29.362, 0], [13.391, -29.362, 8.525], [12.976, -28.452, 8.525], [12.976, -28.452, 4.263], [9.656, -21.174, 4.263], [9.656, -21.174, 8.525], [9.241, -20.264, 8.525], [9.241, -20.264, 0]] - , [[18.778, -26.783, 0], [18.778, -26.783, 8.687], [18.204, -25.964, 8.687], [18.204, -25.964, 4.343], [13.611, -19.414, 4.343], [13.611, -19.414, 8.687], [13.037, -18.595, 8.687], [13.037, -18.595, 0]] - , [[23.592, -23.275, 0], [23.592, -23.275, 8.848], [22.881, -22.573, 8.848], [22.881, -22.573, 4.424], [17.186, -16.954, 4.424], [17.186, -16.954, 8.848], [16.474, -16.252, 8.848], [16.474, -16.252, 0]] - , [[27.689, -18.973, 0], [27.689, -18.973, 9.01], [26.865, -18.407, 9.01], [26.865, -18.407, 4.505], [20.265, -13.886, 4.505], [20.265, -13.886, 9.01], [19.44, -13.32, 9.01], [19.44, -13.32, 0]] - , [[30.955, -14.027, 0], [30.955, -14.027, 9.172], [30.044, -13.614, 9.172], [30.044, -13.614, 4.586], [22.757, -10.312, 4.586], [22.757, -10.312, 9.172], [21.846, -9.899, 9.172], [21.846, -9.899, 0]] - , [[33.304, -8.601, 0], [33.304, -8.601, 9.333], [32.336, -8.351, 9.333], [32.336, -8.351, 4.667], [24.59, -6.351, 4.667], [24.59, -6.351, 9.333], [23.622, -6.101, 9.333], [23.622, -6.101, 0]] - , [[34.685, -2.866, 0], [34.685, -2.866, 9.495], [33.688, -2.784, 9.495], [33.688, -2.784, 4.747], [25.716, -2.125, 4.747], [25.716, -2.125, 9.495], [24.719, -2.043, 9.495], [24.719, -2.043, 0]] - , [[35.076, 3.007, 0], [35.076, 3.007, 9.657], [34.079, 2.921, 9.657], [34.079, 2.921, 4.828], [26.108, 2.238, 4.828], [26.108, 2.238, 9.657], [25.112, 2.153, 9.657], [25.112, 2.153, 0]] - , [[34.482, 8.85, 0], [34.482, 8.85, 9.818], [33.514, 8.602, 9.818], [33.514, 8.602, 4.909], [25.765, 6.613, 4.909], [25.765, 6.613, 9.818], [24.796, 6.364, 9.818], [24.796, 6.364, 0]] - , [[32.938, 14.505, 0], [32.938, 14.505, 9.98], [32.023, 14.102, 9.98], [32.023, 14.102, 4.99], [24.701, 10.878, 4.99], [24.701, 10.878, 9.98], [23.786, 10.475, 9.98], [23.786, 10.475, 0]] - , [[30.5, 19.823, 0], [30.5, 19.823, 10.141], [29.661, 19.279, 10.141], [29.661, 19.279, 5.071], [22.954, 14.919, 5.071], [22.954, 14.919, 10.141], [22.115, 14.374, 10.141], [22.115, 14.374, 0]] - , [[27.246, 24.672, 0], [27.246, 24.672, 10.303], [26.505, 24.001, 10.303], [26.505, 24.001, 5.152], [20.575, 18.631, 5.152], [20.575, 18.631, 10.303], [19.833, 17.96, 10.303], [19.833, 17.96, 0]] - , [[23.271, 28.936, 0], [23.271, 28.936, 10.465], [22.645, 28.157, 10.465], [22.645, 28.157, 5.232], [17.631, 21.923, 5.232], [17.631, 21.923, 10.465], [17.004, 21.144, 10.465], [17.004, 21.144, 0]] - , [[18.686, 32.518, 0], [18.686, 32.518, 10.626], [18.188, 31.651, 10.626], [18.188, 31.651, 5.313], [14.202, 24.715, 5.313], [14.202, 24.715, 10.626], [13.704, 23.848, 10.626], [13.704, 23.848, 0]] - , [[13.61, 35.343, 0], [13.61, 35.343, 10.788], [13.25, 34.409, 10.788], [13.25, 34.409, 5.394], [10.376, 26.944, 5.394], [10.376, 26.944, 10.788], [10.016, 26.011, 10.788], [10.016, 26.011, 0]] - , [[8.17, 37.353, 0], [8.17, 37.353, 10.949], [7.956, 36.376, 10.949], [7.956, 36.376, 5.475], [6.247, 28.561, 5.475], [6.247, 28.561, 10.949], [6.033, 27.584, 10.949], [6.033, 27.584, 0]] - , [[2.497, 38.515, 0], [2.497, 38.515, 11.111], [2.433, 37.517, 11.111], [2.433, 37.517, 5.556], [1.915, 29.533, 5.556], [1.915, 29.533, 11.111], [1.85, 28.536, 11.111], [1.85, 28.536, 0]] - , [[-3.277, 38.813, 0], [-3.277, 38.813, 11.273], [-3.192, 37.817, 11.273], [-3.192, 37.817, 5.636], [-2.519, 29.845, 5.636], [-2.519, 29.845, 11.273], [-2.435, 28.848, 11.273], [-2.435, 28.848, 0]] - , [[-9.022, 38.253, 0], [-9.022, 38.253, 11.434], [-8.793, 37.28, 11.434], [-8.793, 37.28, 5.717], [-6.956, 29.494, 5.717], [-6.956, 29.494, 11.434], [-6.727, 28.52, 11.434], [-6.727, 28.52, 0]] - , [[-14.616, 36.859, 0], [-14.616, 36.859, 11.596], [-14.247, 35.93, 11.596], [-14.247, 35.93, 5.798], [-11.298, 28.493, 5.798], [-11.298, 28.493, 11.596], [-10.93, 27.563, 11.596], [-10.93, 27.563, 0]] - , [[-19.94, 34.671, 0], [-19.94, 34.671, 11.758], [-19.442, 33.804, 11.758], [-19.442, 33.804, 5.879], [-15.453, 26.869, 5.879], [-15.453, 26.869, 11.758], [-14.955, 26.002, 11.758], [-14.955, 26.002, 0]] - , [[-24.888, 31.744, 0], [-24.888, 31.744, 11.919], [-24.271, 30.957, 11.919], [-24.271, 30.957, 5.96], [-19.335, 24.661, 5.96], [-19.335, 24.661, 11.919], [-18.718, 23.874, 11.919], [-18.718, 23.874, 0]] - , [[-29.363, 28.148, 0], [-29.363, 28.148, 12.081], [-28.642, 27.456, 12.081], [-28.642, 27.456, 6.04], [-22.866, 21.919, 6.04], [-22.866, 21.919, 12.081], [-22.145, 21.227, 12.081], [-22.145, 21.227, 0]] - , [[-33.282, 23.961, 0], [-33.282, 23.961, 12.242], [-32.471, 23.377, 12.242], [-32.471, 23.377, 6.121], [-25.978, 18.703, 6.121], [-25.978, 18.703, 12.242], [-25.167, 18.119, 12.242], [-25.167, 18.119, 0]] - , 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7.33333], [-8.36597, -35.7347, 7.33333], [-8.36597, -35.7347, 14.6667], [-8.13802, -34.7611, 14.6667], [-8.13802, -34.7611, 0]], [[-4.91415, -45.7312, 0], [-4.91415, -45.7312, 14.8283], [-4.80731, -44.7369, 14.8283], [-4.80731, -44.7369, 7.41414], [-3.95257, -36.7827, 7.41414], [-3.95257, -36.7827, 14.8283], [-3.84573, -35.7884, 14.8283], [-3.84573, -35.7884, 0]], [[0.694121, -46.2806, 0], [0.694121, -46.2806, 14.9899], [0.679124, -45.2807, 14.9899], [0.679124, -45.2807, 7.49495], [0.559153, -37.2816, 7.49495], [0.559153, -37.2816, 14.9899], [0.544157, -36.2817, 14.9899], [0.544157, -36.2817, 0]], [[6.32293, -46.1439, 0], [6.32293, -46.1439, 15.1515], [6.18717, -45.1532, 15.1515], [6.18717, -45.1532, 7.57576], [5.10111, -37.2272, 7.57576], [5.10111, -37.2272, 15.1515], [4.96535, -36.2365, 15.1515], [4.96535, -36.2365, 0]], [[11.8895, -45.329, 0], [11.8895, -45.329, 15.3131], [11.6358, -44.3618, 15.3131], [11.6358, -44.3618, 7.65657], [9.60611, -36.6235, 7.65657], [9.60611, -36.6235, 15.3131], [9.3524, -35.6562, 15.3131], [9.3524, -35.6562, 0]], [[17.3139, -43.8535, 0], [17.3139, -43.8535, 15.4747], [16.9466, -42.9234, 15.4747], [16.9466, -42.9234, 7.73737], [14.0088, -35.4824, 7.73737], [14.0088, -35.4824, 15.4747], [13.6416, -34.5522, 15.4747], [13.6416, -34.5522, 0]], [[22.5198, -41.744, 0], [22.5198, -41.744, 15.6364], [22.045, -40.8639, 15.6364], [22.045, -40.8639, 7.81818], [18.2467, -33.8231, 7.81818], [18.2467, -33.8231, 15.6364], [17.7719, -32.943, 15.6364], [17.7719, -32.943, 0]], [[27.4358, -39.0354, 0], [27.4358, -39.0354, 15.798], [26.8608, -38.2173, 15.798], [26.8608, -38.2173, 7.89899], [22.2606, -31.6722, 7.89899], [22.2606, -31.6722, 15.798], [21.6856, -30.854, 15.798], [21.6856, -30.854, 0]], [[31.996, -35.7702, 0], [31.996, -35.7702, 15.9596], [31.3293, -35.0249, 15.9596], [31.3293, -35.0249, 7.9798], [25.9957, -29.0622, 7.9798], [25.9957, -29.0622, 15.9596], [25.329, -28.3168, 15.9596], [25.329, -28.3168, 0]], [[36.1406, -31.9976, 0], [36.1406, -31.9976, 16.1212], [35.3919, -31.3347, 16.1212], [35.3919, -31.3347, 8.06061], [29.4021, -26.0316, 8.06061], [29.4021, -26.0316, 16.1212], [28.6534, -25.3687, 16.1212], [28.6534, -25.3687, 0]], [[39.817, -27.7727, 0], [39.817, -27.7727, 16.2828], [38.9968, -27.2006, 16.2828], [38.9968, -27.2006, 8.14141], [32.4353, -22.6239, 8.14141], [32.4353, -22.6239, 16.2828], [31.6151, -22.0518, 16.2828], [31.6151, -22.0518, 0]], [[42.9796, -23.1554, 0], [42.9796, -23.1554, 16.4444], [42.0992, -22.6811, 16.4444], [42.0992, -22.6811, 8.22222], [35.0563, -18.8867, 8.22222], [35.0563, -18.8867, 16.4444], [34.1759, -18.4124, 16.4444], [34.1759, -18.4124, 0]], [[45.5907, -18.2096, 0], [45.5907, -18.2096, 16.6061], [44.662, -17.8387, 16.6061], [44.662, -17.8387, 8.30303], [37.2327, -14.8713, 8.30303], [37.2327, -14.8713, 16.6061], [36.3041, -14.5004, 16.6061], [36.3041, -14.5004, 0]], [[47.6205, -13.0024, 0], [47.6205, -13.0024, 16.7677], [46.6558, -12.739, 16.7677], [46.6558, -12.739, 8.38384], [38.9383, -10.6318, 8.38384], [38.9383, -10.6318, 16.7677], [37.9736, -10.3684, 16.7677], [37.9736, -10.3684, 0]], [[49.0472, -7.60249, 0], [49.0472, -7.60249, 16.9293], [48.059, -7.44932, 16.9293], [48.059, -7.44932, 8.46465], [40.1534, -6.22392, 8.46465], [40.1534, -6.22392, 16.9293], [39.1652, -6.07075, 16.9293], [39.1652, -6.07075, 0]], [[49.8571, -2.08005, 0], [49.8571, -2.08005, 17.0909], [48.8579, -2.03837, 17.0909], [48.8579, -2.03837, 8.54545], [40.8649, -1.7049, 8.54545], [40.8649, -1.7049, 17.0909], [39.8658, -1.66321, 17.0909], [39.8658, -1.66321, 0]], [[50.0446, 3.49472, 0], [50.0446, 3.49472, 17.2525], [49.047, 3.42506, 17.2525], [49.047, 3.42506, 8.62626], [41.0664, 2.86776, 8.62626], [41.0664, 2.86776, 17.2525], [40.0688, 2.79809, 17.2525], [40.0688, 2.79809, 0]], [[49.6118, 9.05229, 0], [49.6118, 9.05229, 17.4141], [48.628, 8.87279, 17.4141], [48.628, 8.87279, 8.70707], [40.7579, 7.4368, 8.70707], [40.7579, 7.4368, 17.4141], [39.7742, 7.2573, 17.4141], [39.7742, 7.2573, 0]], [[48.5684, 14.5247, 0], [48.5684, 14.5247, 17.5758], [47.6103, 14.2381, 17.5758], [47.6103, 14.2381, 8.78788], [39.9457, 11.946, 8.78788], [39.9457, 11.946, 17.5758], [38.9876, 11.6595, 17.5758], [38.9876, 11.6595, 0]], [[46.9314, 19.8461, 0], [46.9314, 19.8461, 17.7374], [46.0103, 19.4566, 17.7374], [46.0103, 19.4566, 8.86869], [38.6421, 16.3408, 8.86869], [38.6421, 16.3408, 17.7374], [37.721, 15.9513, 17.7374], [37.721, 15.9513, 0]], [[44.7244, 24.9539, 0], [44.7244, 24.9539, 17.899], [43.8512, 24.4667, 17.899], [43.8512, 24.4667, 8.94949], [36.865, 20.5688, 8.94949], [36.865, 20.5688, 17.899], [35.9917, 20.0815, 17.899], [35.9917, 20.0815, 0]], [[41.9776, 29.7891, 0], [41.9776, 29.7891, 18.0606], [41.1621, 29.2103, 18.0606], [41.1621, 29.2103, 9.0303], [34.6379, 24.5805, 9.0303], [34.6379, 24.5805, 18.0606], [33.8224, 24.0018, 18.0606], [33.8224, 24.0018, 0]], [[38.7267, 34.2968, 0], [38.7267, 34.2968, 18.2222], [37.9781, 33.6338, 18.2222], [37.9781, 33.6338, 9.11111], [31.9891, 28.3299, 9.11111], [31.9891, 28.3299, 18.2222], [31.2404, 27.6669, 18.2222], [31.2404, 27.6669, 0]], [[35.0127, 38.4271, 0], [35.0127, 38.4271, 18.3838], [34.3392, 37.6879, 18.3838], [34.3392, 37.6879, 9.19192], [28.9512, 31.7744, 9.19192], [28.9512, 31.7744, 18.3838], [28.2777, 31.0353, 18.3838], [28.2777, 31.0353, 0]], [[30.8813, 42.1351, 0], [30.8813, 42.1351, 18.5455], [30.2902, 41.3285, 18.5455], [30.2902, 41.3285, 9.27273], [25.561, 34.876, 9.27273], [25.561, 34.876, 18.5455], [24.9699, 34.0694, 18.5455], [24.9699, 34.0694, 0]], [[26.382, 45.3816, 0], [26.382, 45.3816, 18.7071], [25.8794, 44.5171, 18.7071], [25.8794, 44.5171, 9.35354], [21.8587, 37.6009, 9.35354], [21.8587, 37.6009, 18.7071], [21.3561, 36.7363, 18.7071], [21.3561, 36.7363, 0]], [[21.5675, 48.1332, 0], [21.5675, 48.1332, 18.8687], [21.1586, 47.2206, 18.8687], [21.1586, 47.2206, 9.43434], [17.8873, 39.92, 9.43434], [17.8873, 39.92, 18.8687], [17.4784, 39.0075, 18.8687], [17.4784, 39.0075, 0]], [[16.4932, 50.3625, 0], [16.4932, 50.3625, 19.0303], [16.182, 49.4122, 19.0303], [16.182, 49.4122, 9.51515], [13.6922, 41.8095, 9.51515], [13.6922, 41.8095, 19.0303], [13.381, 40.8592, 19.0303], [13.381, 40.8592, 0]], [[11.2166, 52.0484, 0], [11.2166, 52.0484, 19.1919], [11.0059, 51.0708, 19.1919], [11.0059, 51.0708, 9.59596], [9.32057, 43.2504, 9.59596], [9.32057, 43.2504, 19.1919], [9.1099, 42.2728, 19.1919], [9.1099, 42.2728, 0]], [[5.79603, 53.1759, 0], [5.79603, 53.1759, 19.3535], [5.68767, 52.1817, 19.3535], [5.68767, 52.1817, 9.67677], [4.82083, 44.2288, 9.67677], [4.82083, 44.2288, 19.3535], [4.71247, 43.2347, 19.3535], [4.71247, 43.2347, 0]], [[0.290748, 53.7363, 0], [0.290748, 53.7363, 19.5152], [0.285338, 52.7363, 19.5152], [0.285338, 52.7363, 9.75758], [0.242053, 44.7364, 9.75758], [0.242053, 44.7364, 19.5152], [0.236643, 43.7364, 19.5152], [0.236643, 43.7364, 0]], [[-5.24019, 53.7272, 0], [-5.24019, 53.7272, 19.6768], [-5.14311, 52.7319, 19.6768], [-5.14311, 52.7319, 9.83838], [-4.36653, 44.7697, 9.83838], [-4.36653, 44.7697, 19.6768], [-4.26946, 43.7744, 19.6768], [-4.26946, 43.7744, 0]], [[-10.7384, 53.152, 0], [-10.7384, 53.152, 19.8384], [-10.5404, 52.1718, 19.8384], [-10.5404, 52.1718, 9.91919], [-8.95611, 44.3302, 9.91919], [-8.95611, 44.3302, 19.8384], [-8.75808, 43.35, 19.8384], [-8.75808, 43.35, 0]], [[-16.1467, 52.0202, 0], [-16.1467, 52.0202, 20], [-15.8503, 51.0651, 20], [-15.8503, 51.0651, 10], [-13.4788, 43.4247, 10], [-13.4788, 43.4247, 20], [-13.1823, 42.4697, 20], [-13.1823, 42.4697, 0]]]; + for(i = [0:len(expected) - 1]) { - assertEqualPoints(expected[i], sections[i], float_digits = 3); + assertEqualPoints(expected[i], sections[i]); } } diff --git a/test/test_bend.scad b/test/test_bend.scad index 7301f40c..8603174c 100644 --- a/test/test_bend.scad +++ b/test/test_bend.scad @@ -13,7 +13,7 @@ module test_bend() { expected_angle = 11.25; assertEqualPoints(expected_points, points); - assertEqual(expected_angle, angle); + assertEqualNum(expected_angle, angle); } bend(size = [x, y, z], angle = 270) diff --git a/test/test_bezier_curve.scad b/test/test_bezier_curve.scad index fb6cb44c..51f94396 100644 --- a/test/test_bezier_curve.scad +++ b/test/test_bezier_curve.scad @@ -12,16 +12,12 @@ module test_bezier_curve() { p2 = [-50, 90, 0]; p3 = [0, 200, -35]; - expected = [[0, 0, 0], [5.0588, 8.7888, 4.7338], [8.37, 17.21, 8.47], [10.1363, 25.3463, 11.2613], [10.56, 33.28, 13.16], [9.8438, 41.0938, 14.2188], [8.19, 48.87, 14.49], [5.8013, 56.6913, 14.0263], [2.88, 64.64, 12.88], [-0.3712, 72.7987, 11.1038], [-3.75, 81.25, 8.75], [-7.0537, 90.0762, 5.8713], [-10.08, 99.36, 2.52], [-12.6263, 109.184, -1.2513], [-14.49, 119.63, -5.39], [-15.4688, 130.781, -9.8438], [-15.36, 142.72, -14.56], [-13.9612, 155.529, -19.4863], [-11.07, 169.29, -24.57], [-6.4837, 184.086, -29.7588], [0, 200, -35]]; - + expected = [[0, 0, 0], [5.05875, 8.78875, 4.73375], [8.37, 17.21, 8.47], [10.1363, 25.3463, 11.2613], [10.56, 33.28, 13.16], [9.84375, 41.0938, 14.2188], [8.19, 48.87, 14.49], [5.80125, 56.6912, 14.0262], [2.88, 64.64, 12.88], [-0.37125, 72.7988, 11.1038], [-3.75, 81.25, 8.75], [-7.05375, 90.0763, 5.87125], [-10.08, 99.36, 2.52], [-12.6263, 109.184, -1.25125], [-14.49, 119.63, -5.39], [-15.4688, 130.781, -9.84375], [-15.36, 142.72, -14.56], [-13.9612, 155.529, -19.4863], [-11.07, 169.29, -24.57], [-6.48375, 184.086, -29.7588], [0, 200, -35]]; actual = bezier_curve(t_step, [p0, p1, p2, p3] ); - - // round_echo_pts(actual, float_digits = 3); - assertEqualPoints(expected, actual, float_digits = 3); - + assertEqualPoints(expected, actual, 0.0005); } test_bezier_curve(); \ No newline at end of file diff --git a/test/test_bezier_surface.scad b/test/test_bezier_surface.scad index aa5dc186..31337295 100644 --- a/test/test_bezier_surface.scad +++ b/test/test_bezier_surface.scad @@ -15,14 +15,13 @@ module test_bezier_surface() { [[0, 150, 0], [60, 150, -35], [90, 180, 60], [200, 150, 45]] ]; - expected = [[[0, 0, 20], [0, 7.5, 21.209], [0, 15, 21.87], [0, 22.5, 22.036], [0, 30, 21.76], [0, 37.5, 21.094], [0, 45, 20.09], [0, 52.5, 18.801], [0, 60, 17.28], [0, 67.5, 15.579], [0, 75, 13.75], [0, 82.5, 11.846], [0, 90, 9.92], [0, 97.5, 8.024], [0, 105, 6.21], [0, 112.5, 4.531], [0, 120, 3.04], [0, 127.5, 1.789], [0, 135, 0.83], [0, 142.5, 0.216], [0, 150, 0]], [[8.789, 0, 12.837], [9.551, 7.703, 14.183], [10.157, 15.402, 15.13], [10.619, 23.096, 15.706], [10.95, 30.781, 15.941], [11.163, 38.455, 15.86], [11.271, 46.114, 15.492], [11.286, 53.756, 14.865], [11.22, 61.378, 14.006], [11.087, 68.977, 12.943], [10.9, 76.55, 11.703], [10.669, 84.094, 10.315], [10.41, 91.606, 8.805], [10.133, 99.083, 7.202], [9.853, 106.523, 5.534], [9.58, 113.923, 3.827], [9.329, 121.279, 2.111], [9.112, 128.589, 0.411], [8.941, 135.85, -1.243], [8.829, 143.059, -2.824], [8.789, 150.214, -4.305]], [[17.21, 0, 7.7], [18.635, 7.864, 9.251], [19.769, 15.723, 10.508], [20.634, 23.572, 11.48], [21.254, 31.406, 12.175], [21.652, 39.221, 12.604], [21.854, 47.012, 12.775], [21.881, 54.774, 12.697], [21.759, 62.501, 12.38], [21.51, 70.19, 11.831], [21.159, 77.835, 11.061], [20.728, 85.431, 10.079], [20.243, 92.974, 8.892], [19.725, 100.459, 7.512], [19.2, 107.88, 5.945], [18.691, 115.234, 4.203], [18.221, 122.514, 2.293], [17.814, 129.717, 0.224], [17.494, 136.837, -1.993], [17.285, 143.87, -4.351], [17.21, 150.81, -6.84]], [[25.346, 0, 4.362], [27.34, 7.987, 6.174], [28.925, 15.967, 7.756], [30.134, 23.936, 9.103], [31.001, 31.886, 10.213], [31.559, 39.813, 11.08], [31.841, 47.709, 11.7], [31.879, 55.569, 12.07], [31.708, 63.387, 12.186], [31.36, 71.157, 12.043], [30.869, 78.873, 11.636], [30.267, 86.528, 10.963], [29.587, 94.117, 10.019], [28.864, 101.634, 8.8], [28.13, 109.072, 7.301], [27.417, 116.427, 5.519], [26.76, 123.69, 3.45], [26.191, 130.858, 1.089], [25.744, 137.923, -1.568], [25.451, 144.879, -4.525], [25.346, 151.721, -7.785]], [[33.28, 0, 2.6], [35.749, 8.075, 4.712], [37.712, 16.143, 6.625], [39.21, 24.199, 8.325], [40.284, 32.235, 9.801], [40.975, 40.245, 11.04], [41.324, 48.223, 12.029], [41.372, 56.162, 12.756], [41.16, 64.055, 13.209], [40.729, 71.897, 13.374], [40.12, 79.68, 13.24], [39.374, 87.399, 12.794], [38.533, 95.046, 12.023], [37.637, 102.615, 10.916], [36.727, 110.1, 9.459], [35.845, 117.495, 7.64], [35.031, 124.792, 5.447], [34.327, 131.986, 2.867], [33.772, 139.069, -0.113], [33.41, 146.036, -3.504], [33.28, 152.88, -7.32]], [[41.094, 0, 2.188], [43.949, 8.132, 4.626], [46.22, 16.257, 6.867], [47.952, 24.37, 8.894], [49.194, 32.464, 10.69], [49.993, 40.532, 12.239], [50.396, 48.569, 13.523], [50.451, 56.568, 14.527], [50.206, 64.523, 15.233], [49.708, 72.426, 15.624], [49.004, 80.273, 15.684], [48.142, 88.057, 15.395], [47.169, 95.771, 14.743], [46.133, 103.409, 13.708], [45.08, 110.965, 12.275], [44.06, 118.433, 10.427], [43.119, 125.805, 8.147], [42.304, 133.076, 5.419], [41.663, 140.24, 2.225], [41.244, 147.289, -1.45], [41.094, 154.219, 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141.396, 5.30111], [49.0361, 148.587, 1.47759], [48.87, 155.67, -2.88]], [[56.6912, 0, 4.5125], [60.0636, 8.16467, 7.61896], [62.7447, 16.3247, 10.4733], [64.7905, 24.4756, 13.0598], [66.2572, 32.6126, 15.3626], [67.2007, 40.7312, 17.3658], [67.6771, 48.8268, 19.0538], [67.7425, 56.8947, 20.4107], [67.4529, 64.9304, 21.4208], [66.8644, 72.9292, 22.0681], [66.033, 80.8866, 22.337], [65.0147, 88.7979, 22.2117], [63.8657, 96.6585, 21.6762], [62.6419, 104.464, 20.7149], [61.3995, 112.209, 19.312], [60.1944, 119.89, 17.4516], [59.0827, 127.502, 15.1179], [58.1205, 135.04, 12.2953], [57.3639, 142.5, 8.96774], [56.8687, 149.877, 5.11958], [56.6912, 157.166, 0.735]], [[64.64, 0, 6.8], [68.1489, 8.14746, 10.2192], [70.9386, 16.2917, 13.3409], [73.0672, 24.4294, 16.1531], [74.5933, 32.5574, 18.6438], [75.575, 40.6725, 20.8013], [76.0707, 48.7714, 22.6134], [76.1388, 56.8508, 24.0682], [75.8374, 64.9075, 25.1539], [75.2251, 72.9383, 25.8585], [74.36, 80.94, 26.17], [73.3005, 88.9093, 26.0765], [72.105, 96.8429, 25.5661], [70.8316, 104.738, 24.6268], [69.5389, 112.59, 23.2466], [68.285, 120.398, 21.4138], [67.1283, 128.156, 19.1162], [66.1272, 135.863, 16.3419], [65.3398, 143.515, 13.0791], [64.8247, 151.108, 9.31579], [64.64, 158.64, 5.04]], [[72.7988, 0, 9.5375], [76.3671, 8.11228, 13.2355], [79.2039, 16.2229, 16.5864], [81.3686, 24.3302, 19.5835], [82.9205, 32.4324, 22.2201], [83.9188, 40.528, 24.4893], [84.423, 48.6152, 26.3845], [84.4922, 56.6924, 27.8988], [84.1857, 64.7579, 29.0255], [83.563, 72.8101, 29.7579], [82.6833, 80.8472, 30.0892], [81.6059, 88.8676, 30.0126], [80.3901, 96.8696, 29.5215], [79.0952, 104.852, 28.6089], [77.7806, 112.812, 27.2682], [76.5054, 120.749, 25.4926], [75.3292, 128.661, 23.2754], [74.3111, 136.546, 20.6098], [73.5104, 144.402, 17.489], [72.9866, 152.229, 13.9064], [72.7988, 160.024, 9.855]], [[81.25, 0, 12.5], [84.8036, 8.0625, 16.428], [87.6288, 16.125, 19.9612], [89.7845, 24.1875, 23.0989], [91.33, 32.25, 25.84], [92.3242, 40.3125, 28.1836], [92.8263, 48.375, 30.1288], [92.8952, 56.4375, 31.6745], [92.59, 64.5, 32.82], [91.9698, 72.5625, 33.5642], [91.0938, 80.625, 33.9063], [90.0208, 88.6875, 33.8452], [88.81, 96.75, 33.38], [87.5205, 104.813, 32.5098], [86.2112, 112.875, 31.2337], [84.9414, 120.938, 29.5508], [83.77, 129, 27.46], [82.7561, 137.063, 24.9605], [81.9588, 145.125, 22.0512], [81.437, 153.188, 18.7314], [81.25, 161.25, 15]], [[90.0763, 0, 15.4625], [93.544, 8.00147, 19.5569], [96.301, 16.0046, 23.2168], [98.4047, 24.0111, 26.447], [99.9129, 32.0226, 29.2523], [100.883, 40.0407, 31.6376], [101.373, 48.0673, 33.6077], [101.44, 56.1038, 35.1675], [101.142, 64.1521, 36.3217], [100.537, 72.2137, 37.0751], [99.6823, 80.2903, 37.4327], [98.6353, 88.3837, 37.3991], [97.4537, 96.4954, 36.9793], [96.1953, 104.627, 36.1781], [94.9177, 112.781, 35.0003], [93.6785, 120.958, 33.4507], [92.5354, 129.159, 31.5342], [91.546, 137.388, 29.2555], [90.7679, 145.645, 26.6195], [90.2588, 153.932, 23.6311], [90.0763, 162.251, 20.295]], [[99.36, 0, 18.2], [102.674, 7.93254, 22.3824], [105.309, 15.8683, 26.1043], [107.319, 23.8106, 29.3755], [108.76, 31.7626, 32.2058], [109.688, 39.7275, 34.605], [110.156, 47.7086, 36.583], [110.22, 55.7092, 38.1497], [109.935, 63.7325, 39.3149], [109.357, 71.7817, 40.0884], [108.54, 79.86, 40.48], [107.539, 87.9707, 40.4996], [106.41, 96.1171, 40.1571], [105.208, 104.302, 39.4623], [103.987, 112.53, 38.425], [102.802, 120.802, 37.055], [101.71, 129.124, 35.3622], [100.765, 137.497, 33.3565], [100.021, 145.925, 31.0477], [99.5344, 154.412, 28.4456], [99.36, 162.96, 25.56]], [[109.184, 0, 20.4875], [112.279, 7.85908, 24.6648], [114.74, 15.7228, 28.3752], [116.617, 23.5957, 31.6322], [117.963, 31.4824, 34.449], [118.829, 39.3875, 36.8392], [119.267, 47.3157, 38.8162], [119.327, 55.2715, 40.3933], [119.061, 63.2596, 41.584], [118.521, 71.2845, 42.4017], [117.758, 79.3509, 42.8598], [116.823, 87.4634, 42.9718], [115.769, 95.6265, 42.751], [114.645, 103.845, 42.2108], [113.505, 112.123, 41.3647], [112.399, 120.466, 40.2262], [111.379, 128.878, 38.8085], [110.496, 137.364, 37.1251], [109.801, 145.928, 35.1894], [109.347, 154.574, 33.0149], [109.184, 163.309, 30.615]], [[119.63, 0, 22.1], [122.444, 7.78445, 26.1643], [124.682, 15.5746, 29.7809], [126.389, 23.376, 32.9648], [127.613, 31.1945, 35.7309], [128.401, 39.0356, 38.0939], [128.798, 46.9051, 40.0688], [128.853, 54.8086, 41.6703], [128.611, 62.7518, 42.9134], [128.12, 70.7404, 43.813], [127.426, 78.78, 44.3838], [126.576, 86.8763, 44.6407], [125.618, 95.035, 44.5986], [124.596, 103.262, 44.2723], [123.559, 111.562, 43.6767], [122.554, 119.942, 42.8267], [121.626, 128.407, 41.7371], [120.823, 136.962, 40.4228], [120.191, 145.614, 38.8986], [119.778, 154.368, 37.1794], [119.63, 163.23, 35.28]], [[130.781, 0, 22.8125], [133.256, 7.71199, 26.6409], [135.224, 15.4303, 30.0727], [136.725, 23.1613, 33.1212], [137.801, 30.9113, 35.8], [138.494, 38.6865, 38.1226], [138.843, 46.4934, 40.1023], [138.891, 54.3383, 41.7528], [138.679, 62.2275, 43.0875], [138.247, 70.1673, 44.1198], [137.637, 78.1641, 44.8633], [136.889, 86.2241, 45.3313], [136.046, 94.3538, 45.5375], [135.148, 102.559, 45.4952], [134.236, 110.847, 45.218], [133.352, 119.224, 44.7192], [132.536, 127.695, 44.0125], [131.83, 136.268, 43.1112], [131.275, 144.948, 42.0289], [130.912, 153.742, 40.779], [130.781, 162.656, 39.375]], [[142.72, 0, 22.4], [144.799, 7.64508, 25.855], [146.452, 15.2966, 29.0018], [147.714, 22.9612, 31.849], [148.618, 30.6451, 34.4051], [149.2, 38.355, 36.6788], [149.494, 46.0973, 38.6785], [149.534, 53.8784, 40.4129], [149.356, 61.705, 41.8906], [148.993, 69.5833, 43.1201], [148.48, 77.52, 44.11], [147.852, 85.5215, 44.8689], [147.144, 93.5942, 45.4054], [146.389, 101.745, 45.7281], [145.623, 109.98, 45.8455], [144.88, 118.305, 45.7663], [144.195, 126.728, 45.4989], [143.601, 135.254, 45.052], [143.135, 143.891, 44.4342], [142.829, 152.644, 43.654], [142.72, 161.52, 42.72]], [[155.529, 0, 20.6375], [157.16, 7.58707, 23.5668], [158.457, 15.1802, 26.3198], [159.446, 22.7853, 28.896], [160.155, 30.4085, 31.295], [160.612, 38.0558, 33.516], [160.842, 45.7333, 35.5587], [160.874, 53.4468, 37.4226], [160.734, 61.2026, 39.107], [160.449, 69.0065, 40.6115], [160.047, 76.8647, 41.9355], [159.555, 84.7831, 43.0785], [158.999, 92.7678, 44.04], [158.407, 100.825, 44.8195], [157.806, 108.96, 45.4164], [157.223, 117.18, 45.8303], [156.685, 125.49, 46.0605], [156.22, 133.896, 46.1067], [155.854, 142.405, 45.9681], [155.615, 151.022, 45.6444], [155.529, 159.754, 45.135]], [[169.29, 0, 17.3], [170.423, 7.54131, 19.5364], [171.324, 15.0875, 21.7779], [172.011, 22.6434, 24.0101], [172.504, 30.2138, 26.2182], [172.821, 37.8038, 28.388], [172.981, 45.418, 30.5047], [173.003, 53.0613, 32.5539], [172.906, 60.7387, 34.5211], [172.708, 68.455, 36.3917], [172.429, 76.215, 38.1513], [172.087, 84.0236, 39.7851], [171.701, 91.8857, 41.2789], [171.289, 99.8061, 42.6179], [170.872, 107.79, 43.7878], [170.467, 115.841, 44.7739], [170.094, 123.966, 45.5618], [169.77, 132.168, 46.1368], [169.516, 140.453, 46.4846], [169.35, 148.825, 46.5905], [169.29, 157.29, 46.44]], [[184.086, 0, 12.1625], [184.675, 7.51117, 13.5241], [185.142, 15.0252, 15.1275], [185.499, 22.545, 16.9388], [185.755, 30.0735, 18.9237], [185.92, 37.6136, 21.0481], [186.003, 45.168, 23.2779], [186.014, 52.7398, 25.5791], [185.964, 60.3317, 27.9173], [185.861, 67.9468, 30.2587], [185.716, 75.5878, 32.5689], [185.538, 83.2577, 34.8139], [185.338, 90.9593, 36.9597], [185.124, 98.6956, 38.9719], [184.908, 106.469, 40.8166], [184.697, 114.283, 42.4596], [184.503, 122.141, 43.8668], [184.336, 130.045, 45.0041], [184.204, 137.997, 45.8373], [184.117, 146.002, 46.3323], [184.086, 154.061, 46.455]], [[200, 0, 5], [200, 7.5, 5.29], [200, 15, 6.12], [200, 22.5, 7.43], [200, 30, 9.16], [200, 37.5, 11.25], [200, 45, 13.64], [200, 52.5, 16.27], [200, 60, 19.08], [200, 67.5, 22.01], [200, 75, 25], [200, 82.5, 27.99], [200, 90, 30.92], [200, 97.5, 33.73], [200, 105, 36.36], [200, 112.5, 38.75], [200, 120, 40.84], [200, 127.5, 42.57], [200, 135, 43.88], [200, 142.5, 44.71], [200, 150, 45]]]; actual = bezier_surface(t_step, ctrl_pts); - - for(i = [0:len(expected) - 1]) { - assertEqualPoints(expected[i], actual[i], float_digits = 3); - } + for(i = [0:len(expected) - 1]) { + assertEqualPoints(expected[i], actual[i], 0.0006); + } } test_bezier_surface(); \ No newline at end of file diff --git a/test/test_cross_sections.scad b/test/test_cross_sections.scad index 33e8b238..4ec60d30 100644 --- a/test/test_cross_sections.scad +++ b/test/test_cross_sections.scad @@ -26,108 +26,7 @@ module test_cross_sections() { for(i = [0:len(pts_angles) - 1]) [90, 0, pts_angles[i][1]] ]; - expected = [ - [[-8, 0, -10], [-8, 0, 10], [-12, 0, 10], [-12, 0, -10]] - ,[[-8.6994, -4.8132, -9.967], [-8.1492, -4.5088, 9.8412], [-11.6157, -6.4267, 9.967], [-12.1659, -6.7311, -9.8412]] - ,[[-6.878, -9.4072, -9.923], [-6.143, -8.4019, 9.6739], [-8.4562, -11.5658, 9.923], [-9.1913, -12.5711, -9.6739]] - ,[[-3.1918, -12.8199, -9.8682], [-2.745, -11.0255, 9.4983], [-3.6808, -14.784, 9.8682], [-4.1275, -16.5785, -9.4983]] - ,[[1.5997, -14.5687, -9.8028], [1.3334, -12.1435, 9.3149], [1.7507, -15.9442, 9.8028], [2.017, -18.3694, -9.3149]] - ,[[6.7711, -14.5108, -9.7272], [5.4956, -11.7773, 9.1239], [7.0899, -15.1939, 9.7272], [8.3654, -17.9273, -9.1239]] - ,[[11.6997, -12.74, -9.6415], [9.2792, -10.1043, 8.9258], [11.791, -12.8394, 9.6415], [14.2115, -15.4751, -8.9258]] - ,[[15.8948, -9.5061, -9.5462], [12.3539, -7.3884, 8.721], [15.4894, -9.2636, 9.5462], [19.0303, -11.3813, -8.721]] - ,[[19.0056, -5.1511, -9.4413], [14.5101, -3.9327, 8.5098], [17.9753, -4.8719, 9.4413], [22.4707, -6.0903, -8.5098]] - ,[[20.8154, -0.0611, -9.3273], [15.6418, -0.0459, 8.2925], [19.1657, -0.0562, 9.3273], [24.3394, -0.0714, -8.2925]] - ,[[21.2291, 5.3718, -9.2043], [15.7291, 3.9801, 8.0697], [19.0783, 4.8276, 9.2043], [24.5783, 6.2193, -8.0697]] - ,[[20.2549, 10.776, -9.0729], [14.8199, 7.8845, 7.8416], [17.8064, 9.4734, 9.0729], [23.2414, 12.3649, -7.8416]] - ,[[17.986, 15.8198, -8.9331], [13.0134, 11.4461, 7.6087], [15.4976, 13.6311, 8.9331], [20.4701, 18.0048, -7.6087]] - ,[[14.5805, 20.2234, -8.7855], [10.4452, 14.4877, 7.3713], [12.335, 17.1089, 8.7855], [16.4703, 22.8446, -7.3713]] - ,[[10.2434, 23.766, -8.6303], [7.2741, 16.8768, 7.1299], [8.5217, 19.7714, 8.6303], [11.4911, 26.6606, -7.1299]] - ,[[5.2094, 26.2883, -8.4678], [3.6709, 18.5244, 6.8848], [4.2677, 21.5364, 8.4678], [5.8063, 29.3002, -6.8848]] - ,[[-0.2725, 27.6913, -8.2984], [-0.1907, 19.3821, 6.6365], [-0.2201, 22.369, 8.2984], [-0.3019, 30.6781, -6.6365]] - ,[[-5.9515, 27.9334, -8.1224], [-4.1415, 19.4382, 6.3853], [-4.7462, 22.2761, 8.1224], [-6.5562, 30.7712, -6.3853]] - ,[[-11.5863, 27.0248, -7.9403], [-8.0228, 18.713, 6.1316], [-9.1318, 21.2997, 7.9403], [-12.6953, 29.6115, -6.1316]] - ,[[-16.9534, 25.0213, -7.7523], [-11.6906, 17.2541, 5.8758], [-13.2195, 19.5105, 7.7523], [-18.4823, 27.2778, -5.8758]] - ,[[-21.8538, 22.017, -7.5588], [-15.0189, 15.1311, 5.6184], [-16.8755, 17.0015, 7.5588], [-23.7104, 23.8874, -5.6184]] - ,[[-26.1178, 18.1367, -7.3602], [-17.9016, 12.4312, 5.3596], [-19.9911, 13.8822, 7.3602], [-28.2073, 19.5877, -5.3596]] - ,[[-29.608, 13.5285, -7.1568], [-20.2537, 9.2543, 5.0999], [-22.4833, 10.2731, 7.1568], [-31.8377, 14.5473, -5.0999]] - ,[[-32.2209, 8.3567, -6.9491], [-22.0116, 5.7089, 4.8397], [-24.2938, 6.3008, 6.9491], [-34.5031, 8.9486, -4.8397]] - ,[[-33.8866, 2.7944, -6.7373], [-23.1328, 1.9076, 4.5793], [-25.3884, 2.0936, 6.7373], [-36.1423, 2.9804, -4.5793]] - ,[[-34.5686, -2.9822, -6.5219], [-23.595, -2.0355, 4.3191], [-25.7552, -2.2219, 6.5219], [-36.7288, -3.1685, -4.3191]] - ,[[-34.2616, -8.7996, -6.3033], [-23.3951, -6.0087, 4.0594], [-25.4025, -6.5243, 6.3033], [-36.269, -9.3152, -4.0594]] - ,[[-32.989, -14.492, -6.0817], [-22.5472, -9.9049, 3.8007], [-24.3567, -10.6998, 6.0817], [-34.7986, -15.2869, -3.8007]] - ,[[-30.7999, -19.9048, -5.8576], [-21.0812, -13.624, 3.5433], [-22.6603, -14.6445, 5.8576], [-32.3791, -20.9253, -3.5433]] - ,[[-27.766, -24.8987, -5.6314], [-19.0409, -17.0746, 3.2875], [-20.3689, -18.2655, 5.6314], [-29.094, -26.0896, -3.2875]] - ,[[-23.9774, -29.3515, -5.4034], [-16.4816, -20.1756, 3.0338], [-17.5491, -21.4824, 5.4034], [-25.0449, -30.6583, -3.0338]] - ,[[-19.5393, -33.1603, -5.174], [-13.4683, -22.8572, 2.7823], [-14.2762, -24.2281, 5.174], [-20.3472, -34.5313, -2.7823]] - ,[[-14.5684, -36.2426, -4.9436], [-10.0739, -25.0615, 2.5334], [-10.6316, -26.449, 4.9436], [-15.1261, -37.6301, -2.5334]] - ,[[-9.1885, -38.5369, -4.7124], [-6.3765, -26.7431, 2.2876], [-6.7012, -28.1049, 4.7124], [-9.5132, -39.8987, -2.2876]] - ,[[-3.5281, -40.0022, -4.481], [-2.458, -27.8692, 2.045], [-2.5727, -29.1693, 4.481], [-3.6428, -41.3023, -2.045]] - ,[[2.2837, -40.6181, -4.2495], [1.5978, -28.4193, 1.8059], [1.6658, -29.6285, 4.2495], [2.3516, -41.8273, -1.8059]] - ,[[8.1196, -40.3838, -4.0185], [5.7071, -28.3853, 1.5707], [5.9275, -29.4812, 4.0185], [8.3399, -41.4797, -1.5707]] - ,[[13.857, -39.3164, -3.7881], [9.7877, -27.7704, 1.3397], [10.1286, -28.7377, 3.7881], [14.1979, -40.2837, -1.3397]] - ,[[19.3804, -37.4498, -3.5589], [13.7599, -26.5891, 1.1131], [14.1894, -27.4189, 3.5589], [19.8098, -38.2796, -1.1131]] - ,[[24.5828, -34.8326, -3.331], [17.5487, -24.8656, 0.8912], [18.0357, -25.5555, 3.331], [25.0697, -35.5225, -0.8912]] - ,[[29.3681, -31.5265, -3.1048], [21.0842, -22.6338, 0.6742], [21.5994, -23.1868, 3.1048], [29.8833, -32.0795, -0.6742]] - ,[[33.6516, -27.6041, -2.8807], [24.3027, -19.9353, 0.4623], [24.8196, -20.3593, 2.8807], [34.1685, -28.0282, -0.4623]] - ,[[37.3613, -23.147, -2.6589], [27.1475, -16.8191, 0.2559], [27.6431, -17.1261, 2.6589], [37.8568, -23.454, -0.2559]] - ,[[40.4386, -18.2435, -2.4398], [29.5699, -13.3402, 0.0551], [30.0247, -13.5454, 2.4398], [40.8934, -18.4487, -0.0551]] - ,[[42.8383, 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[-8.45619, -11.5658, 9.92296], [-9.19124, -12.5712, -9.67387]], [[-3.19172, -12.82, -9.86815], [-2.74495, -11.0255, 9.4983], [-3.6807, -14.784, 9.86815], [-4.12747, -16.5785, -9.4983]], [[1.59972, -14.5687, -9.80282], [1.33342, -12.1435, 9.31486], [1.75076, -15.9442, 9.80282], [2.01706, -18.3694, -9.31486]], [[6.77117, -14.5107, -9.72719], [5.49566, -11.7773, 9.12391], [7.08993, -15.1939, 9.72719], [8.36544, -17.9273, -9.12391]], [[11.6998, -12.74, -9.64155], [9.27924, -10.1042, 8.92583], [11.791, -12.8393, 9.64155], [14.2116, -15.4751, -8.92583]], [[15.8949, -9.50598, -9.54615], [12.354, -7.38833, 8.72099], [15.4894, -9.26352, 9.54615], [19.0303, -11.3812, -8.72099]], [[19.0056, -5.15104, -9.44129], [14.5101, -3.93264, 8.50976], [17.9753, -4.8718, 9.44129], [22.4708, -6.0902, -8.50976]], [[20.8154, -0.0609642, -9.32725], [15.6418, -0.0458117, 8.29253], [19.1657, -0.0561326, 9.32725], [24.3394, -0.0712851, -8.29253]], [[21.229, 5.37195, -9.20434], [15.7291, 3.9802, 8.06968], [19.0783, 4.82771, 9.20434], [24.5783, 6.21946, -8.06968]], [[20.2549, 10.7762, -9.07287], [14.8198, 7.88457, 7.8416], [17.8063, 9.47349, 9.07287], [23.2414, 12.3651, -7.8416]], [[17.9859, 15.8199, -8.93315], [13.0133, 11.4462, 7.60868], [15.4975, 13.6312, 8.93315], [20.47, 18.0049, -7.60868]], [[14.5804, 20.2235, -8.78551], [10.4452, 14.4878, 7.37132], [12.3349, 17.1089, 8.78551], [16.4701, 22.8447, -7.37132]], [[10.2433, 23.7661, -8.63027], [7.27401, 16.8769, 7.1299], [8.5216, 19.7715, 8.63027], [11.4909, 26.6607, -7.1299]], [[5.20923, 26.2883, -8.46779], [3.67076, 18.5244, 6.88482], [4.26761, 21.5364, 8.46779], [5.80607, 29.3003, -6.88482]], [[-0.272672, 27.6913, -8.29839], [-0.190853, 19.3821, 6.63649], [-0.220264, 22.369, 8.29839], [-0.302083, 30.6781, -6.63649]], [[-5.95173, 27.9333, -8.12244], [-4.14168, 19.4382, 6.38528], [-4.74634, 22.276, 8.12244], [-6.55639, 30.7712, -6.38528]], [[-11.5865, 27.0247, -7.94028], [-8.02297, 18.713, 6.13159], [-9.13197, 21.2996, 7.94028], [-12.6955, 29.6114, -6.13159]], [[-16.9536, 25.0212, -7.75228], [-11.6908, 17.254, 5.87583], [-13.2196, 19.5104, 7.75228], [-18.4825, 27.2776, -5.87583]], [[-21.8539, 22.0168, -7.55879], [-15.019, 15.131, 5.61836], [-16.8756, 17.0014, 7.55879], [-23.7105, 23.8873, -5.61836]], [[-26.1179, 18.1365, -7.36018], [-17.9017, 12.4311, 5.35959], [-19.9912, 13.8821, 7.36018], [-28.2075, 19.5875, -5.35959]], [[-29.6081, 13.5283, -7.15682], [-20.2537, 9.25418, 5.0999], [-22.4834, 10.2729, 7.15682], [-31.8378, 14.5471, -5.0999]], [[-32.2209, 8.35645, -6.94907], [-22.0116, 5.70868, 4.83966], [-24.2939, 6.30058, 6.94907], [-34.5032, 8.94835, -4.83966]], [[-33.8866, 2.79414, -6.73732], [-23.1328, 1.90742, 4.57925], [-25.3885, 2.09342, 6.73732], [-36.1423, 2.98013, -4.57925]], [[-34.5686, -2.98247, -6.52192], [-23.595, -2.0357, 4.31905], [-25.7552, -2.22208, 6.52192], [-36.7288, -3.16884, -4.31905]], [[-34.2615, -8.79991, -6.30327], [-23.395, -6.0089, 4.05942], [-25.4024, -6.52448, 6.30327], [-36.2689, -9.31549, -4.05942]], [[-32.9889, -14.4922, -6.08172], [-22.5471, -9.90508, 3.80073], [-24.3566, -10.7, 6.08172], [-34.7984, -15.2872, -3.80073]], [[-30.7998, -19.9051, -5.85765], [-21.0811, -13.6241, 3.54332], [-22.6602, -14.6447, 5.85765], [-32.3789, -20.9256, -3.54332]], [[-27.7658, -24.8989, -5.63143], [-19.0407, -17.0747, 3.28755], [-20.3687, -18.2656, 5.63143], [-29.0938, -26.0898, -3.28755]], [[-23.9771, -29.3517, -5.40343], [-16.4814, -20.1757, 3.03376], [-17.5489, -21.4826, 5.40343], [-25.0447, -30.6585, -3.03376]], [[-19.5391, -33.1605, -5.17403], [-13.4681, -22.8573, 2.78228], [-14.276, -24.2283, 5.17403], [-20.3469, -34.5314, -2.78228]], [[-14.568, -36.2428, -4.94357], [-10.0737, -25.0616, 2.53344], [-10.6314, -26.4491, 4.94357], [-15.1258, -37.6303, -2.53344]], [[-9.18817, -38.5369, -4.71244], [-6.37624, -26.7432, 2.28756], [-6.70093, -28.105, 4.71244], [-9.51286, -39.8988, -2.28756]], [[-3.52774, -40.0022, -4.48097], [-2.45775, -27.8692, 2.04496], [-2.5724, -29.1693, 4.48097], [-3.64239, -41.3023, -2.04496]], [[2.28404, -40.6181, -4.24954], [1.59808, -28.4193, 1.80592], [1.66607, -29.6285, 4.24954], [2.35204, -41.8273, -1.80592]], [[8.11996, -40.3838, -4.01848], [5.70741, -28.3852, 1.57074], [5.92777, -29.4811, 4.01848], [8.34031, -41.4797, -1.57074]], [[13.8574, -39.3163, -3.78814], [9.78792, -27.7703, 1.33971], [10.1288, -28.7376, 3.78814], [14.1983, -40.2835, -1.33971]], [[19.3807, -37.4496, -3.55887], [13.7602, -26.5889, 1.1131], [14.1896, -27.4188, 3.55887], [19.8102, -38.2794, -1.1131]], [[24.5832, -34.8323, -3.33099], [17.549, -24.8655, 0.891165], [18.0359, -25.5554, 3.33099], [25.0701, -35.5222, -0.891165]], [[29.3684, -31.5262, -3.10482], [21.0844, -22.6336, 0.674163], [21.5996, -23.1866, 3.10482], [29.8836, -32.0792, -0.674163]], [[33.6518, -27.6038, -2.8807], [24.3029, -19.9351, 0.462334], [24.8198, -20.3591, 2.8807], [34.1688, -28.0278, -0.462334]], [[37.3615, -23.1466, -2.65893], [27.1477, -16.8188, 0.255906], [27.6433, -17.1259, 2.65893], [37.8571, -23.4537, -0.255906]], [[40.4388, -18.2431, -2.43982], [29.57, -13.3399, 0.0550995], [30.0248, -13.545, 2.43982], [40.8936, -18.4483, -0.0550995]], [[42.8385, -12.9862, -2.22366], [31.529, -9.55782, -0.13988], [31.9278, -9.67872, 2.22366], [43.2373, -13.1071, 0.13988]], [[44.529, -7.47204, -2.01074], [32.9924, -5.53618, -0.328838], [33.3241, -5.59185, 2.01074], [44.8607, -7.52771, 0.328838]], [[45.4921, -1.79751, -1.80134], [33.9365, -1.34092, -0.51159], [34.1942, -1.3511, 1.80134], [45.7499, -1.8077, 0.51159]], [[45.7226, 3.94115, -1.59574], [34.3463, 2.96055, -0.687966], [34.5272, 2.97614, 1.59574], [45.9035, 3.95674, 0.687966]], [[45.2274, 9.65004, -1.39418], [34.2153, 7.30043, -0.857807], [34.3202, 7.32281, 1.39418], [45.3323, 9.67243, 0.857807]], [[44.025, 15.239, -1.19694], [33.5455, 11.6116, -1.02097], [33.5788, 11.6231, 1.19694], [44.0583, 15.2505, 1.02097]], [[42.1445, 20.6229, -1.00423], [32.3469, 15.8286, -1.17731], [32.3158, 15.8134, 1.00423], [42.1134, 20.6077, 1.17731]], [[39.6244, 25.7227, -0.8163], [30.6369, 19.8884, -1.32672], [30.5513, 19.8328, 0.8163], [39.5387, 25.6671, 1.32672]], [[36.5118, 30.4663, -0.633365], [28.4403, 23.7313, -1.46909], [28.312, 23.6242, 0.633365], [36.3834, 30.3592, 1.46909]], [[32.8609, 34.7894, -0.455635], [25.7884, 27.3018, -1.60432], [25.6306, 27.1348, 0.455635], [32.7032, 34.6224, 1.60432]], [[28.7323, 38.636, -0.283306], [22.7182, 30.5489, -1.73233], [22.5453, 30.3164, 0.283306], [28.5594, 38.4035, 1.73233]], [[24.1911, 41.9588, -0.116567], [19.2722, 33.4271, -1.85305], [19.0988, 33.1262, 0.116567], [24.0177, 41.6579, 1.85305]], [[19.3063, 44.7193, 0.0444085], [15.4973, 35.8963, -1.96642], [15.3379, 35.5271, -0.0444085], [19.1469, 44.3501, 1.96642]], [[14.1494, 46.8882, 0.199456], [11.4439, 37.9228, -2.0724], [11.3127, 37.4878, -0.199456], [14.0182, 46.4532, 2.0724]], [[8.79326, 48.4452, 0.348425], [7.16581, 39.479, -2.17096], [7.07582, 38.9832, -0.348425], [8.70327, 47.9494, 2.17096]], [[3.31108, 49.3786, 0.491176], [2.71867, 40.5439, -2.26209], [2.68183, 39.9944, -0.491176], [3.27424, 48.8292, 2.26209]], [[-2.22457, 49.6854, 0.627581], [-1.84032, 41.1031, -2.34576], [-1.81372, 40.509, -0.627581], [-2.19797, 49.0913, 2.34576]], [[-7.74272, 49.3709, 0.757525], [-6.45329, 41.1489, -2.42201], [-6.35477, 40.5207, -0.757525], [-7.64419, 48.7426, 2.42201]], [[-13.1748, 48.4477, 0.880906], [-11.0625, 40.6802, -2.49083], [-10.8856, 40.0295, -0.880906], [-12.9979, 47.797, 2.49083]], [[-18.4555, 46.936, 0.997633], [-15.611, 39.702, -2.55228], [-15.3512, 39.0412, -0.997633], [-18.1957, 46.2753, 2.55228]], [[-23.5232, 44.8624, 1.10763], [-20.0433, 38.2257, -2.60638], [-19.6983, 37.5678, -1.10763], [-23.1783, 44.2046, 2.60638]], [[-28.3209, 42.2594, 1.21083], [-24.306, 36.2684, -2.65321], [-23.8757, 35.6265, -1.21083], [-27.8907, 41.6174, 2.65321]], [[-32.7964, 39.1648, 1.30718], [-28.3484, 33.853, -2.69282], [-27.8347, 33.2397, -1.30718], [-32.2828, 38.5514, 2.69282]], [[-36.9028, 35.621, 1.39664], [-32.123, 31.0072, -2.7253], [-31.5298, 30.4347, -1.39664], [-36.3096, 35.0485, 2.7253]], [[-40.5987, 31.6744, 1.47919], [-35.586, 27.7636, -2.75075], [-34.919, 27.2432, -1.47919], [-39.9317, 31.154, 2.75075]], [[-43.8488, 27.3743, 1.5548], [-38.6979, 24.1587, -2.76926], [-37.9643, 23.7007, -1.5548], [-43.1152, 26.9164, 2.76926]], [[-46.6235, 22.7728, 1.62348], [-41.4233, 20.2328, -2.78095], [-40.6318, 19.8462, -1.62348], [-45.8319, 22.3862, 2.78095]], [[-48.8992, 17.9235, 1.68524], [-43.7318, 16.0295, -2.78595], [-42.8922, 15.7217, -1.68524], [-48.0596, 17.6158, 2.78595]], [[-50.6585, 12.8814, 1.74009], [-45.598, 11.5946, -2.7844], [-44.721, 11.3716, -1.74009], [-49.7815, 12.6584, 2.7844]], [[-51.8899, 7.70161, 1.78808], [-47.0016, 6.97608, -2.77644], [-46.0986, 6.84206, -1.78808], [-50.9869, 7.56758, 2.77644]], [[-52.5875, 2.43952, 1.82925], [-47.9276, 2.22335, -2.76223], [-47.0103, 2.1808, -1.82925], [-51.6702, 2.39697, 2.76223]], [[-52.7511, -2.85036, 1.86365], [-48.3661, -2.61342, -2.74193], [-47.4463, -2.56372, -1.86365], [-51.8313, -2.80066, 2.74193]], [[-52.386, -8.11469, 1.89136], [-48.3128, -7.48374, -2.71573], [-47.4022, -7.34269, -1.89136], [-51.4755, -7.97365, 2.71573]], [[-51.5025, -13.3018, 1.91246], [-47.7683, -12.3374, -2.68381], [-46.8782, -12.1075, -1.91246], [-50.6124, -13.072, 2.68381]], [[-50.1155, -18.3622, 1.92704], [-46.7385, -17.1249, -2.64636], [-45.8796, -16.8102, -1.92704], [-49.2566, -18.0476, 2.64636]], [[-48.2446, -23.2489, 1.93521], [-45.2341, -21.7982, -2.60358], [-44.4163, -21.4041, -1.93521], [-47.4268, -22.8548, 2.60358]], [[-45.9133, -27.9177, 1.93709], [-43.2704, -26.3107, -2.5557], [-42.5027, -25.8439, -1.93709], [-45.1455, -27.4508, 2.5557]], [[-43.1488, -32.3276, 1.93279], [-40.8674, -30.6183, -2.50292], [-40.1574, -30.0864, -1.93279], [-42.4388, -31.7957, 2.50292]], [[-39.9817, -36.441, 1.92245], [-38.0489, -34.6794, -2.44547], [-37.4033, -34.0909, -1.92245], [-39.336, -35.8525, 2.44547]], [[-36.4453, -40.2239, 1.90622], [-34.8427, -38.4552, -2.38358], [-34.2666, -37.8194, -1.90622], [-35.8692, -39.5881, 2.38358]], [[-32.5754, -43.6462, 1.88427], [-31.2798, -41.9102, -2.3175], [-30.7772, -41.2368, -1.88427], [-32.0728, -42.9727, 2.3175]], [[-28.4101, -46.6815, 1.85674], [-27.3944, -45.0126, -2.24747], [-26.9677, -44.3114, -1.85674], [-27.9833, -45.9803, 2.24747]], [[-23.9887, -49.3074, 1.82383], [-23.2234, -47.7342, -2.17373], [-22.8736, -47.0152, -1.82383], [-23.639, -48.5884, 2.17373]], [[-19.3523, -51.5056, 1.78571], [-18.8056, -50.0507, -2.09656], [-18.5325, -49.3239, -1.78571], [-19.0792, -50.7788, 2.09656]], [[-14.5423, -53.2619, 1.74258], [-14.182, -51.9421, -2.01619], [-13.984, -51.2169, -1.74258], [-14.3443, -52.5367, 2.01619]], [[-9.60108, -54.5658, 1.69463], [-9.39462, -53.3924, -1.93291], [-9.2689, -52.6779, -1.69463], [-9.47536, -53.8513, 1.93291]], [[-4.57088, -55.4109, 1.64208], [-4.48665, -54.3899, -1.84698], [-4.42929, -53.6945, -1.64208], [-4.51351, -54.7155, 1.84698]], [[0.506175, -55.7947, 1.58515], [0.498304, -54.9272, -1.75867], [0.492238, -54.2584, -1.58515], [0.500108, -55.126, 1.75867]], [[5.58849, -55.7184, 1.52406], [5.51653, -55.0009, -1.66826], [5.45282, -54.3657, -1.52406], [5.52477, -55.0831, 1.66826]], [[10.6353, -55.1865, 1.45903], [10.5246, -54.6121, -1.57602], [10.4097, -54.0161, -1.45903], [10.5204, -54.5905, 1.57602]], [[15.607, -54.2074, 1.39031], [15.4798, -53.7657, -1.48224], [15.3208, -53.2136, -1.39031], [15.448, -53.6553, 1.48224]], [[20.4652, -52.7924, 1.31814], [20.3404, -52.4705, -1.38719], [20.1448, -51.966, -1.31814], [20.2696, -52.2879, 1.38719]], [[25.1733, -50.956, 1.24277], [25.0661, -50.7391, -1.29116], [24.8416, -50.2847, -1.24277], [24.9488, -50.5017, 1.29116]], [[29.6964, -48.7156, 1.16445], [29.6183, -48.5876, -1.19443], [29.3728, -48.1848, -1.16445], [29.4508, -48.3128, 1.19443]], [[34.0016, -46.0913, 1.08344], [33.9605, -46.0356, -1.09728], [33.7016, -45.6846, -1.08344], [33.7427, -45.7403, 1.09728]], [[38.0584, -43.1054, 1], [38.0584, -43.1054, -1], [37.7937, -42.8055, -1], [37.7937, -42.8055, 1]]]; sects = cross_sections(shape_pts, pts, angles, twist = 180, scale = 0.1); diff --git a/test/test_ellipse_extrude.scad b/test/test_ellipse_extrude.scad index 8655c3c0..3b4573a1 100644 --- a/test/test_ellipse_extrude.scad +++ b/test/test_ellipse_extrude.scad @@ -13,11 +13,11 @@ module test_ellipse_extrude() { expected_zs = [0, 0.392295, 0.782172, 1.16723, 1.54508, 1.91342, 2.26995, 2.61249, 2.93893, 3.24724, 3.53553, 3.80203, 4.04508, 4.2632, 4.45503, 4.6194, 4.75528, 4.86185, 4.93844, 4.98459, 5]; for(i = [0:len(expected_fs) - 1]) { - assertEqual(expected_fs[i], child_fs[i]); + assertEqualNum(expected_fs[i], child_fs[i]); } for(i = [0:len(expected_zs) - 1]) { - assertEqual(expected_zs[i], pre_zs[i]); + assertEqualNum(expected_zs[i], pre_zs[i]); } diff --git a/test/test_function_grapher.scad b/test/test_function_grapher.scad index b78ab755..17e4ec98 100644 --- a/test/test_function_grapher.scad +++ b/test/test_function_grapher.scad @@ -33,7 +33,7 @@ module test_function_grapher_default() { expected_faces = [[0, 5, 1], [1, 6, 2], [2, 7, 3], [4, 9, 5], [5, 10, 6], [6, 11, 7], [8, 13, 9], [9, 14, 10], [10, 15, 11], [0, 4, 5], [1, 5, 6], [2, 6, 7], [4, 8, 9], [5, 9, 10], [6, 10, 11], [8, 12, 13], [9, 13, 14], [10, 14, 15], [17, 21, 16], [18, 22, 17], [19, 23, 18], [21, 25, 20], [22, 26, 21], [23, 27, 22], [25, 29, 24], [26, 30, 25], [27, 31, 26], [21, 20, 16], [22, 21, 17], [23, 22, 18], [25, 24, 20], [26, 25, 21], [27, 26, 22], [29, 28, 24], [30, 29, 25], [31, 30, 26], [0, 1, 17, 16], [1, 2, 18, 17], [2, 3, 19, 18], [3, 7, 23, 19], [7, 11, 27, 23], [11, 15, 31, 27], [13, 12, 28, 29], [14, 13, 29, 30], [15, 14, 30, 31], [4, 0, 16, 20], [8, 4, 20, 24], [12, 8, 24, 28]]; for(i = [0:len(expected_faces) - 1]) { - assertTrue(expected_faces[i] == faces[i]); + assert(expected_faces[i] == faces[i]); } } diff --git a/test/test_golden_spiral.scad b/test/test_golden_spiral.scad index de2963c9..cf6f658b 100644 --- a/test/test_golden_spiral.scad +++ b/test/test_golden_spiral.scad @@ -12,20 +12,19 @@ module test_golden_spiral() { point_distance = 1 ); - expected_pts = [[2, 0], [1.8478, 0.7654], [1.4142, 1.4142], [0.7654, 1.8478], [0, 2], [-0.9271, 1.8532], [-1.7634, 1.4271], [-2.4271, 0.7634], [-2.8532, -0.0729], [-3, -1], [-2.9039, -1.9755], [-2.6194, -2.9134], [-2.1573, -3.7779], [-1.5355, -4.5355], [-0.7779, -5.1573], [0.0866, -5.6194], [1.0245, -5.9039], [2, -6], [2.9643, -5.9417], [3.9145, -5.7675], [4.8368, -5.4801], [5.7178, -5.0836], [6.5445, -4.5839], [7.305, -3.9881], [7.9881, -3.305], [8.5839, -2.5445], [9.0836, -1.7178], [9.4801, -0.8368], [9.7675, 0.0855], [9.9417, 1.0357], [10, 2], [10, 2], [9.9636, 2.9715], [9.8548, 3.9375], [9.6741, 4.8928], [9.4224, 5.8318], [9.1014, 6.7494], [8.7126, 7.6405], [8.2583, 8.5], [7.7411, 9.3232], [7.1638, 10.1054], [6.5297, 10.8422], [5.8422, 11.5297], [5.1054, 12.1638], [4.3232, 12.7411], [3.5, 13.2583], [2.6405, 13.7126], [1.7494, 14.1014], [0.8318, 14.4224], [-0.1072, 14.6741], [-1.0625, 14.8548], [-2.0285, 14.9636], [-3, 15], [-3.9992, 14.9762], [-4.9962, 14.9049], [-5.9886, 14.7863], [-6.9743, 14.6205], [-7.9509, 14.408], [-8.9164, 14.1494], [-9.8684, 13.845], [-10.8049, 13.4957], [-11.7237, 13.1023], [-12.6228, 12.6655], [-13.5, 12.1865], [-14.3535, 11.6663], [-15.1812, 11.1061], [-15.9813, 10.5071], [-16.7521, 9.8707], [-17.4917, 9.1984], [-18.1984, 8.4917], [-18.8707, 7.7521], [-19.5071, 6.9813], [-20.1061, 6.1812], [-20.6663, 5.3535], [-21.1865, 4.5], [-21.6655, 3.6228], [-22.1023, 2.7237], [-22.4957, 1.8049], [-22.845, 0.8684], [-23.1494, -0.0836], [-23.408, -1.0491], [-23.6205, -2.0257], [-23.7863, -3.0114], [-23.9049, -4.0038], [-23.9762, -5.0008], [-24, -6], [-23.9856, -6.9889], [-23.9425, -7.9769], [-23.8706, -8.9633], [-23.7701, -9.9472], [-23.641, -10.9277], [-23.4835, -11.904], [-23.2976, -12.8754], [-23.0835, -13.8409], [-22.8415, -14.7998], [-22.5716, -15.7513], [-22.2742, -16.6945], [-21.9495, -17.6287], [-21.5978, -18.553], [-21.2193, -19.4667], [-20.8145, -20.369], [-20.3835, -21.2592], [-19.9268, -22.1364], [-19.4449, -23], [-18.938, -23.8492], [-18.4066, -24.6833], [-17.8512, -25.5016], [-17.2722, -26.3034], [-16.6701, -27.088], [-16.0455, -27.8548], [-15.3989, -28.6031], [-14.7307, -29.3322], [-14.0416, -30.0416], [-13.3322, -30.7307], [-12.6031, -31.3989], [-11.8548, -32.0455], [-11.088, -32.6701], [-10.3034, -33.2722], [-9.5016, -33.8512], [-8.6833, -34.4066], [-7.8492, -34.938], [-7, -35.4449], [-6.1364, -35.9268], [-5.2592, -36.3835], [-4.369, -36.8145], [-3.4667, -37.2193], [-2.553, -37.5978], [-1.6287, -37.9495], [-0.6945, -38.2742], [0.2487, -38.5716], [1.2002, -38.8415], [2.1591, -39.0835], [3.1246, -39.2976], [4.096, -39.4835], [5.0723, -39.641], [6.0528, -39.7701], [7.0367, -39.8706], [8.0231, -39.9425], [9.0111, -39.9856], [10, -40], [10.993, -39.991], [11.9856, -39.9641], [12.9776, -39.9193], [13.9687, -39.8566], [14.9584, -39.776], [15.9465, -39.6776], [16.9327, -39.5613], [17.9167, -39.4273], [18.898, -39.2755], [19.8765, -39.106], [20.8517, -38.9188], [21.8234, -38.7141], [22.7912, -38.4919], [23.7549, -38.2523], [24.7141, -37.9952], [25.6684, -37.721], [26.6177, -37.4295], [27.5616, -37.1209], [28.4997, -36.7954], [29.4318, -36.4529], [30.3576, -36.0937], [31.2767, -35.7179], [32.1889, -35.3255], [33.0939, -34.9166], [33.9913, -34.4916], [34.881, -34.0504], [35.7625, -33.5932], [36.6356, -33.1201], [37.5, -32.6314], [38.3555, -32.1271], [39.2017, -31.6075], [40.0384, -31.0727], [40.8653, -30.5229], [41.6821, -29.9582], [42.4887, -29.3789], [43.2846, -28.7851], [44.0697, -28.1771], [44.8436, -27.5549], [45.6062, -26.9189], [46.3573, -26.2692], [47.0964, -25.6061], [47.8235, -24.9298], [48.5382, -24.2404], [49.2404, -23.5382], [49.9298, -22.8235], [50.6061, -22.0964], [51.2692, -21.3573], [51.9189, -20.6062], [52.5549, -19.8436], [53.1771, -19.0697], [53.7851, -18.2846], [54.3789, -17.4887], [54.9582, -16.6821], [55.5229, -15.8653], [56.0727, -15.0384], [56.6075, -14.2017], [57.1271, -13.3555], [57.6314, -12.5], [58.1201, -11.6356], [58.5932, -10.7625], [59.0504, -9.881], [59.4916, -8.9913], [59.9166, -8.0939], [60.3255, -7.1889], [60.7179, -6.2767], [61.0937, -5.3576], [61.4529, -4.4318], [61.7954, -3.4997], [62.1209, -2.5616], [62.4295, -1.6177], [62.721, -0.6684], [62.9952, 0.2859], [63.2523, 1.2451], [63.4919, 2.2088], [63.7141, 3.1766], [63.9188, 4.1483], [64.106, 5.1235], [64.2755, 6.102], [64.4273, 7.0833], [64.5613, 8.0673], [64.6776, 9.0535], [64.776, 10.0416], [64.8566, 11.0313], [64.9193, 12.0224], [64.9641, 13.0144], [64.991, 14.007], [65, 15]]; - + expected_pts = [[2, 0], [1.84776, 0.765367], [1.41421, 1.41421], [0.765367, 1.84776], [0, 2], [-0.927051, 1.85317], [-1.76336, 1.42705], [-2.42705, 0.763356], [-2.85317, -0.072949], [-3, -1], [-2.90393, -1.97545], [-2.6194, -2.91342], [-2.15735, -3.77785], [-1.53553, -4.53553], [-0.777851, -5.15735], [0.0865828, -5.6194], [1.02455, -5.90393], [2, -6], [2.96429, -5.94167], [3.91453, -5.76753], [4.83684, -5.48013], [5.71779, -5.08365], [6.54452, -4.58387], [7.30498, -3.98809], [7.98809, -3.30498], [8.58387, -2.54452], [9.08365, -1.71779], [9.48013, -0.836839], [9.76753, 0.0854747], [9.94167, 1.03571], [10, 2], [10, 2], [9.96365, 2.97149], [9.8548, 3.93755], [9.67406, 4.89277], [9.42245, 5.83182], [9.10136, 6.74943], [8.7126, 7.64049], [8.25833, 8.5], [7.7411, 9.32316], [7.16381, 10.1054], [6.52967, 10.8422], [5.84225, 11.5297], [5.10537, 12.1638], [4.32316, 12.7411], [3.5, 13.2583], [2.64049, 13.7126], [1.74943, 14.1014], [0.831817, 14.4224], [-0.107228, 14.6741], [-1.06245, 14.8548], [-2.02851, 14.9636], [-3, 15], [-3.99922, 14.9762], [-4.99618, 14.9049], [-5.98861, 14.7863], [-6.97428, 14.6205], [-7.95094, 14.408], [-8.91638, 14.1494], [-9.86843, 13.845], [-10.8049, 13.4957], [-11.7237, 13.1023], [-12.6228, 12.6655], [-13.5, 12.1865], [-14.3535, 11.6663], [-15.1812, 11.1061], [-15.9813, 10.5071], [-16.7521, 9.87074], [-17.4917, 9.19841], [-18.1984, 8.49166], [-18.8707, 7.75208], [-19.5071, 6.98134], [-20.1061, 6.1812], [-20.6663, 5.35346], [-21.1865, 4.5], [-21.6655, 3.62276], [-22.1023, 2.72372], [-22.4957, 1.80491], [-22.845, 0.868427], [-23.1494, -0.0836163], [-23.408, -1.04906], [-23.6205, -2.02572], [-23.7863, -3.01139], [-23.9049, -4.00382], [-23.9762, -5.00078], [-24, -6], [-23.9856, -6.98888], [-23.9425, -7.97692], [-23.8706, -8.9633], [-23.7701, -9.94716], [-23.641, -10.9277], [-23.4835, -11.904], [-23.2976, -12.8754], [-23.0835, -13.8409], [-22.8415, -14.7998], [-22.5716, -15.7513], [-22.2742, -16.6945], [-21.9495, -17.6287], [-21.5978, -18.553], [-21.2193, -19.4667], [-20.8145, -20.369], [-20.3835, -21.2592], [-19.9268, -22.1364], [-19.4449, -23], [-18.938, -23.8492], [-18.4066, -24.6833], [-17.8512, -25.5016], [-17.2722, -26.3034], [-16.6701, -27.088], [-16.0455, -27.8548], [-15.3989, -28.6031], [-14.7307, -29.3322], [-14.0416, -30.0416], [-13.3322, -30.7307], [-12.6031, -31.3989], [-11.8548, -32.0455], [-11.088, -32.6701], [-10.3034, -33.2722], [-9.5016, -33.8512], [-8.68331, -34.4066], [-7.8492, -34.938], [-7, -35.4449], [-6.13641, -35.9268], [-5.25917, -36.3835], [-4.36902, -36.8145], [-3.46671, -37.2193], [-2.55301, -37.5978], [-1.62868, -37.9495], [-0.694522, -38.2742], [0.24869, -38.5716], [1.20015, -38.8415], [2.15906, -39.0835], [3.1246, -39.2976], [4.09596, -39.4835], [5.07232, -39.641], [6.05284, -39.7701], [7.0367, -39.8706], [8.02308, -39.9425], [9.01112, -39.9856], [10, -40], [10.993, -39.991], [11.9856, -39.9641], [12.9776, -39.9193], [13.9687, -39.8566], [14.9584, -39.776], [15.9465, -39.6776], [16.9327, -39.5613], [17.9167, -39.4273], [18.898, -39.2755], [19.8765, -39.106], [20.8517, -38.9188], [21.8234, -38.7141], [22.7912, -38.4919], [23.7549, -38.2523], [24.7141, -37.9952], [25.6684, -37.721], [26.6177, -37.4295], [27.5616, -37.1209], [28.4997, -36.7954], [29.4318, -36.4529], [30.3576, -36.0937], [31.2767, -35.7179], [32.1889, -35.3255], [33.0939, -34.9166], [33.9913, -34.4916], [34.881, -34.0504], [35.7625, -33.5932], [36.6356, -33.1201], [37.5, -32.6314], [38.3555, -32.1271], [39.2017, -31.6075], [40.0384, -31.0727], [40.8653, -30.5229], [41.6821, -29.9582], [42.4887, -29.3789], [43.2846, -28.7851], [44.0697, -28.1771], [44.8436, -27.5549], [45.6062, -26.9189], [46.3573, -26.2692], [47.0964, -25.6061], [47.8235, -24.9298], [48.5382, -24.2404], [49.2404, -23.5382], [49.9298, -22.8235], [50.6061, -22.0964], [51.2692, -21.3573], [51.9189, -20.6062], [52.5549, -19.8436], [53.1771, -19.0697], [53.7851, -18.2846], [54.3789, -17.4887], [54.9582, -16.6821], [55.5229, -15.8653], [56.0727, -15.0384], [56.6075, -14.2017], [57.1271, -13.3555], [57.6314, -12.5], [58.1201, -11.6356], [58.5932, -10.7625], [59.0504, -9.88096], [59.4916, -8.99134], [59.9166, -8.0939], [60.3255, -7.18893], [60.7179, -6.27673], [61.0937, -5.3576], [61.4529, -4.43183], [61.7954, -3.49972], [62.1209, -2.56158], [62.4295, -1.61772], [62.721, -0.668445], [62.9952, 0.285941], [63.2523, 1.24512], [63.4919, 2.20879], [63.7141, 3.17663], [63.9188, 4.14832], [64.106, 5.12354], [64.2755, 6.10199], [64.4273, 7.08334], [64.5613, 8.06727], [64.6776, 9.05345], [64.776, 10.0416], [64.8566, 11.0313], [64.9193, 12.0224], [64.9641, 13.0144], [64.991, 14.007], [65, 15]]; actual_pts = [for(pt_angle = pts_angles) pt_angle[0]]; - - expected_angles = [0, 22.5, 45, 67.5, 90, 108, 126, 144, 162, 180, 191.25, 202.5, 213.75, 225, 236.25, 247.5, 258.75, 270, 276.923, 283.846, 290.769, 297.692, 304.615, 311.538, 318.462, 325.385, 332.308, 339.231, 346.154, 353.077, 360, 360, 364.286, 368.571, 372.857, 377.143, 381.429, 385.714, 390, 394.286, 398.571, 402.857, 407.143, 411.429, 415.714, 420, 424.286, 428.571, 432.857, 437.143, 441.429, 445.714, 450, 452.727, 455.455, 458.182, 460.909, 463.636, 466.364, 469.091, 471.818, 474.545, 477.273, 480, 482.727, 485.455, 488.182, 490.909, 493.636, 496.364, 499.091, 501.818, 504.545, 507.273, 510, 512.727, 515.455, 518.182, 520.909, 523.636, 526.364, 529.091, 531.818, 534.545, 537.273, 540, 541.667, 543.333, 545, 546.667, 548.333, 550, 551.667, 553.333, 555, 556.667, 558.333, 560, 561.667, 563.333, 565, 566.667, 568.333, 570, 571.667, 573.333, 575, 576.667, 578.333, 580, 581.667, 583.333, 585, 586.667, 588.333, 590, 591.667, 593.333, 595, 596.667, 598.333, 600, 601.667, 603.333, 605, 606.667, 608.333, 610, 611.667, 613.333, 615, 616.667, 618.333, 620, 621.667, 623.333, 625, 626.667, 628.333, 630, 631.034, 632.069, 633.103, 634.138, 635.172, 636.207, 637.241, 638.276, 639.31, 640.345, 641.379, 642.414, 643.448, 644.483, 645.517, 646.552, 647.586, 648.621, 649.655, 650.69, 651.724, 652.759, 653.793, 654.828, 655.862, 656.897, 657.931, 658.966, 660, 661.034, 662.069, 663.103, 664.138, 665.172, 666.207, 667.241, 668.276, 669.31, 670.345, 671.379, 672.414, 673.448, 674.483, 675.517, 676.552, 677.586, 678.621, 679.655, 680.69, 681.724, 682.759, 683.793, 684.828, 685.862, 686.897, 687.931, 688.966, 690, 691.034, 692.069, 693.103, 694.138, 695.172, 696.207, 697.241, 698.276, 699.31, 700.345, 701.379, 702.414, 703.448, 704.483, 705.517, 706.552, 707.586, 708.621, 709.655, 710.69, 711.724, 712.759, 713.793, 714.828, 715.862, 716.897, 717.931, 718.966, 720]; - actual_angles = [for(pt_angle = pts_angles) round_n(pt_angle[1], float_digits = 3)]; - + expected_angles = [0, 22.5, 45, 67.5, 90, 108, 126, 144, 162, 180, 191.25, 202.5, 213.75, 225, 236.25, 247.5, 258.75, 270, 276.923, 283.846, 290.769, 297.692, 304.615, 311.538, 318.462, 325.385, 332.308, 339.231, 346.154, 353.077, 360, 360, 364.286, 368.571, 372.857, 377.143, 381.429, 385.714, 390, 394.286, 398.571, 402.857, 407.143, 411.429, 415.714, 420, 424.286, 428.571, 432.857, 437.143, 441.429, 445.714, 450, 452.727, 455.455, 458.182, 460.909, 463.636, 466.364, 469.091, 471.818, 474.545, 477.273, 480, 482.727, 485.455, 488.182, 490.909, 493.636, 496.364, 499.091, 501.818, 504.545, 507.273, 510, 512.727, 515.455, 518.182, 520.909, 523.636, 526.364, 529.091, 531.818, 534.545, 537.273, 540, 541.667, 543.333, 545, 546.667, 548.333, 550, 551.667, 553.333, 555, 556.667, 558.333, 560, 561.667, 563.333, 565, 566.667, 568.333, 570, 571.667, 573.333, 575, 576.667, 578.333, 580, 581.667, 583.333, 585, 586.667, 588.333, 590, 591.667, 593.333, 595, 596.667, 598.333, 600, 601.667, 603.333, 605, 606.667, 608.333, 610, 611.667, 613.333, 615, 616.667, 618.333, 620, 621.667, 623.333, 625, 626.667, 628.333, 630, 631.034, 632.069, 633.103, 634.138, 635.172, 636.207, 637.241, 638.276, 639.31, 640.345, 641.379, 642.414, 643.448, 644.483, 645.517, 646.552, 647.586, 648.621, 649.655, 650.69, 651.724, 652.759, 653.793, 654.828, 655.862, 656.897, 657.931, 658.966, 660, 661.034, 662.069, 663.103, 664.138, 665.172, 666.207, 667.241, 668.276, 669.31, 670.345, 671.379, 672.414, 673.448, 674.483, 675.517, 676.552, 677.586, 678.621, 679.655, 680.69, 681.724, 682.759, 683.793, 684.828, 685.862, 686.897, 687.931, 688.966, 690, 691.034, 692.069, 693.103, 694.138, 695.172, 696.207, 697.241, 698.276, 699.31, 700.345, 701.379, 702.414, 703.448, 704.483, 705.517, 706.552, 707.586, 708.621, 709.655, 710.69, 711.724, 712.759, 713.793, 714.828, 715.862, 716.897, 717.931, 718.966, 720]; + actual_angles = [for(pt_angle = pts_angles) pt_angle[1]]; + assertEqualPoints(expected_pts, actual_pts); for(i = [0:len(expected_angles) - 1]) { - assertEqual( + assertEqualNum( expected_angles[i], - actual_angles[i] + actual_angles[i], + 0.0005 ); } } diff --git a/test/test_golden_spiral_extrude.scad b/test/test_golden_spiral_extrude.scad index bb8e4ad8..900414a9 100644 --- a/test/test_golden_spiral_extrude.scad +++ b/test/test_golden_spiral_extrude.scad @@ -13,239 +13,10 @@ module test_golden_spiral_extrude_solid() { include ; module test_golden_spiral_extrude(sections) { - expected = [ - [[0, 0, -10], [0, 0, 10], [0, 4, 10], [0, 4, -10]] - , [[-0.05, -0.12, -9.932], [0.056, 0.135, 9.987], [1.58, 3.815, 9.932], [1.475, 3.561, -9.987]] - , [[-0.182, -0.182, -9.862], [0.206, 0.206, 9.972], [3.011, 3.011, 9.862], [2.623, 2.623, -9.972]] - , [[-0.355, -0.147, -9.791], [0.402, 0.167, 9.955], [4.051, 1.678, 9.791], [3.293, 1.364, -9.955]] - , [[-0.51, 0, -9.717], [0.579, 0, 9.935], [4.51, 0, 9.717], [3.421, 0, -9.935]] - , [[-0.651, -0.113, -9.643], [0.638, -0.532, 9.914], [4.358, -1.741, 9.643], [3.069, -1.322, -9.914]] - , [[-0.802, -0.144, -9.567], [0.508, -1.096, 9.89], [3.656, -3.383, 9.567], [2.346, -2.431, -9.89]] - , [[-0.927, -0.1, -9.489], [0.179, -1.622, 9.865], [2.454, -4.754, 9.489], [1.348, -3.232, -9.865]] - , [[-0.998, -0.005, -9.41], [-0.337, -2.04, 9.838], [0.852, -5.701, 9.41], [0.191, -3.666, -9.838]] - , [[-1, 0.112, -9.329], [-1, -2.284, 9.808], [-1, -6.112, 9.329], [-1, -3.716, -9.808]] - , [[-1.346, 0.261, -9.247], [-1.863, -2.338, 9.777], [-2.605, -6.069, 9.247], [-2.088, -3.47, -9.777]] - , [[-1.635, 0.467, -9.163], [-2.745, -2.213, 9.743], [-4.192, -5.706, 9.163], [-3.082, -3.026, -9.743]] - , [[-1.859, 0.714, -9.078], [-3.609, -1.904, 9.708], [-5.696, -5.029, 9.078], [-3.947, -2.41, -9.708]] - , [[-2.016, 0.984, -8.992], [-4.416, -1.416, 9.671], [-7.055, -4.055, 8.992], [-4.655, -1.655, -9.671]] - , [[-2.104, 1.262, -8.904], [-5.128, -0.758, 9.632], [-8.211, -2.818, 8.904], [-5.187, -0.797, -9.632]] - , [[-2.128, 1.533, -8.816], [-5.71, 0.049, 9.591], [-9.111, -1.36, 8.816], [-5.529, 0.124, -9.591]] - , [[-2.094, 1.782, -8.726], [-6.129, 0.98, 9.548], [-9.714, 0.267, 8.726], [-5.679, 1.069, -9.548]] - , [[-2.012, 2, -8.634], [-6.36, 2, 9.504], [-9.988, 2, 8.634], [-5.64, 2, -9.504]] - , [[-1.911, 2, -8.542], [-6.49, 2, 9.458], [-10.089, 2, 8.542], [-5.51, 2, -9.458]] - , [[-1.783, 2.459, -8.448], [-6.555, 3.039, 9.41], [-10.1, 3.469, 8.448], [-5.328, 2.89, -9.41]] - , [[-1.605, 2.888, -8.353], [-6.491, 4.093, 9.36], [-9.93, 4.941, 8.353], [-5.044, 3.736, -9.36]] - , [[-1.381, 3.282, -8.258], [-6.294, 5.145, 9.308], [-9.579, 6.391, 8.258], [-4.666, 4.528, -9.308]] - , [[-1.119, 3.637, -8.161], [-5.965, 6.18, 9.255], [-9.049, 7.799, 8.161], [-4.203, 5.255, -9.255]] - , [[-0.822, 3.948, -8.063], [-5.504, 7.18, 9.2], [-8.345, 9.141, 8.063], [-3.664, 5.909, -9.2]] - , [[-0.499, 4.214, -7.964], [-4.916, 8.127, 9.144], [-7.477, 10.396, 7.964], [-3.06, 6.483, -9.144]] - , [[-0.155, 4.433, -7.864], [-4.207, 9.006, 9.086], [-6.455, 11.544, 7.864], [-2.403, 6.97, -9.086]] - , [[0.203, 4.603, -7.763], [-3.385, 9.801, 9.026], [-5.292, 12.565, 7.763], [-1.704, 7.366, -9.026]] - , [[0.57, 4.725, -7.661], [-2.46, 10.498, 8.965], [-4.005, 13.442, 7.661], [-0.976, 7.67, -8.965]] - , [[0.938, 4.8, -7.559], [-1.444, 11.082, 8.903], [-2.612, 14.16, 7.559], [-0.229, 7.878, -8.903]] - , [[1.303, 4.829, -7.455], [-0.352, 11.542, 8.838], [-1.132, 14.707, 7.455], [0.523, 7.993, -8.838]] - , [[1.658, 4.813, -7.351], [0.802, 11.869, 8.773], [0.413, 15.07, 7.351], [1.27, 8.014, -8.773]] - , [[2, 4.756, -7.246], [2, 12.053, 8.706], [2, 15.244, 7.246], [2, 7.947, -8.706]] - , [[2.971, 4.644, -7.141], [2.971, 12.127, 8.637], [2.971, 15.283, 7.141], [2.971, 7.8, -8.637]] - , [[3.535, 4.477, -7.034], [4.107, 12.121, 8.567], [4.341, 15.233, 7.034], [3.768, 7.588, -8.567]] - , [[4.078, 4.27, -6.927], [5.248, 12.028, 8.496], [5.707, 15.078, 6.927], [4.538, 7.32, -8.496]] - , [[4.6, 4.026, -6.819], [6.385, 11.846, 8.424], [7.063, 14.818, 6.819], [5.279, 6.999, -8.424]] - , [[5.098, 3.748, -6.711], [7.513, 11.577, 8.35], [8.401, 14.455, 6.711], [5.986, 6.626, -8.35]] - , [[5.569, 3.436, -6.602], [8.624, 11.22, 8.275], [9.712, 13.989, 6.602], [6.657, 6.205, -8.275]] - , [[6.013, 3.093, -6.493], [9.712, 10.776, 8.198], [10.987, 13.423, 6.493], [7.288, 5.741, -8.198]] - , [[6.426, 2.723, -6.383], [10.77, 10.247, 8.121], [12.221, 12.76, 6.383], [7.876, 5.235, -8.121]] - , [[6.807, 2.326, -6.273], [11.791, 9.636, 8.042], [13.404, 12.002, 6.273], [8.42, 4.692, -8.042]] - , [[7.155, 1.906, -6.162], [12.768, 8.944, 7.962], [14.529, 11.153, 6.162], [8.917, 4.115, -7.962]] - , [[7.469, 1.466, -6.051], [13.695, 8.176, 7.881], [15.59, 10.218, 6.051], [9.364, 3.509, -7.881]] - , [[7.748, 1.008, -5.939], [14.566, 7.334, 7.799], [16.58, 9.203, 5.939], [9.762, 2.877, -7.799]] - , [[7.99, 0.535, -5.827], [15.374, 6.423, 7.716], [17.492, 8.112, 5.827], [10.108, 2.223, -7.716]] - , [[8.196, 0.049, -5.715], [16.115, 5.448, 7.632], [18.321, 6.951, 5.715], [10.402, 1.552, -7.632]] - , [[8.364, -0.447, -5.602], [16.783, 4.413, 7.547], [19.061, 5.728, 5.602], [10.642, 0.868, -7.547]] - , [[8.495, -0.95, -5.49], [17.374, 3.325, 7.461], [19.707, 4.449, 5.49], [10.829, 0.174, -7.461]] - , [[8.589, -1.458, -5.377], [17.882, 2.19, 7.373], [20.256, 3.121, 5.377], [10.963, -0.526, -7.373]] - , [[8.645, -1.967, -5.264], [18.305, 1.013, 7.285], [20.703, 1.753, 5.264], [11.043, -1.227, -7.285]] - , [[8.664, -2.476, -5.15], [18.639, -0.199, 7.197], [21.046, 0.351, 5.15], [11.071, -1.926, -7.197]] - , [[8.646, -2.981, -5.037], [18.88, -1.438, 7.107], [21.282, -1.076, 5.037], [11.047, -2.619, -7.107]] - , [[8.592, -3.48, -4.923], [19.027, -2.698, 7.016], [21.408, -2.52, 4.923], [10.973, -3.302, -7.016]] - , [[8.515, -3.999, -4.81], [19.091, -3.999, 6.925], [21.438, -3.999, 4.81], [10.862, -3.999, -6.925]] - , [[8.418, -4.687, -4.696], [19.089, -5.195, 6.833], [21.392, -5.305, 4.696], [10.721, -4.797, -6.833]] - , [[8.29, -5.368, -4.583], [19.028, -6.394, 6.74], [21.283, -6.609, 4.583], [10.544, -5.584, -6.74]] - , [[8.132, -6.041, -4.469], [18.909, -7.591, 6.647], [21.109, -7.907, 4.469], [10.332, -6.358, -6.647]] - , [[7.944, -6.705, -4.356], [18.73, -8.784, 6.552], [20.872, -9.197, 4.356], [10.086, -7.118, -6.552]] - , [[7.727, -7.358, -4.242], [18.492, -9.97, 6.458], [20.571, -10.474, 4.242], [9.807, -7.863, -6.458]] - , [[7.481, -8, -4.129], [18.195, -11.146, 6.362], [20.209, -11.737, 4.129], [9.495, -8.591, -6.362]] - , [[7.208, -8.629, -4.016], [17.84, -12.309, 6.266], [19.784, -12.981, 4.016], [9.151, -9.301, -6.266]] - , [[6.906, -9.243, -3.903], [17.428, -13.455, 6.17], [19.298, -14.204, 3.903], [8.777, -9.992, -6.17]] - , [[6.578, -9.843, -3.79], [16.959, -14.583, 6.073], [18.753, -15.403, 3.79], [8.372, -10.662, -6.073]] - , [[6.224, -10.426, -3.678], [16.433, -15.689, 5.975], [18.149, -16.574, 3.678], [7.94, -11.311, -5.975]] - , [[5.844, -10.992, -3.566], [15.853, -16.771, 5.877], [17.489, -17.715, 3.566], [7.48, -11.936, -5.877]] - , [[5.439, -11.539, -3.454], [15.219, -17.825, 5.779], [16.773, -18.823, 3.454], [6.993, -12.538, -5.779]] - , [[5.011, -12.068, -3.343], [14.533, -18.848, 5.68], [16.003, -19.895, 3.343], [6.481, -13.115, -5.68]] - , [[4.56, -12.576, -3.231], [13.796, -19.839, 5.581], [15.181, -20.928, 3.231], [5.946, -13.665, -5.581]] - , [[4.087, -13.063, -3.121], [13.01, -20.794, 5.482], [14.31, -21.921, 3.121], [5.387, -14.189, -5.482]] - , [[3.593, -13.527, -3.01], [12.176, -21.711, 5.382], [13.391, -22.87, 3.01], [4.808, -14.686, -5.382]] - , [[3.078, -13.969, -2.901], [11.296, -22.588, 5.282], [12.426, -23.772, 2.901], [4.208, -15.153, -5.282]] - , [[2.545, -14.387, -2.791], [10.374, -23.422, 5.182], [11.418, -24.627, 2.791], [3.589, -15.592, -5.182]] - , [[1.993, -14.78, -2.682], [9.41, -24.211, 5.082], [10.369, -25.432, 2.682], [2.953, -16.001, -5.082]] - , [[1.424, -15.148, -2.574], [8.406, -24.953, 4.981], [9.283, -26.184, 2.574], [2.301, -16.379, -4.981]] - , [[0.839, -15.49, -2.466], [7.366, -25.647, 4.88], [8.161, -26.883, 2.466], [1.634, -16.727, -4.88]] - , [[0.24, -15.806, -2.359], [6.292, -26.289, 4.78], [7.006, -27.525, 2.359], [0.953, -17.042, -4.78]] - , [[-0.374, -16.094, -2.252], [5.186, -26.879, 4.679], [5.821, -28.111, 2.252], [0.261, -17.326, -4.679]] - , [[-1, -16.354, -2.146], [4.051, -27.414, 4.578], [4.61, -28.637, 2.146], [-0.441, -17.577, -4.578]] - , [[-1.637, -16.586, -2.041], [2.89, -27.894, 4.477], [3.374, -29.104, 2.041], [-1.153, -17.796, -4.477]] - , [[-2.285, -16.789, -1.936], [1.705, -28.317, 4.376], [2.118, -29.51, 1.936], [-1.872, -17.982, -4.376]] - , [[-2.942, -16.962, -1.832], [0.5, -28.682, 4.275], [0.844, -29.854, 1.832], [-2.598, -18.134, -4.275]] - , [[-3.606, -17.106, -1.729], [-0.724, -28.988, 4.174], [-0.445, -30.135, 1.729], [-3.328, -18.253, -4.174]] - , [[-4.277, -17.219, -1.626], [-1.961, -29.234, 4.073], [-1.746, -30.353, 1.626], [-4.061, -18.339, -4.073]] - , [[-4.953, -17.303, -1.525], [-3.211, -29.419, 3.973], [-3.055, -30.507, 1.525], [-4.797, -18.391, -3.973]] - , [[-5.633, -17.355, -1.424], [-4.469, -29.543, 3.872], [-4.369, -30.597, 1.424], [-5.532, -18.41, -3.872]] - , [[-6.315, -17.377, -1.324], [-5.733, -29.605, 3.772], [-5.685, -30.623, 1.324], [-6.267, -18.395, -3.772]] - , [[-6.989, -17.377, -1.224], [-6.989, -29.615, 3.672], [-6.989, -30.594, 1.224], [-6.989, -18.356, -3.672]] - , [[-7.785, -17.36, -1.126], [-8.141, -29.585, 3.572], [-8.168, -30.525, 1.126], [-7.813, -18.3, -3.572]] - , [[-8.582, -17.322, -1.028], [-9.292, -29.521, 3.472], [-9.345, -30.419, 1.028], [-8.634, -18.221, -3.472]] - , [[-9.378, -17.262, -0.932], [-10.442, -29.421, 3.373], [-10.517, -30.279, 0.932], [-9.453, -18.119, -3.373]] - , [[-10.172, -17.179, -0.836], [-11.588, -29.286, 3.274], [-11.683, -30.103, 0.836], [-10.268, -17.996, -3.274]] - , [[-10.965, -17.075, -0.741], [-12.729, -29.116, 3.175], [-12.843, -29.891, 0.741], [-11.079, -17.851, -3.175]] - , [[-11.756, -16.95, -0.648], [-13.865, -28.912, 3.077], [-13.995, -29.645, 0.648], [-11.885, -17.683, -3.077]] - , [[-12.544, -16.802, -0.555], [-14.995, -28.673, 2.979], [-15.138, -29.365, 0.555], [-12.687, -17.494, -2.979]] - , [[-13.328, -16.633, -0.463], [-16.117, -28.399, 2.882], [-16.271, -29.05, 0.463], [-13.483, -17.284, -2.882]] - , [[-14.109, -16.442, -0.373], [-17.23, -28.091, 2.785], [-17.394, -28.701, 0.373], [-14.272, -17.052, -2.785]] - , [[-14.885, -16.229, -0.283], [-18.334, -27.75, 2.688], [-18.504, -28.319, 0.283], [-15.055, -16.798, -2.688]] - , [[-15.656, -15.995, -0.194], [-19.427, -27.375, 2.592], [-19.602, -27.904, 0.194], [-15.831, -16.524, -2.592]] - , [[-16.421, -15.739, -0.107], [-20.507, -26.967, 2.496], [-20.685, -27.457, 0.107], [-16.599, -16.228, -2.496]] - , [[-17.179, -15.462, -0.02], [-21.575, -26.527, 2.402], [-21.754, -26.977, 0.02], [-17.358, -15.912, -2.402]] - , [[-17.931, -15.163, 0.065], [-22.629, -26.054, 2.307], [-22.807, -26.466, -0.065], [-18.109, -15.575, -2.307]] - , [[-18.676, -14.844, 0.149], [-23.668, -25.549, 2.213], [-23.842, -25.923, -0.149], [-18.85, -15.218, -2.213]] - , [[-19.412, -14.503, 0.232], [-24.691, -25.013, 2.12], [-24.86, -25.351, -0.232], [-19.582, -14.84, -2.12]] - , [[-20.14, -14.141, 0.314], [-25.697, -24.447, 2.027], [-25.86, -24.748, -0.314], [-20.303, -14.443, -2.027]] - , [[-20.859, -13.759, 0.395], [-26.685, -23.85, 1.936], [-26.839, -24.117, -0.395], [-21.013, -14.026, -1.936]] - , [[-21.568, -13.356, 0.474], [-27.654, -23.224, 1.844], [-27.798, -23.457, -0.474], [-21.712, -13.59, -1.844]] - , [[-22.267, -12.933, 0.553], [-28.604, -22.568, 1.754], [-28.736, -22.769, -0.553], [-22.399, -13.134, -1.754]] - , [[-22.955, -12.49, 0.63], [-29.533, -21.885, 1.664], [-29.652, -22.054, -0.63], [-23.074, -12.66, -1.664]] - , [[-23.631, -12.027, 0.705], [-30.441, -21.174, 1.575], [-30.545, -21.313, -0.705], [-23.735, -12.167, -1.575]] - , [[-24.296, -11.544, 0.78], [-31.326, -20.436, 1.487], [-31.414, -20.547, -0.78], [-24.383, -11.655, -1.487]] - , [[-24.948, -11.043, 0.853], [-32.188, -19.672, 1.399], [-32.258, -19.755, -0.853], [-25.018, -11.126, -1.399]] - , [[-25.586, -10.522, 0.925], [-33.027, -18.882, 1.313], [-33.078, -18.94, -0.925], [-25.638, -10.579, -1.313]] - , [[-26.211, -9.982, 0.996], [-33.84, -18.068, 1.227], [-33.872, -18.101, -0.996], [-26.243, -10.015, -1.227]] - , [[-26.822, -9.424, 1.066], [-34.628, -17.23, 1.142], [-34.639, -17.241, -1.066], [-26.833, -9.435, -1.142]] - , [[-27.418, -8.848, 1.134], [-35.39, -16.369, 1.058], [-35.379, -16.358, -1.134], [-27.407, -8.837, -1.058]] - , [[-27.999, -8.254, 1.201], [-36.126, -15.486, 0.975], [-36.092, -15.456, -1.201], [-27.965, -8.224, -0.975]] - , [[-28.564, -7.642, 1.266], [-36.834, -14.582, 0.893], [-36.776, -14.534, -1.266], [-28.507, -7.594, -0.893]] - , [[-29.112, -7.014, 1.331], [-37.513, -13.657, 0.811], [-37.432, -13.593, -1.331], [-29.031, -6.95, -0.811]] - , [[-29.644, -6.369, 1.393], [-38.165, -12.713, 0.731], [-38.058, -12.634, -1.393], [-29.538, -6.29, -0.731]] - , [[-30.158, -5.709, 1.455], [-38.787, -11.75, 0.652], [-38.655, -11.658, -1.455], [-30.027, -5.616, -0.652]] - , [[-30.655, -5.032, 1.515], [-39.379, -10.77, 0.573], [-39.221, -10.666, -1.515], [-30.497, -4.928, -0.573]] - , [[-31.132, -4.34, 1.574], [-39.941, -9.773, 0.496], [-39.757, -9.66, -1.574], [-30.949, -4.227, -0.496]] - , [[-31.591, -3.633, 1.631], [-40.472, -8.761, 0.42], [-40.262, -8.639, -1.631], [-31.382, -3.512, -0.42]] - , [[-32.031, -2.912, 1.687], [-40.972, -7.733, 0.344], [-40.736, -7.606, -1.687], [-31.795, -2.785, -0.344]] - , [[-32.451, -2.178, 1.742], [-41.441, -6.693, 0.27], [-41.178, -6.56, -1.742], [-32.188, -2.045, -0.27]] - , [[-32.851, -1.43, 1.795], [-41.878, -5.639, 0.197], [-41.588, -5.504, -1.795], [-32.561, -1.294, -0.197]] - , [[-33.229, -0.669, 1.847], [-42.283, -4.574, 0.125], [-41.966, -4.437, -1.847], [-32.913, -0.532, -0.125]] - , [[-33.587, 0.104, 1.898], [-42.655, -3.498, 0.053], [-42.312, -3.362, -1.898], [-33.244, 0.241, -0.053]] - , [[-33.924, 0.889, 1.947], [-42.994, -2.412, -0.016], [-42.625, -2.278, -1.947], [-33.555, 1.023, 0.016]] - , [[-34.238, 1.685, 1.995], [-43.3, -1.318, -0.085], [-42.905, -1.187, -1.995], [-33.843, 1.816, 0.085]] - , [[-34.53, 2.491, 2.041], [-43.573, -0.216, -0.153], [-43.153, -0.091, -2.041], [-34.11, 2.617, 0.153]] - , [[-34.799, 3.307, 2.086], [-43.813, 0.892, -0.219], [-43.368, 1.011, -2.086], [-34.354, 3.426, 0.219]] - , [[-35.046, 4.132, 2.129], [-44.019, 2.006, -0.285], [-43.55, 2.117, -2.129], [-34.576, 4.244, 0.285]] - , [[-35.269, 4.966, 2.171], [-44.192, 3.124, -0.349], [-43.698, 3.226, -2.171], [-34.775, 5.068, 0.349]] - , [[-35.468, 5.808, 2.212], [-44.331, 4.245, -0.412], [-43.814, 4.336, -2.212], [-34.951, 5.899, 0.412]] - , [[-35.643, 6.657, 2.251], [-44.436, 5.369, -0.474], [-43.897, 5.448, -2.251], [-35.104, 6.736, 0.474]] - , [[-35.794, 7.513, 2.289], [-44.508, 6.495, -0.535], [-43.947, 6.56, -2.289], [-35.234, 7.579, 0.535]] - , [[-35.921, 8.375, 2.325], [-44.546, 7.62, -0.594], [-43.964, 7.671, -2.325], [-35.339, 8.426, 0.594]] - , [[-36.023, 9.242, 2.36], [-44.55, 8.745, -0.652], [-43.948, 8.78, -2.36], [-35.421, 9.277, 0.652]] - , [[-36.1, 10.113, 2.394], [-44.521, 9.868, -0.709], [-43.9, 9.887, -2.394], [-35.479, 10.132, 0.709]] - , [[-36.166, 10, 2.426], [-44.473, 10, -0.765], [-43.834, 10, -2.426], [-35.527, 10, 0.765]] - , [[-36.225, 10.925, 2.457], [-44.412, 11.073, -0.819], [-43.757, 11.061, -2.457], [-35.57, 10.913, 0.819]] - , [[-36.268, 11.852, 2.486], [-44.332, 12.143, -0.872], [-43.66, 12.119, -2.486], [-35.597, 11.828, 0.872]] - , [[-36.294, 12.781, 2.514], [-44.231, 13.211, -0.924], [-43.545, 13.174, -2.514], [-35.607, 12.744, 0.924]] - , [[-36.303, 13.712, 2.541], [-44.111, 14.276, -0.975], [-43.41, 14.226, -2.541], [-35.602, 13.661, 0.975]] - , [[-36.296, 14.643, 2.566], [-43.971, 15.338, -1.024], [-43.256, 15.273, -2.566], [-35.581, 14.579, 1.024]] - , [[-36.271, 15.576, 2.59], [-43.812, 16.396, -1.073], [-43.084, 16.317, -2.59], [-35.543, 15.497, 1.073]] - , [[-36.23, 16.509, 2.612], [-43.633, 17.45, -1.119], [-42.893, 17.356, -2.612], [-35.49, 16.415, 1.119]] - , [[-36.171, 17.443, 2.633], [-43.435, 18.5, -1.165], [-42.683, 18.39, -2.633], [-35.42, 17.334, 1.165]] - , [[-36.096, 18.377, 2.652], [-43.217, 19.544, -1.209], [-42.455, 19.419, -2.652], [-35.333, 18.252, 1.209]] - , [[-36.003, 19.31, 2.671], [-42.981, 20.584, -1.252], [-42.209, 20.443, -2.671], [-35.231, 19.169, 1.252]] - , [[-35.893, 20.243, 2.688], [-42.725, 21.618, -1.294], [-41.945, 21.461, -2.688], [-35.112, 20.086, 1.294]] - , [[-35.766, 21.174, 2.703], [-42.451, 22.646, -1.334], [-41.663, 22.472, -2.703], [-34.977, 21.001, 1.334]] - , [[-35.621, 22.105, 2.717], [-42.158, 23.668, -1.373], [-41.363, 23.478, -2.717], [-34.826, 21.915, 1.373]] - , [[-35.46, 23.034, 2.73], [-41.847, 24.683, -1.411], [-41.045, 24.476, -2.73], [-34.658, 22.826, 1.411]] - , [[-35.281, 23.96, 2.741], [-41.517, 25.692, -1.447], [-40.71, 25.468, -2.741], [-34.473, 23.736, 1.447]] - , [[-35.084, 24.885, 2.752], [-41.169, 26.693, -1.482], [-40.358, 26.452, -2.752], [-34.273, 24.644, 1.482]] - , [[-34.871, 25.807, 2.76], [-40.803, 27.687, -1.516], [-39.988, 27.429, -2.76], [-34.056, 25.548, 1.516]] - , [[-34.64, 26.726, 2.768], [-40.42, 28.673, -1.548], [-39.602, 28.397, -2.768], [-33.822, 26.45, 1.548]] - , [[-34.392, 27.641, 2.774], [-40.018, 29.651, -1.579], [-39.199, 29.358, -2.774], [-33.572, 27.349, 1.579]] - , [[-34.127, 28.553, 2.779], [-39.6, 30.62, -1.609], [-38.779, 30.31, -2.779], [-33.306, 28.243, 1.609]] - , [[-33.845, 29.461, 2.783], [-39.164, 31.581, -1.637], [-38.343, 31.254, -2.783], [-33.023, 29.134, 1.637]] - , [[-33.545, 30.365, 2.785], [-38.711, 32.532, -1.665], [-37.891, 32.188, -2.785], [-32.725, 30.021, 1.665]] - , [[-33.229, 31.264, 2.786], [-38.242, 33.475, -1.69], [-37.422, 33.113, -2.786], [-32.409, 30.903, 1.69]] - , [[-32.895, 32.159, 2.786], [-37.755, 34.407, -1.715], [-36.938, 34.029, -2.786], [-32.078, 31.781, 1.715]] - , [[-32.544, 33.047, 2.785], [-37.253, 35.33, -1.738], [-36.439, 34.935, -2.785], [-31.73, 32.653, 1.738]] - , [[-32.177, 33.931, 2.782], [-36.734, 36.242, -1.76], [-35.924, 35.831, -2.782], [-31.367, 33.52, 1.76]] - , [[-31.792, 34.808, 2.778], [-36.2, 37.144, -1.781], [-35.394, 36.717, -2.778], [-30.987, 34.381, 1.781]] - , [[-31.391, 35.679, 2.773], [-35.649, 38.036, -1.8], [-34.849, 37.593, -2.773], [-30.591, 35.236, 1.8]] - , [[-30.973, 36.543, 2.767], [-35.084, 38.916, -1.818], [-34.29, 38.457, -2.767], [-30.179, 36.084, 1.818]] - , [[-30.539, 37.4, 2.76], [-34.503, 39.785, -1.835], [-33.715, 39.311, -2.76], [-29.752, 36.926, 1.835]] - , [[-30.088, 38.25, 2.751], [-33.907, 40.642, -1.85], [-33.127, 40.154, -2.751], [-29.308, 37.761, 1.85]] - , [[-29.621, 39.092, 2.742], [-33.296, 41.488, -1.864], [-32.525, 40.985, -2.742], [-28.849, 38.589, 1.864]] - , [[-29.137, 39.926, 2.731], [-32.671, 42.322, -1.877], [-31.909, 41.805, -2.731], [-28.374, 39.409, 1.877]] - , [[-28.638, 40.752, 2.719], [-32.032, 43.144, -1.889], [-31.279, 42.613, -2.719], [-27.884, 40.221, 1.889]] - , [[-28.122, 41.569, 2.706], [-31.379, 43.953, -1.899], [-30.636, 43.409, -2.706], [-27.379, 41.025, 1.899]] - , [[-27.591, 42.377, 2.692], [-30.712, 44.749, -1.908], [-29.979, 44.193, -2.692], [-26.858, 41.82, 1.908]] - , [[-27.044, 43.175, 2.677], [-30.031, 45.533, -1.916], [-29.31, 44.964, -2.677], [-26.323, 42.606, 1.916]] - , [[-26.481, 43.964, 2.661], [-29.338, 46.304, -1.922], [-28.629, 45.723, -2.661], [-25.772, 43.384, 1.922]] - , [[-25.903, 44.744, 2.644], [-28.631, 47.061, -1.928], [-27.935, 46.469, -2.644], [-25.206, 44.152, 1.928]] - , [[-25.31, 45.512, 2.626], [-27.912, 47.805, -1.932], [-27.228, 47.202, -2.626], [-24.626, 44.91, 1.932]] - , [[-24.702, 46.27, 2.606], [-27.181, 48.535, -1.935], [-26.51, 47.922, -2.606], [-24.031, 45.658, 1.935]] - , [[-24.079, 47.018, 2.586], [-26.437, 49.251, -1.937], [-25.78, 48.629, -2.586], [-23.422, 46.396, 1.937]] - , [[-23.442, 47.754, 2.565], [-25.682, 49.954, -1.937], [-25.039, 49.323, -2.565], [-22.799, 47.123, 1.937]] - , [[-22.79, 48.478, 2.543], [-24.915, 50.642, -1.937], [-24.287, 50.003, -2.543], [-22.162, 47.839, 1.937]] - , [[-22.123, 49.191, 2.52], [-24.136, 51.316, -1.935], [-23.523, 50.669, -2.52], [-21.511, 48.544, 1.935]] - , [[-21.443, 49.891, 2.496], [-23.347, 51.975, -1.932], [-22.75, 51.321, -2.496], [-20.846, 49.237, 1.932]] - , [[-20.749, 50.579, 2.472], [-22.547, 52.619, -1.928], [-21.965, 51.959, -2.472], [-20.168, 49.919, 1.928]] - , [[-20.042, 51.255, 2.446], [-21.736, 53.249, -1.923], [-21.171, 52.583, -2.446], [-19.476, 50.589, 1.923]] - , [[-19.321, 51.917, 2.42], [-20.915, 53.864, -1.916], [-20.366, 53.193, -2.42], [-18.772, 51.246, 1.916]] - , [[-18.587, 52.566, 2.392], [-20.085, 54.464, -1.909], [-19.552, 53.788, -2.392], [-18.054, 51.89, 1.909]] - , [[-17.841, 53.201, 2.364], [-19.245, 55.048, -1.9], [-18.728, 54.369, -2.364], [-17.325, 52.522, 1.9]] - , [[-17.082, 53.823, 2.335], [-18.395, 55.617, -1.891], [-17.896, 54.935, -2.335], [-16.582, 53.141, 1.891]] - , [[-16.31, 54.43, 2.306], [-17.536, 56.171, -1.88], [-17.054, 55.486, -2.306], [-15.828, 53.746, 1.88]] - , [[-15.527, 55.023, 2.275], [-16.669, 56.708, -1.868], [-16.204, 56.023, -2.275], [-15.061, 54.337, 1.868]] - , [[-14.731, 55.602, 2.244], [-15.793, 57.231, -1.855], [-15.345, 56.544, -2.244], [-14.283, 54.915, 1.855]] - , [[-13.925, 56.165, 2.213], [-14.909, 57.737, -1.842], [-14.479, 57.05, -2.213], [-13.494, 55.478, 1.842]] - , [[-13.107, 56.714, 2.18], [-14.017, 58.227, -1.827], [-13.604, 57.541, -2.18], [-12.694, 56.027, 1.827]] - , [[-12.278, 57.247, 2.147], [-13.118, 58.701, -1.811], [-12.722, 58.016, -2.147], [-11.882, 56.561, 1.811]] - , [[-11.439, 57.764, 2.113], [-12.211, 59.16, -1.794], [-11.833, 58.476, -2.113], [-11.06, 57.081, 1.794]] - , [[-10.589, 58.266, 2.079], [-11.297, 59.602, -1.776], [-10.936, 58.92, -2.079], [-10.228, 57.585, 1.776]] - , [[-9.729, 58.752, 2.044], [-10.376, 60.027, -1.758], [-10.032, 59.349, -2.044], [-9.385, 58.074, 1.758]] - , [[-8.86, 59.221, 2.008], [-9.449, 60.436, -1.738], [-9.122, 59.762, -2.008], [-8.533, 58.547, 1.738]] - , [[-7.982, 59.674, 1.972], [-8.516, 60.829, -1.718], [-8.206, 60.159, -1.972], [-7.672, 59.004, 1.718]] - , [[-7.094, 60.11, 1.936], [-7.577, 61.205, -1.696], [-7.284, 60.541, -1.936], [-6.801, 59.446, 1.696]] - , [[-6.198, 60.53, 1.898], [-6.632, 61.565, -1.674], [-6.356, 60.906, -1.898], [-5.921, 59.871, 1.674]] - , [[-5.293, 60.932, 1.861], [-5.682, 61.908, -1.651], [-5.422, 61.255, -1.861], [-5.033, 60.28, 1.651]] - , [[-4.381, 61.317, 1.823], [-4.727, 62.234, -1.627], [-4.483, 61.589, -1.823], [-4.137, 60.672, 1.627]] - , [[-3.46, 61.685, 1.784], [-3.767, 62.543, -1.602], [-3.539, 61.906, -1.784], [-3.233, 61.047, 1.602]] - , [[-2.533, 62.035, 1.745], [-2.803, 62.836, -1.576], [-2.59, 62.207, -1.745], [-2.321, 61.406, 1.576]] - , [[-1.598, 62.368, 1.706], [-1.834, 63.112, -1.55], [-1.637, 62.491, -1.706], [-1.401, 61.747, 1.55]] - , [[-0.657, 62.683, 1.666], [-0.862, 63.371, -1.523], [-0.68, 62.759, -1.666], [-0.475, 62.071, 1.523]] - , [[0.29, 62.979, 1.626], [0.115, 63.613, -1.495], [0.282, 63.011, -1.626], [0.457, 62.378, 1.495]] - , [[1.244, 63.258, 1.586], [1.094, 63.838, -1.466], [1.247, 63.247, -1.586], [1.396, 62.667, 1.466]] - , [[2.203, 63.518, 1.545], [2.076, 64.046, -1.437], [2.215, 63.466, -1.545], [2.341, 62.938, 1.437]] - , [[3.166, 63.76, 1.504], [3.062, 64.237, -1.407], [3.187, 63.668, -1.504], [3.292, 63.192, 1.407]] - , [[4.135, 63.984, 1.463], [4.049, 64.411, -1.376], [4.161, 63.854, -1.463], [4.247, 63.427, 1.376]] - , [[5.108, 64.189, 1.422], [5.039, 64.568, -1.345], [5.139, 64.023, -1.422], [5.208, 63.644, 1.345]] - , [[6.086, 64.375, 1.38], [6.031, 64.708, -1.313], [6.118, 64.176, -1.38], [6.173, 63.843, 1.313]] - , [[7.067, 64.542, 1.338], [7.025, 64.83, -1.28], [7.1, 64.312, -1.338], [7.142, 64.024, 1.28]] - , [[8.051, 64.691, 1.296], [8.02, 64.936, -1.247], [8.084, 64.432, -1.296], [8.115, 64.186, 1.247]] - , [[9.038, 64.821, 1.254], [9.016, 65.025, -1.213], [9.069, 64.534, -1.254], [9.091, 64.33, 1.213]] - , [[10.027, 64.932, 1.212], [10.013, 65.097, -1.179], [10.056, 64.62, -1.212], [10.071, 64.455, 1.179]] - , [[11.019, 65.023, 1.17], [11.01, 65.151, -1.144], [11.043, 64.69, -1.17], [11.053, 64.562, 1.144]] - , [[12.013, 65.096, 1.127], [12.008, 65.189, -1.109], [12.032, 64.742, -1.127], [12.037, 64.65, 1.109]] - , [[13.008, 65.15, 1.085], [13.005, 65.21, -1.073], [13.021, 64.778, -1.085], [13.023, 64.719, 1.073]] - , [[14.004, 65.185, 1.042], [14.003, 65.213, -1.037], [14.011, 64.798, -1.042], [14.011, 64.769, 1.037]] - , [[15, 65.2, 1], [15, 65.2, -1], [15, 64.8, -1], [15, 64.8, 1]] - ]; + expected = [[[0, 0, -10], [0, 0, 10], [0, 4, 10], [0, 4, -10]], [[-0.0496427, -0.119848, -9.93183], [0.0558577, 0.134853, 9.98697], [1.58038, 3.81537, 9.93183], [1.47488, 3.56067, -9.98697]], [[-0.182394, -0.182394, -9.86199], [0.205896, 0.205896, 9.97182], [3.01082, 3.01082, 9.86199], [2.62253, 2.62253, -9.97182]], [[-0.355362, -0.147196, -9.79052], [0.402464, 0.166706, 9.95457], [4.05088, 1.67793, 9.79052], [3.29305, 1.36403, -9.95457]], [[-0.509794, 0, -9.71743], [0.57926, 0, 9.93524], [4.50979, 0, 9.71743], [3.42074, 0, -9.93524]], [[-0.651326, -0.113291, -9.64276], [0.637777, -0.532146, 9.91385], [4.35767, -1.74081, 9.64276], [3.06856, -1.32196, -9.91385]], [[-0.802105, -0.143779, -9.56654], [0.508005, -1.09563, 9.89042], [3.65621, -3.38293, 9.56654], [2.3461, -2.43108, -9.89042]], [[-0.926991, -0.100488, -9.4888], [0.178532, -1.62211, 9.86496], [2.4537, -4.75361, 9.4888], [1.34818, -3.23199, -9.86496]], [[-0.998322, -0.0051646, -9.40956], [-0.33711, -2.04017, 9.83751], [0.852424, -5.70117, 9.40956], [0.191212, -3.66617, -9.83751]], [[-1, 0.11171, -9.32886], [-1, -2.28432, 9.80807], [-1, -6.11171, 9.32886], [-1, -3.71568, -9.80807]], [[-1.34586, 0.261256, -9.24673], [-1.86279, -2.33753, 9.77667], [-2.60505, -6.06911, 9.24673], [-2.08811, -3.47032, -9.77667]], [[-1.63487, 0.467284, -9.1632], [-2.74492, -2.21261, 9.74333], [-4.19196, -5.70608, 9.1632], [-3.08192, -3.02619, -9.74333]], [[-1.8594, 0.713813, -9.07829], [-3.60887, -1.90445, 9.70808], [-5.6963, -5.02851, 9.07829], [-3.94683, -2.41025, -9.70808]], [[-2.01574, 0.984259, -8.99204], [-4.41598, -1.41598, 9.67094], [-7.05533, -4.05533, 8.99204], [-4.65508, -1.65508, -9.67094]], [[-2.10402, 1.26232, -8.90449], [-5.12819, -0.758368, 9.63192], [-8.21068, -2.81802, 8.90449], [-5.18651, -0.797335, -9.63192]], [[-2.12791, 1.5328, -8.81565], [-5.70977, 0.049149, 9.59105], [-9.11089, -1.35964, 8.81565], [-5.52902, 0.124017, -9.59105]], [[-2.09421, 1.78235, -8.72557], [-6.12909, 0.979761, 9.54836], [-9.71365, 0.266748, 8.72557], [-5.67877, 1.06934, -9.54836]], [[-2.01222, 2, -8.63427], [-6.36016, 2, 9.50386], [-9.98778, 2, 8.63427], [-5.63984, 2, -9.50386]], [[-1.91057, 2, -8.54179], [-6.48956, 2, 9.45759], [-10.0894, 2, 8.54179], [-5.51044, 2, -9.45759]], [[-1.78292, 2.45933, -8.44815], [-6.55492, 3.03875, 9.40956], [-10.1004, 3.46926, 8.44815], [-5.32843, 2.88983, -9.40956]], [[-1.60477, 2.8885, -8.3534], [-6.4906, 4.09274, 9.3598], [-9.9303, 4.94055, 8.3534], [-5.04447, 3.73631, -9.3598]], [[-1.38141, 3.2824, -8.25755], [-6.29397, 5.14549, 9.30835], [-9.57885, 6.39128, 8.25755], [-4.66629, 4.52819, -9.30835]], [[-1.11859, 3.63676, -8.16065], [-5.96451, 6.1801, 9.25521], [-9.04871, 7.79881, 8.16065], [-4.20278, 5.25547, -9.25521]], [[-0.822378, 3.94815, -8.06272], [-5.50391, 7.17957, 9.20042], [-8.34536, 9.14089, 8.06272], [-3.66383, 5.90946, -9.20042]], [[-0.499073, 4.21399, -7.9638], [-4.91603, 8.12706, 9.144], [-7.4771, 10.396, 7.9638], [-3.06015, 6.4829, -9.144]], [[-0.155059, 4.43256, -7.86392], [-4.20693, 9.00618, 9.08598], [-6.4549, 11.5436, 7.86392], [-2.40303, 6.97, -9.08598]], [[0.203284, 4.60299, -7.76311], [-3.38482, 9.80125, 9.02638], [-5.29232, 12.5647, 7.76311], [-1.70422, 7.36649, -9.02638]], [[0.569696, 4.72522, -7.66141], [-2.45991, 10.4976, 8.96524], [-4.00527, 13.4421, 7.66141], [-0.975662, 7.66965, -8.96524]], [[0.938127, 4.79993, -7.55885], [-1.44435, 11.082, 8.90258], [-2.61181, 14.1603, 7.55885], [-0.229333, 7.87827, -8.90258]], [[1.30283, 4.82853, -7.45545], [-0.352005, 11.5425, 8.83842], [-1.13188, 14.7065, 7.45545], [0.522954, 7.99261, -8.83842]], [[1.65843, 4.81308, -7.35126], [0.801691, 11.869, 8.7728], [0.412983, 15.0703, 7.35126], [1.26972, 8.01438, -8.7728]], [[2, 4.7562, -7.2463], [2, 12.0534, 8.70574], [2, 15.2438, 7.2463], [2, 7.94661, -8.70574]], [[2.97149, 4.64423, -7.14061], [2.97149, 12.1275, 8.63727], [2.97149, 15.2831, 7.14061], [2.97149, 7.7998, -8.63727]], [[3.53452, 4.47675, -7.03423], [4.1074, 12.1212, 8.56741], [4.34058, 15.2329, 7.03423], [3.7677, 7.58835, -8.56741]], [[4.07827, 4.27018, -6.92717], [5.24753, 12.0277, 8.49621], [5.70728, 15.0779, 6.92717], [4.53802, 7.3204, -8.49621]], [[4.60021, 4.02643, -6.81949], [6.38504, 11.8463, 8.42367], [7.06342, 14.8185, 6.81949], [5.2786, 6.99863, -8.42367]], [[5.098, 3.74755, -6.7112], [7.513, 11.5768, 8.34984], [8.40086, 14.4552, 6.7112], [5.98587, 6.62594, -8.34984]], [[5.56947, 3.43573, -6.60234], [8.62446, 11.2197, 8.27474], [9.7115, 13.9895, 6.60234], [6.65651, 6.20547, -8.27474]], [[6.01264, 3.09327, -6.49295], [9.71249, 10.7761, 8.19841], [10.9874, 13.4234, 6.49295], [7.28751, 5.74056, -8.19841]], [[6.4257, 2.72256, -6.38305], [10.7702, 10.2475, 8.12086], [12.2206, 12.7596, 6.38305], [7.87609, 5.23471, -8.12086]], [[6.80707, 2.32609, -6.27269], [11.7909, 9.63603, 8.04214], [13.4037, 12.0015, 6.27269], [8.41983, 4.69158, -8.04214]], [[7.15533, 1.90642, -6.16188], [12.7679, 8.94439, 7.96226], [14.5292, 11.1529, 6.16188], [8.91658, 4.11496, -7.96226]], [[7.46927, 1.46617, -6.05068], [13.6949, 8.17576, 7.88127], [15.5901, 10.2183, 6.05068], [9.36449, 3.50873, -7.88127]], [[7.74787, 1.00798, -5.93909], [14.5656, 7.33388, 7.79918], [16.5797, 9.20276, 5.93909], [9.76205, 2.87686, -7.79918]], [[7.99032, 0.534539, -5.82717], [15.3742, 6.42297, 7.71604], [17.4919, 8.11178, 5.82717], [10.108, 2.22335, -7.71604]], [[8.19599, 0.048554, -5.71494], [16.1151, 5.44774, 7.63186], [18.3207, 6.95145, 5.71494], [10.4015, 1.55226, -7.63186]], [[8.36443, -0.447276, -5.60244], [16.7833, 4.41334, 7.54668], [19.0608, 5.72825, 5.60244], [10.6419, 0.867636, -7.54668]], [[8.49539, -0.950257, -5.48969], [17.3738, 3.32535, 7.46054], [19.7073, 4.44912, 5.48969], [10.8289, 0.173521, -7.46054]], [[8.58881, -1.45772, -5.37672], [17.8823, 2.18972, 7.37345], [20.2561, 3.12135, 5.37672], [10.9626, -0.526085, -7.37345]], [[8.64478, -1.96702, -5.26358], [18.305, 1.01278, 7.28546], [20.7033, 1.75256, 5.26358], [11.0431, -1.22724, -7.28546]], [[8.66358, -2.47556, -5.15029], [18.6386, -0.198832, 7.19659], [21.046, 0.350655, 5.15029], [11.071, -1.92607, -7.19659]], [[8.64566, -2.98079, -5.03688], [18.88, -1.43821, 7.10687], [21.2816, -1.07622, 5.03688], [11.0473, -2.61881, -7.10687]], [[8.59162, -3.48024, -4.92338], [19.0271, -2.69821, 7.01633], [21.4084, -2.51976, 4.92338], [10.9729, -3.30179, -7.01633]], [[8.51477, -3.99922, -4.80983], [19.0907, -3.99922, 6.92501], [21.4377, -3.99922, 4.80983], [10.8617, -3.99922, -6.92501]], [[8.41765, -4.68715, -4.69626], [19.0889, -5.19549, 6.83294], [21.3922, -5.3052, 4.69626], [10.7209, -4.79687, -6.83294]], [[8.2899, -5.36829, -4.58269], [19.0283, -6.39368, 6.74014], [21.2826, -6.60894, 4.58269], [10.5442, -5.58355, -6.74014]], [[8.13194, -6.04136, -4.46916], [18.9085, -7.5908, 6.64665], [21.1091, -7.90719, 4.46916], [10.3325, -6.35775, -6.64665]], [[7.94421, -6.70514, -4.35571], [18.7297, -8.78386, 6.55249], [20.8719, -9.19674, 4.35571], [10.0864, -7.11801, -6.55249]], [[7.72722, -7.35839, -4.24235], [18.4918, -9.96985, 6.45771], [20.5715, -10.4744, 4.24235], [9.8069, -7.86292, -6.45771]], [[7.4815, -7.99993, -4.12911], [18.1952, -11.1458, 6.36232], [20.2085, -11.7369, 4.12911], [9.49479, -8.59109, -6.36232]], [[7.20763, -8.62858, -4.01604], [17.8404, -12.3086, 6.26637], [19.7838, -12.9812, 4.01604], [9.15101, -9.30119, -6.26637]], [[6.90625, -9.2432, -3.90316], [17.428, -13.4555, 6.16988], [19.2983, -14.2042, 3.90316], [8.77655, -9.99196, -6.16988]], [[6.57802, -9.84268, -3.79049], [16.9587, -14.5834, 6.07288], [18.7531, -15.4028, 3.79049], [8.37243, -10.6622, -6.07288]], [[6.22364, -10.4259, -3.67808], [16.4334, -15.6894, 5.9754], [18.1494, -16.5741, 3.67808], [7.93971, -11.3106, -5.9754]], [[5.84386, -10.9919, -3.56594], [15.8531, -16.7707, 5.87748], [17.4888, -17.7151, 3.56594], [7.47951, 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[-8.63422, -18.2205, -3.47235]], [[-9.37774, -17.2616, -0.931863], [-10.4415, -29.4209, 3.37303], [-10.5166, -30.2786, 0.931863], [-9.45277, -18.1193, -3.37303]], [[-10.1724, -17.1794, -0.836202], [-11.5875, -29.2861, 3.27402], [-11.6829, -30.1026, 0.836202], [-10.2679, -17.9959, -3.27402]], [[-10.9654, -17.0755, -0.741491], [-12.7291, -29.1163, 3.17536], [-12.8427, -29.8914, 0.741491], [-11.0789, -17.8506, -3.17536]], [[-11.7561, -16.9497, -0.64775], [-13.8653, -28.9118, 3.07706], [-13.9947, -29.6454, 0.64775], [-11.8855, -17.6834, -3.07706]], [[-12.544, -16.8022, -0.554998], [-14.995, -28.6726, 2.97916], [-15.1379, -29.3648, 0.554998], [-12.6869, -17.4944, -2.97916]], [[-13.3284, -16.6329, -0.463255], [-16.117, -28.3991, 2.88168], [-16.2713, -29.0501, 0.463255], [-13.4827, -17.2839, -2.88168]], [[-14.1088, -16.4419, -0.37254], [-17.2303, -28.0915, 2.78465], [-17.3938, -28.7014, 0.37254], [-14.2723, -17.0518, -2.78465]], [[-14.8847, -16.2292, -0.28287], [-18.3339, -27.7501, 2.68809], 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53.8228, 2.33536], [-18.3951, 55.617, -1.89062], [-17.8958, 54.9351, -2.33536], [-16.5822, 53.1408, 1.89062]], [[-16.31, 54.4302, 2.30574], [-17.5365, 56.1705, -1.87993], [-17.0542, 55.4863, -2.30574], [-15.8278, 53.7459, 1.87993]], [[-15.5265, 55.0233, 2.27538], [-16.6691, 56.7084, -1.86819], [-16.204, 56.0225, -2.27538], [-15.0615, 54.3374, 1.86819]], [[-14.7313, 55.6017, 2.24429], [-15.7933, 57.2306, -1.85541], [-15.3455, 56.5437, -2.24429], [-14.2835, 54.9149, 1.85541]], [[-13.9246, 56.1653, 2.21251], [-14.9093, 57.7369, -1.8416], [-14.4788, 57.0498, -2.21251], [-13.4941, 55.4782, 1.8416]], [[-13.1067, 56.7138, 2.18004], [-14.0173, 58.2272, -1.82679], [-13.6042, 57.5405, -2.18004], [-12.6936, 56.0271, 1.82679]], [[-12.278, 57.2468, 2.14691], [-13.1178, 58.7015, -1.81098], [-12.722, 58.016, -2.14691], [-11.8822, 56.5613, 1.81098]], [[-11.4386, 57.7643, 2.11315], [-12.211, 59.1596, -1.7942], [-11.8325, 58.4759, -2.11315], [-11.0602, 57.0806, 1.7942]], [[-10.589, 58.266, 2.07877], [-11.2971, 59.6015, -1.77645], [-10.9359, 58.9203, -2.07877], [-10.2279, 57.5848, 1.77645]], [[-9.72944, 58.7517, 2.04379], [-10.3764, 60.0271, -1.75776], [-10.0325, 59.3491, -2.04379], [-9.38549, 58.0736, 1.75776]], [[-8.8602, 59.221, 2.00825], [-9.44932, 60.4363, -1.73814], [-9.12248, 59.7621, -2.00825], [-8.53336, 58.5468, 1.73814]], [[-7.98163, 59.674, 1.97215], [-8.51603, 60.8291, -1.71761], [-8.20617, 60.1593, -1.97215], [-7.67177, 59.0042, 1.71761]], [[-7.09405, 60.1103, 1.93552], [-7.57685, 61.2053, -1.69618], [-7.28381, 60.5406, -1.93552], [-6.80102, 59.4457, 1.69618]], [[-6.1978, 60.5297, 1.89839], [-6.63206, 61.5648, -1.67388], [-6.35567, 60.906, -1.89839], [-5.92141, 59.8709, 1.67388]], [[-5.2932, 60.9321, 1.86077], [-5.68195, 61.9078, -1.65072], [-5.422, 61.2554, -1.86077], [-5.03325, 60.2797, 1.65072]], [[-4.38059, 61.3173, 1.8227], [-4.7268, 62.234, -1.62671], [-4.48306, 61.5886, -1.8227], [-4.13685, 60.6719, 1.62671]], [[-3.46032, 61.6851, 1.78419], [-3.76691, 62.5434, -1.60189], [-3.53912, 61.9057, -1.78419], [-3.23253, 61.0473, 1.60189]], [[-2.53274, 62.0353, 1.74526], [-2.80254, 62.8361, -1.57626], [-2.59043, 62.2065, -1.74526], [-2.32063, 61.4058, 1.57626]], [[-1.59819, 62.3679, 1.70594], [-1.834, 63.1118, -1.54985], [-1.63726, 62.4911, -1.70594], [-1.40145, 61.7471, 1.54985]], [[-0.657032, 62.6826, 1.66625], [-0.861549, 63.3707, -1.52267], [-0.679857, 62.7594, -1.66625], [-0.47534, 62.0712, 1.52267]], [[0.290379, 62.9793, 1.62621], [0.114516, 63.6127, -1.49474], [0.281504, 63.0112, -1.62621], [0.457367, 62.3778, 1.49474]], [[1.24368, 63.2579, 1.58585], [1.09392, 63.8377, -1.46608], [1.24657, 63.2467, -1.58585], [1.39633, 62.6669, 1.46608]], [[2.20251, 63.5182, 1.54519], [2.07637, 64.0457, -1.43672], [2.21507, 63.4656, -1.54519], [2.34121, 62.9382, 1.43672]], [[3.16649, 63.7602, 1.50426], [3.0616, 64.2367, -1.40667], [3.18676, 63.6681, -1.50426], [3.29165, 63.1916, 1.40667]], [[4.13527, 63.9837, 1.46307], [4.04933, 64.4107, -1.37596], [4.16136, 63.854, -1.46307], [4.2473, 63.427, 1.37596]], [[5.10846, 64.1886, 1.42165], [5.03927, 64.5676, -1.34459], [5.13862, 64.0234, -1.42165], [5.20781, 63.6443, 1.34459]], [[6.0857, 64.3748, 1.38003], [6.03116, 64.7075, -1.3126], [6.11828, 64.1761, -1.38003], [6.17282, 63.8434, 1.3126]], [[7.0666, 64.5423, 1.33822], [7.0247, 64.8304, -1.28001], [7.10008, 64.3122, -1.33822], [7.14197, 64.0241, 1.28001]], [[8.05079, 64.691, 1.29626], [8.01963, 64.9362, -1.24683], [8.08375, 64.4316, -1.29626], [8.1149, 64.1865, 1.24683]], [[9.03788, 64.8208, 1.25415], [9.01568, 65.0249, -1.21309], [9.06903, 64.5344, -1.25415], [9.09123, 64.3302, 1.21309]], [[10.0275, 64.9316, 1.21194], [10.0126, 65.0966, -1.1788], [10.0557, 64.6204, -1.21194], [10.0706, 64.4554, 1.1788]], [[11.0193, 65.0234, 1.16964], [11.01, 65.1513, -1.14399], [11.0434, 64.6898, -1.16964], [11.0526, 64.5619, 1.14399]], [[12.0128, 65.0962, 1.12727], [12.0077, 65.189, -1.10869], [12.032, 64.7424, -1.12727], [12.037, 64.6497, 1.10869]], [[13.0077, 65.1499, 1.08486], [13.0055, 65.2096, -1.07291], [13.0211, 64.7784, -1.08486], [13.0232, 64.7187, 1.07291]], [[14.0035, 65.1845, 1.04243], [14.003, 65.2133, -1.03667], [14.0105, 64.7975, -1.04243], [14.011, 64.7688, 1.03667]], [[15, 65.2, 1], [15, 65.2, -1], [15, 64.8, -1], [15, 64.8, 1]]]; for(i = [0:len(expected) - 1]) { - assertEqualPoints(expected[i], sections[i], float_digits = 3); + assertEqualPoints(expected[i], sections[i]); } } @@ -276,229 +47,10 @@ module test_golden_spiral_extrude_hollow() { include ; module test_golden_spiral_extrude(sections) { - expected = [ - [[8, 0, 0], [7.598, 0, 1.5], [6.5, 0, 2.598], [5, 0, 3], [3.5, 0, 2.598], [2.402, 0, 1.5], [2, 0, 0], [2.402, 0, -1.5], [3.5, 0, -2.598], [5, 0, -3], [6.5, 0, -2.598], [7.598, 0, -1.5], [7, 0, 0], [6.732, 0, 1], [6, 0, 1.732], [5, 0, 2], [4, 0, 1.732], [3.268, 0, 1], [3, 0, 0], [3.268, 0, -1], [4, 0, -1.732], [5, 0, -2], [6, 0, -1.732], [6.732, 0, -1]] - , [[7.968, 1.585, 0], [7.558, 1.503, 1.562], [6.436, 1.28, 2.706], [4.904, 0.975, 3.124], [3.372, 0.671, 2.706], [2.25, 0.448, 1.562], [1.84, 0.366, 0], [2.25, 0.448, -1.562], [3.372, 0.671, -2.706], [4.904, 0.975, -3.124], [6.436, 1.28, -2.706], [7.558, 1.503, -1.562], [6.947, 1.382, 0], [6.673, 1.327, 1.041], [5.925, 1.179, 1.804], [4.904, 0.975, 2.083], [3.882, 0.772, 1.804], [3.135, 0.624, 1.041], [2.861, 0.569, 0], [3.135, 0.624, -1.041], [3.882, 0.772, -1.804], [4.904, 0.975, -2.083], [5.925, 1.179, -1.804], [6.673, 1.327, -1.041]] - , [[7.621, 3.157, 0], [7.219, 2.99, 1.624], [6.12, 2.535, 2.814], [4.619, 1.913, 3.249], [3.119, 1.292, 2.814], [2.02, 0.837, 1.624], [1.618, 0.67, 0], [2.02, 0.837, -1.624], [3.119, 1.292, -2.814], [4.619, 1.913, -3.249], [6.12, 2.535, -2.814], [7.219, 2.99, -1.624], [6.62, 2.742, 0], [6.352, 2.631, 1.083], [5.62, 2.328, 1.876], [4.619, 1.913, 2.166], [3.619, 1.499, 1.876], [2.886, 1.196, 1.083], [2.618, 1.085, 0], [2.886, 1.196, -1.083], [3.619, 1.499, -1.876], [4.619, 1.913, -2.166], [5.62, 2.328, -1.876], [6.352, 2.631, -1.083]] - , [[6.962, 4.652, 0], [6.586, 4.401, 1.687], [5.56, 3.715, 2.921], [4.157, 2.778, 3.373], [2.755, 1.841, 2.921], [1.728, 1.155, 1.687], [1.353, 0.904, 0], [1.728, 1.155, -1.687], [2.755, 1.841, -2.921], [4.157, 2.778, -3.373], [5.56, 3.715, -2.921], [6.586, 4.401, -1.687], [6.027, 4.027, 0], [5.777, 3.86, 1.124], [5.092, 3.403, 1.948], [4.157, 2.778, 2.249], [3.222, 2.153, 1.948], [2.538, 1.696, 1.124], [2.287, 1.528, 0], [2.538, 1.696, -1.124], [3.222, 2.153, -1.948], [4.157, 2.778, -2.249], [5.092, 3.403, -1.948], [5.777, 3.86, -1.124]] - , [[6.009, 6.009, 0], [5.677, 5.677, 1.749], [4.772, 4.772, 3.029], [3.536, 3.536, 3.498], [2.299, 2.299, 3.029], [1.394, 1.394, 1.749], [1.062, 1.062, 0], [1.394, 1.394, -1.749], [2.299, 2.299, -3.029], [3.536, 3.536, -3.498], [4.772, 4.772, -3.029], [5.677, 5.677, -1.749], [5.184, 5.184, 0], [4.963, 4.963, 1.166], [4.36, 4.36, 2.019], [3.536, 3.536, 2.332], [2.711, 2.711, 2.019], [2.108, 2.108, 1.166], [1.887, 1.887, 0], [2.108, 2.108, -1.166], [2.711, 2.711, -2.019], [3.536, 3.536, -2.332], [4.36, 4.36, -2.019], [4.963, 4.963, -1.166]] - , [[4.79, 7.169, 0], [4.521, 6.766, 1.811], [3.784, 5.663, 3.137], [2.778, 4.157, 3.622], [1.772, 2.652, 3.137], [1.035, 1.549, 1.811], [0.766, 1.146, 0], [1.035, 1.549, -1.811], [1.772, 2.652, -3.137], [2.778, 4.157, -3.622], [3.784, 5.663, -3.137], [4.521, 6.766, -1.811], [4.119, 6.165, 0], [3.94, 5.896, 1.207], [3.449, 5.161, 2.091], [2.778, 4.157, 2.415], [2.107, 3.153, 2.091], [1.616, 2.419, 1.207], [1.436, 2.15, 0], [1.616, 2.419, -1.207], [2.107, 3.153, -2.091], [2.778, 4.157, -2.415], [3.449, 5.161, -2.091], [3.94, 5.896, -1.207]] - , [[3.347, 8.081, 0], [3.155, 7.617, 1.873], [2.63, 6.35, 3.245], [1.913, 4.619, 3.747], [1.197, 2.889, 3.245], [0.672, 1.622, 1.873], [0.48, 1.158, 0], [0.672, 1.622, -1.873], [1.197, 2.889, -3.245], [1.913, 4.619, -3.747], [2.63, 6.35, -3.245], [3.155, 7.617, -1.873], [2.869, 6.927, 0], [2.741, 6.618, 1.249], [2.391, 5.773, 2.163], [1.913, 4.619, 2.498], [1.436, 3.466, 2.163], [1.086, 2.621, 1.249], [0.958, 2.312, 0], [1.086, 2.621, -1.249], [1.436, 3.466, -2.163], [1.913, 4.619, -2.498], [2.391, 5.773, -2.163], [2.741, 6.618, -1.249]] - , [[1.731, 8.701, 0], [1.629, 8.192, 1.935], [1.353, 6.802, 3.352], [0.975, 4.904, 3.871], [0.598, 3.006, 3.352], [0.321, 1.616, 1.935], [0.22, 1.107, 0], [0.321, 1.616, -1.935], [0.598, 3.006, -3.352], [0.975, 4.904, -3.871], [1.353, 6.802, -3.352], [1.629, 8.192, -1.935], [1.479, 7.435, 0], [1.411, 7.096, 1.29], [1.227, 6.169, 2.235], [0.975, 4.904, 2.581], [0.724, 3.638, 2.235], [0.539, 2.712, 1.29], [0.472, 2.373, 0], [0.539, 2.712, -1.29], [0.724, 3.638, -2.235], [0.975, 4.904, -2.581], [1.227, 6.169, -2.235], [1.411, 7.096, -1.29]] - , [[0, 8.995, 0], [0, 8.46, 1.998], [0, 6.998, 3.46], [0, 5, 3.995], [0, 3.002, 3.46], [0, 1.54, 1.998], [0, 1.005, 0], [0, 1.54, -1.998], [0, 3.002, -3.46], [0, 5, -3.995], [0, 6.998, -3.46], [0, 8.46, -1.998], [0, 7.664, 0], [0, 7.307, 1.332], [0, 6.332, 2.307], [0, 5, 2.664], [0, 3.668, 2.307], [0, 2.693, 1.332], [0, 2.336, 0], [0, 2.693, -1.332], [0, 3.668, -2.307], [0, 5, -2.664], [0, 6.332, -2.307], [0, 7.307, -1.332]] - , [[-1.461, 9.031, 0], [-1.394, 8.484, 2.06], [-1.213, 6.987, 3.568], [-0.964, 4.942, 4.12], [-0.716, 2.897, 3.568], [-0.534, 1.4, 2.06], [-0.468, 0.852, 0], [-0.534, 1.4, -2.06], [-0.716, 2.897, -3.568], [-0.964, 4.942, -4.12], [-1.213, 6.987, -3.568], [-1.394, 8.484, -2.06], [-1.295, 7.668, 0], [-1.251, 7.303, 1.373], [-1.13, 6.305, 2.379], [-0.964, 4.942, 2.747], [-0.799, 3.578, 2.379], [-0.678, 2.58, 1.373], [-0.633, 2.215, 0], [-0.678, 2.58, -1.373], [-0.799, 3.578, -2.379], [-0.964, 4.942, -2.747], [-1.13, 6.305, -2.379], [-1.251, 7.303, -1.373]] - , [[-2.93, 8.888, 0], [-2.794, 8.336, 2.122], [-2.422, 6.828, 3.676], [-1.915, 4.768, 4.244], [-1.407, 2.707, 3.676], [-1.035, 1.199, 2.122], [-0.899, 0.647, 0], [-1.035, 1.199, -2.122], [-1.407, 2.707, -3.676], [-1.915, 4.768, -4.244], [-2.422, 6.828, -3.676], [-2.794, 8.336, -2.122], [-2.592, 7.515, 0], [-2.501, 7.147, 1.415], [-2.253, 6.141, 2.45], [-1.915, 4.768, 2.829], [-1.576, 3.394, 2.45], [-1.328, 2.388, 1.415], [-1.237, 2.02, 0], [-1.328, 2.388, -1.415], [-1.576, 3.394, -2.45], [-1.915, 4.768, -2.829], [-2.253, 6.141, -2.45], [-2.501, 7.147, -1.415]] - , [[-4.386, 8.565, 0], [-4.178, 8.018, 2.184], [-3.611, 6.523, 3.783], [-2.837, 4.48, 4.369], [-2.062, 2.438, 3.783], [-1.495, 0.943, 2.184], [-1.288, 0.395, 0], [-1.495, 0.943, -2.184], [-2.062, 2.438, -3.783], [-2.837, 4.48, -4.369], [-3.611, 6.523, -3.783], [-4.178, 8.018, -2.184], [-3.87, 7.203, 0], [-3.731, 6.838, 1.456], [-3.353, 5.842, 2.522], [-2.837, 4.48, 2.912], [-2.32, 3.119, 2.522], [-1.942, 2.122, 1.456], [-1.804, 1.757, 0], [-1.942, 2.122, -1.456], [-2.32, 3.119, -2.522], [-2.837, 4.48, -2.912], [-3.353, 5.842, -2.522], [-3.731, 6.838, -1.456]] - , [[-5.806, 8.062, 0], [-5.526, 7.529, 2.247], [-4.762, 6.073, 3.891], [-3.718, 4.084, 4.493], [-2.674, 2.094, 3.891], [-1.909, 0.638, 2.247], [-1.63, 0.105, 0], [-1.909, 0.638, -2.247], [-2.674, 2.094, -3.891], [-3.718, 4.084, -4.493], [-4.762, 6.073, -3.891], [-5.526, 7.529, -2.247], [-5.11, 6.736, 0], [-4.923, 6.381, 1.498], [-4.414, 5.41, 2.594], [-3.718, 4.084, 2.995], [-3.022, 2.758, 2.594], [-2.512, 1.787, 1.498], [-2.326, 1.431, 0], [-2.512, 1.787, -1.498], [-3.022, 2.758, -2.594], [-3.718, 4.084, -2.995], [-4.414, 5.41, -2.594], [-4.923, 6.381, -1.498]] - , [[-7.168, 7.384, 0], [-6.816, 6.875, 2.309], [-5.856, 5.484, 3.999], [-4.545, 3.584, 4.618], [-3.233, 1.684, 3.999], [-2.273, 0.293, 2.309], [-1.921, -0.216, 0], [-2.273, 0.293, -2.309], [-3.233, 1.684, -3.999], [-4.545, 3.584, -4.618], [-5.856, 5.484, -3.999], [-6.816, 6.875, -2.309], [-6.293, 6.117, 0], [-6.059, 5.778, 1.539], [-5.419, 4.851, 2.666], [-4.545, 3.584, 3.078], [-3.67, 2.317, 2.666], [-3.03, 1.39, 1.539], [-2.796, 1.05, 0], [-3.03, 1.39, -1.539], [-3.67, 2.317, -2.666], [-4.545, 3.584, -3.078], [-5.419, 4.851, -2.666], [-6.059, 5.778, -1.539]] - , [[-8.449, 6.537, 0], [-8.028, 6.062, 2.371], [-6.877, 4.763, 4.107], [-5.305, 2.988, 4.742], [-3.733, 1.213, 4.107], [-2.582, -0.086, 2.371], [-2.16, -0.561, 0], [-2.582, -0.086, -2.371], [-3.733, 1.213, -4.107], [-5.305, 2.988, -4.742], [-6.877, 4.763, -4.107], [-8.028, 6.062, -2.371], [-7.401, 5.354, 0], [-7.12, 5.037, 1.581], [-6.353, 4.171, 2.738], [-5.305, 2.988, 3.161], [-4.257, 1.805, 2.738], [-3.49, 0.939, 1.581], [-3.209, 0.622, 0], [-3.49, 0.939, -1.581], [-4.257, 1.805, -2.738], [-5.305, 2.988, -3.161], [-6.353, 4.171, -2.738], [-7.12, 5.037, -1.581]] - , [[-9.631, 5.532, 0], [-9.143, 5.1, 2.433], [-7.809, 3.918, 4.214], [-5.988, 2.305, 4.866], [-4.167, 0.691, 4.214], [-2.834, -0.49, 2.433], [-2.346, -0.922, 0], [-2.834, -0.49, -2.433], [-4.167, 0.691, -4.214], [-5.988, 2.305, -4.866], [-7.809, 3.918, -4.214], [-9.143, 5.1, -2.433], [-8.416, 4.456, 0], [-8.091, 4.168, 1.622], [-7.202, 3.381, 2.81], [-5.988, 2.305, 3.244], [-4.774, 1.229, 2.81], [-3.885, 0.442, 1.622], [-3.56, 0.154, 0], [-3.885, 0.442, -1.622], [-4.774, 1.229, -2.81], [-5.988, 2.305, -3.244], [-7.202, 3.381, -2.81], [-8.091, 4.168, -1.622]] - , [[-10.691, 4.38, 0], [-10.141, 4, 2.495], [-8.638, 2.962, 4.322], [-6.584, 1.545, 4.991], [-4.53, 0.127, 4.322], [-3.027, -0.911, 2.495], [-2.477, -1.291, 0], [-3.027, -0.911, -2.495], [-4.53, 0.127, -4.322], [-6.584, 1.545, -4.991], [-8.638, 2.962, -4.322], [-10.141, 4, -2.495], [-9.322, 3.435, 0], [-8.955, 3.181, 1.664], [-7.953, 2.49, 2.881], [-6.584, 1.545, 3.327], [-5.215, 0.599, 2.881], [-4.213, -0.092, 1.664], [-3.846, -0.346, 0], [-4.213, -0.092, -1.664], [-5.215, 0.599, -2.881], [-6.584, 1.545, -3.327], [-7.953, 2.49, -2.881], [-8.955, 3.181, -1.664]] - , [[-11.613, 3.095, 0], [-11.006, 2.776, 2.558], [-9.348, 1.906, 4.43], [-7.084, 0.718, 5.115], [-4.819, -0.471, 4.43], [-3.161, -1.341, 2.558], [-2.554, -1.659, 0], [-3.161, -1.341, -2.558], [-4.819, -0.471, -4.43], 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-16.315], [-61.252, -2.245, -18.839], [-70.372, 0.111, -16.315], [-77.049, 1.835, -9.419]] - , [[-89.096, 3.392, 0], [-85.398, 2.508, 14.191], [-75.294, 0.092, 24.58], [-61.492, -3.209, 28.382], [-47.69, -6.509, 24.58], [-37.586, -8.925, 14.191], [-33.888, -9.81, 0], [-37.586, -8.925, -14.191], [-47.69, -6.509, -24.58], [-61.492, -3.209, -28.382], [-75.294, 0.092, -24.58], [-85.398, 2.508, -14.191], [-79.895, 1.192, 0], [-77.429, 0.602, 9.461], [-70.693, -1.009, 16.387], [-61.492, -3.209, 18.922], [-52.29, -5.409, 16.387], [-45.555, -7.02, 9.461], [-43.089, -7.609, 0], [-45.555, -7.02, -9.461], [-52.29, -5.409, -16.387], [-61.492, -3.209, -18.922], [-70.693, -1.009, -16.387], [-77.429, 0.602, -9.461]] - , [[-89.555, 1.952, 0], [-85.825, 1.131, 14.253], [-75.634, -1.113, 24.688], [-61.714, -4.177, 28.507], [-47.794, -7.241, 24.688], [-37.604, -9.484, 14.253], [-33.874, -10.305, 0], [-37.604, -9.484, -14.253], [-47.794, -7.241, -24.688], [-61.714, -4.177, -28.507], [-75.634, -1.113, -24.688], [-85.825, 1.131, -14.253], [-80.274, -0.091, 0], [-77.788, -0.639, 9.502], [-70.994, -2.134, 16.458], [-61.714, -4.177, 19.005], [-52.434, -6.219, 16.458], [-45.64, -7.715, 9.502], [-43.154, -8.262, 0], [-45.64, -7.715, -9.502], [-52.434, -6.219, -16.458], [-61.714, -4.177, -19.005], [-70.994, -2.134, -16.458], [-77.788, -0.639, -9.502]] - , [[-89.987, 0.501, 0], [-86.227, -0.256, 14.316], [-75.953, -2.324, 24.795], [-61.919, -5.148, 28.631], [-47.885, -7.973, 24.795], [-37.611, -10.041, 14.316], [-33.85, -10.797, 0], [-37.611, -10.041, -14.316], [-47.885, -7.973, -24.795], [-61.919, -5.148, -28.631], [-75.953, -2.324, -24.795], [-86.227, -0.256, -14.316], [-80.631, -1.382, 0], [-78.124, -1.887, 9.544], [-71.275, -3.265, 16.53], [-61.919, -5.148, 19.088], [-52.563, -7.031, 16.53], [-45.713, -8.41, 9.544], [-43.206, -8.914, 0], [-45.713, -8.41, -9.544], [-52.563, -7.031, -16.53], [-61.919, -5.148, -19.088], [-71.275, -3.265, -16.53], [-78.124, -1.887, -9.544]] - , [[-90.394, -0.96, 0], [-86.604, -1.652, 14.378], [-76.25, -3.542, 24.903], [-62.106, -6.124, 28.756], [-47.962, -8.705, 24.903], [-37.608, -10.595, 14.378], [-33.818, -11.287, 0], [-37.608, -10.595, -14.378], [-47.962, -8.705, -24.903], [-62.106, -6.124, -28.756], [-76.25, -3.542, -24.903], [-86.604, -1.652, -14.378], [-80.965, -2.681, 0], [-78.438, -3.142, 9.585], [-71.535, -4.402, 16.602], [-62.106, -6.124, 19.171], [-52.677, -7.845, 16.602], [-45.774, -9.105, 9.585], [-43.247, -9.566, 0], [-45.774, -9.105, -9.585], [-52.677, -7.845, -16.602], [-62.106, -6.124, -19.171], [-71.535, -4.402, -16.602], [-78.438, -3.142, -9.585]] - , [[-90.775, -2.43, 0], [-86.957, -3.056, 14.44], [-76.525, -4.766, 25.011], [-62.275, -7.102, 28.88], [-48.026, -9.438, 25.011], [-37.594, -11.148, 14.44], [-33.776, -11.774, 0], [-37.594, -11.148, -14.44], [-48.026, -9.438, -25.011], [-62.275, -7.102, -28.88], [-76.525, -4.766, -25.011], [-86.957, -3.056, -14.44], [-81.275, -3.987, 0], [-78.73, -4.404, 9.627], [-71.775, -5.545, 16.674], [-62.275, -7.102, 19.253], [-52.776, -8.659, 16.674], [-45.821, -9.8, 9.627], [-43.276, -10.217, 0], [-45.821, -9.8, -9.627], [-52.776, -8.659, -16.674], [-62.275, -7.102, -19.253], [-71.775, -5.545, -16.674], [-78.73, -4.404, -9.627]] - , [[-91.13, -3.908, 0], [-87.284, -4.468, 14.502], [-76.779, -5.996, 25.119], [-62.427, -8.083, 29.005], [-48.076, -10.171, 25.119], [-37.57, -11.699, 14.502], [-33.725, -12.258, 0], [-37.57, -11.699, -14.502], [-48.076, -10.171, -25.119], [-62.427, -8.083, -29.005], [-76.779, -5.996, -25.119], [-87.284, -4.468, -14.502], [-81.562, -5.3, 0], [-78.999, -5.673, 9.668], [-71.995, -6.692, 16.746], [-62.427, -8.083, 19.336], [-52.86, -9.475, 16.746], [-45.856, -10.494, 9.668], [-43.292, -10.867, 0], [-45.856, -10.494, -9.668], [-52.86, -9.475, -16.746], [-62.427, -8.083, -19.336], [-71.995, -6.692, -16.746], [-78.999, -5.673, -9.668]] - , [[-91.458, -5.396, 0], [-87.587, -5.887, 14.565], [-77.01, -7.231, 25.226], [-62.561, -9.067, 29.129], [-48.113, -10.903, 25.226], [-37.536, -12.247, 14.565], [-33.665, -12.739, 0], [-37.536, -12.247, -14.565], [-48.113, -10.903, -25.226], [-62.561, -9.067, -29.129], [-77.01, -7.231, -25.226], [-87.587, -5.887, -14.565], [-81.826, -6.619, 0], [-79.245, -6.947, 9.71], [-72.194, -7.843, 16.818], [-62.561, -9.067, 19.419], [-52.929, -10.291, 16.818], [-45.878, -11.187, 9.71], [-43.297, -11.515, 0], [-45.878, -11.187, -9.71], [-52.929, -10.291, -16.818], [-62.561, -9.067, -19.419], [-72.194, -7.843, -16.818], [-79.245, -6.947, -9.71]] - , [[-91.76, -6.891, 0], [-87.863, -7.314, 14.627], [-77.219, -8.472, 25.334], [-62.678, -10.053, 29.253], [-48.137, -11.635, 25.334], [-37.492, -12.793, 14.627], [-33.596, -13.216, 0], [-37.492, -12.793, -14.627], [-48.137, -11.635, -25.334], [-62.678, -10.053, -29.253], [-77.219, -8.472, -25.334], [-87.863, -7.314, -14.627], [-82.066, -7.945, 0], [-79.468, -8.227, 9.751], [-72.372, -8.999, 16.889], [-62.678, -10.053, 19.502], [-52.984, -11.108, 16.889], [-45.887, -11.88, 9.751], [-43.29, -12.162, 0], [-45.887, -11.88, -9.751], [-52.984, -11.108, -16.889], [-62.678, -10.053, -19.502], [-72.372, -8.999, -16.889], [-79.468, -8.227, -9.751]] - , [[-92.034, -8.393, 0], [-88.114, -8.748, 14.689], [-77.405, -9.717, 25.442], [-62.776, -11.042, 29.378], [-48.147, -12.366, 25.442], [-37.438, -13.335, 14.689], [-33.518, -13.69, 0], [-37.438, -13.335, -14.689], [-48.147, -12.366, -25.442], [-62.776, -11.042, -29.378], [-77.405, -9.717, -25.442], [-88.114, -8.748, -14.689], [-82.282, -9.276, 0], [-79.668, -9.512, 9.793], [-72.529, -10.159, 16.961], [-62.776, -11.042, 19.585], [-53.023, -11.924, 16.961], [-45.884, -12.571, 9.793], [-43.271, -12.807, 0], [-45.884, -12.571, -9.793], [-53.023, -11.924, -16.961], [-62.776, -11.042, -19.585], [-72.529, -10.159, -16.961], [-79.668, -9.512, -9.793]] - , [[-92.282, -9.903, 0], [-88.34, -10.188, 14.751], [-77.569, -10.967, 25.55], [-62.857, -12.031, 29.502], [-48.144, -13.096, 25.55], [-37.373, -13.875, 14.751], [-33.431, -14.16, 0], [-37.373, -13.875, -14.751], [-48.144, -13.096, -25.55], [-62.857, -12.031, -29.502], [-77.569, -10.967, -25.55], [-88.34, -10.188, -14.751], [-82.474, -10.612, 0], [-79.845, -10.802, 9.834], [-72.665, -11.322, 17.033], [-62.857, -12.031, 19.668], [-53.048, -12.741, 17.033], [-45.868, -13.26, 9.834], [-43.24, -13.451, 0], [-45.868, -13.26, -9.834], [-53.048, -12.741, -17.033], [-62.857, -12.031, -19.668], [-72.665, -11.322, -17.033], [-79.845, -10.802, -9.834]] - , [[-92.503, -11.418, 0], [-88.539, -11.633, 14.813], [-77.711, -12.22, 25.657], [-62.919, -13.022, 29.627], [-48.128, -13.824, 25.657], [-37.299, -14.411, 14.813], [-33.336, -14.626, 0], [-37.299, -14.411, -14.813], [-48.128, -13.824, -25.657], [-62.919, -13.022, -29.627], [-77.711, -12.22, -25.657], [-88.539, -11.633, -14.813], [-82.642, -11.953, 0], [-79.999, -12.096, 9.876], [-72.78, -12.488, 17.105], [-62.919, -13.022, 19.751], [-53.058, -13.557, 17.105], [-45.839, -13.948, 9.876], [-43.197, -14.092, 0], [-45.839, -13.948, -9.876], [-53.058, -13.557, -17.105], [-62.919, -13.022, -19.751], [-72.78, -12.488, -17.105], [-79.999, -12.096, -9.876]] - , [[-92.696, -12.94, 0], [-88.713, -13.084, 14.876], [-77.83, -13.477, 25.765], [-62.964, -14.014, 29.751], [-48.098, -14.551, 25.765], [-37.216, -14.945, 14.876], [-33.232, -15.088, 0], [-37.216, -14.945, -14.876], [-48.098, -14.551, -25.765], [-62.964, -14.014, -29.751], [-77.83, -13.477, -25.765], [-88.713, -13.084, -14.876], [-82.785, -13.298, 0], [-80.13, -13.394, 9.917], [-72.875, -13.656, 17.177], [-62.964, -14.014, 19.834], [-53.054, -14.372, 17.177], [-45.799, -14.634, 9.917], [-43.143, -14.73, 0], [-45.799, -14.634, -9.917], [-53.054, -14.372, -17.177], [-62.964, -14.014, -19.834], [-72.875, -13.656, -17.177], [-80.13, -13.394, -9.917]] - , [[-92.862, -14.468, 0], [-88.86, -14.54, 14.938], [-77.926, -14.737, 25.873], [-62.991, -15.007, 29.876], [-48.056, -15.277, 25.873], [-37.122, -15.474, 14.938], [-33.12, -15.546, 0], [-37.122, -15.474, -14.938], [-48.056, -15.277, -25.873], [-62.991, -15.007, -29.876], [-77.926, -14.737, -25.873], [-88.86, -14.54, -14.938], [-82.905, -14.647, 0], [-80.237, -14.696, 9.959], [-72.948, -14.827, 17.249], [-62.991, -15.007, 19.917], [-53.034, -15.187, 17.249], [-45.745, -15.318, 9.959], [-43.077, -15.367, 0], [-45.745, -15.318, -9.959], [-53.034, -15.187, -17.249], [-62.991, -15.007, -19.917], [-72.948, -14.827, -17.249], [-80.237, -14.696, -9.959]] - , [[-93, -16, 0], [-88.981, -16, 15], [-78, -16, 25.981], [-63, -16, 30], [-48, -16, 25.981], [-37.019, -16, 15], [-33, -16, 0], [-37.019, -16, -15], [-48, -16, -25.981], [-63, -16, -30], [-78, -16, -25.981], [-88.981, -16, -15], [-83, -16, 0], [-80.321, -16, 10], [-73, -16, 17.321], [-63, -16, 20], [-53, -16, 17.321], [-45.679, -16, 10], [-43, -16, 0], [-45.679, -16, -10], [-53, -16, -17.321], [-63, -16, -20], [-73, -16, -17.321], [-80.321, -16, -10]] - ]; + expected = [[[8, 0, 0], [7.59808, 0, 1.5], [6.5, 0, 2.59808], [5, 0, 3], [3.5, 0, 2.59808], [2.40192, 0, 1.5], [2, 0, 0], [2.40192, 0, -1.5], [3.5, 0, -2.59808], [5, 0, -3], [6.5, 0, -2.59808], [7.59808, 0, -1.5], [7, 0, 0], [6.73205, 0, 1], [6, 0, 1.73205], [5, 0, 2], [4, 0, 1.73205], [3.26795, 0, 1], [3, 0, 0], [3.26795, 0, -1], [4, 0, -1.73205], [5, 0, -2], [6, 0, -1.73205], [6.73205, 0, -1]], [[7.96832, 1.585, 0], [7.55777, 1.50333, 1.56221], [6.43612, 1.28022, 2.70583], [4.90393, 0.975452, 3.12442], [3.37173, 0.670679, 2.70583], [2.25009, 0.44757, 1.56221], [1.83954, 0.365907, 0], [2.25009, 0.44757, -1.56221], [3.37173, 0.670679, -2.70583], [4.90393, 0.975452, -3.12442], [6.43612, 1.28022, -2.70583], [7.55777, 1.50333, -1.56221], [6.94685, 1.38181, 0], [6.67315, 1.32737, 1.04147], [5.92539, 1.17863, 1.80389], [4.90393, 0.975452, 2.08295], [3.88246, 0.77227, 1.80389], [3.1347, 0.623531, 1.04147], [2.861, 0.569088, 0], [3.1347, 0.623531, -1.04147], [3.88246, 0.77227, -1.80389], [4.90393, 0.975452, -2.08295], [5.92539, 1.17863, -1.80389], 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[-2.2531, 6.14117, -2.45041], [-2.50095, 7.14674, -1.41475]], [[-4.38599, 8.5649, 0], [-4.17844, 8.01765, 2.18433], [-3.61141, 6.52252, 3.78337], [-2.83684, 4.48013, 4.36866], [-2.06226, 2.43774, 3.78337], [-1.49524, 0.942614, 2.18433], [-1.28769, 0.395359, 0], [-1.49524, 0.942614, -2.18433], [-2.06226, 2.43774, -3.78337], [-2.83684, 4.48013, -4.36866], [-3.61141, 6.52252, -3.78337], [-4.17844, 8.01765, -2.18433], [-3.86961, 7.20331, 0], [-3.73124, 6.83847, 1.45622], [-3.35322, 5.84172, 2.52225], [-2.83684, 4.48013, 2.91244], [-2.32046, 3.11854, 2.52225], [-1.94244, 2.12179, 1.45622], [-1.80407, 1.75695, 0], [-1.94244, 2.12179, -1.45622], [-2.32046, 3.11854, -2.52225], [-2.83684, 4.48013, -2.91244], [-3.35322, 5.84172, -2.52225], [-3.73124, 6.83847, -1.45622]], [[-5.80583, 8.06208, 0], [-5.52608, 7.52907, 2.24654], [-4.76181, 6.07286, 3.89113], [-3.71779, 4.08365, 4.49309], [-2.67376, 2.09443, 3.89113], [-1.90949, 0.638226, 2.24654], [-1.62974, 0.105217, 0], [-1.90949, 0.638226, 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[-87.8633, -7.31434, -14.6267], [-82.0656, -7.94488, 0], [-79.4681, -8.22738, 9.75115], [-72.3716, -8.99917, 16.8895], [-62.6776, -10.0535, 19.5023], [-52.9836, -11.1077, 16.8895], [-45.8871, -11.8795, 9.75115], [-43.2896, -12.162, 0], [-45.8871, -11.8795, -9.75115], [-52.9836, -11.1077, -16.8895], [-62.6776, -10.0535, -19.5023], [-72.3716, -8.99917, -16.8895], [-79.4681, -8.22738, -9.75115]], [[-92.0343, -8.39307, 0], [-88.1144, -8.74791, 14.6889], [-77.4052, -9.71733, 25.442], [-62.776, -11.0416, 29.3779], [-48.1469, -12.3658, 25.442], [-37.4376, -13.3353, 14.6889], [-33.5178, -13.6901, 0], [-37.4376, -13.3353, -14.6889], [-48.1469, -12.3658, -25.442], [-62.776, -11.0416, -29.3779], [-77.4052, -9.71733, -25.442], [-88.1144, -8.74791, -14.6889], [-82.2815, -9.27591, 0], [-79.6683, -9.51246, 9.79263], [-72.5288, -10.1587, 16.9613], [-62.776, -11.0416, 19.5853], [-53.0233, -11.9244, 16.9613], [-45.8838, -12.5707, 9.79263], [-43.2705, -12.8073, 0], [-45.8838, -12.5707, -9.79263], [-53.0233, -11.9244, -16.9613], [-62.776, -11.0416, -19.5853], [-72.5288, -10.1587, -16.9613], [-79.6683, -9.51246, -9.79263]], [[-92.282, -9.9025, 0], [-88.3398, -10.1877, 14.7512], [-77.5693, -10.9669, 25.5497], [-62.8566, -12.0313, 29.5023], [-48.1439, -13.0957, 25.5497], [-37.3735, -13.8749, 14.7512], [-33.4312, -14.1601, 0], [-37.3735, -13.8749, -14.7512], [-48.1439, -13.0957, -25.5497], [-62.8566, -12.0313, -29.5023], [-77.5693, -10.9669, -25.5497], [-88.3398, -10.1877, -14.7512], [-82.4736, -10.6121, 0], [-79.8454, -10.8022, 9.8341], [-72.6651, -11.3217, 17.0332], [-62.8566, -12.0313, 19.6682], [-53.0482, -12.7409, 17.0332], [-45.8679, -13.2604, 9.8341], [-43.2397, -13.4505, 0], [-45.8679, -13.2604, -9.8341], [-53.0482, -12.7409, -17.0332], [-62.8566, -12.0313, -19.6682], [-72.6651, -11.3217, -17.0332], [-79.8454, -10.8022, -9.8341]], [[-92.5026, -11.4184, 0], [-88.5392, -11.6333, 14.8134], [-77.711, -12.2204, 25.6575], [-62.9193, -13.0224, 29.6267], [-48.1277, -13.8243, 25.6575], [-37.2995, -14.4114, 14.8134], [-33.3361, -14.6263, 0], [-37.2995, -14.4114, -14.8134], [-48.1277, -13.8243, -25.6575], [-62.9193, -13.0224, -29.6267], [-77.711, -12.2204, -25.6575], [-88.5392, -11.6333, -14.8134], [-82.6415, -11.9531, 0], [-79.9993, -12.0963, 9.87558], [-72.7804, -12.4877, 17.105], [-62.9193, -13.0224, 19.7512], [-53.0582, -13.557, 17.105], [-45.8394, -13.9484, 9.87558], [-43.1972, -14.0917, 0], [-45.8394, -13.9484, -9.87558], [-53.0582, -13.557, -17.105], [-62.9193, -13.0224, -19.7512], [-72.7804, -12.4877, -17.105], [-79.9993, -12.0963, -9.87558]], [[-92.6959, -12.9403, 0], [-88.7126, -13.0842, 14.8756], [-77.83, -13.4773, 25.7653], [-62.9641, -14.0144, 29.7512], [-48.0983, -14.5514, 25.7653], [-37.2157, -14.9446, 14.8756], [-33.2324, -15.0885, 0], [-37.2157, -14.9446, -14.8756], [-48.0983, -14.5514, -25.7653], [-62.9641, -14.0144, -29.7512], [-77.83, -13.4773, -25.7653], [-88.7126, -13.0842, -14.8756], [-82.7853, -13.2983, 0], [-80.1298, -13.3942, 9.91705], [-72.8747, -13.6563, 17.1768], [-62.9641, -14.0144, 19.8341], [-53.0536, -14.3724, 17.1768], [-45.7985, -14.6345, 9.91705], [-43.143, -14.7304, 0], [-45.7985, -14.6345, -9.91705], [-53.0536, -14.3724, -17.1768], [-62.9641, -14.0144, -19.8341], [-72.8747, -13.6563, -17.1768], [-80.1298, -13.3942, -9.91705]], [[-92.8617, -14.4676, 0], [-88.8598, -14.5399, 14.9378], [-77.9264, -14.7373, 25.873], [-62.991, -15.007, 29.8756], [-48.0557, -15.2767, 25.873], [-37.1222, -15.4741, 14.9378], [-33.1203, -15.5464, 0], [-37.1222, -15.4741, -14.9378], [-48.0557, -15.2767, -25.873], [-62.991, -15.007, -29.8756], [-77.9264, -14.7373, -25.873], [-88.8598, -14.5399, -14.9378], [-82.9048, -14.6474, 0], [-80.2369, -14.6956, 9.95853], [-72.9479, -14.8272, 17.2487], [-62.991, -15.007, 19.9171], [-53.0341, -15.1868, 17.2487], [-45.7452, -15.3184, 9.95853], [-43.0772, -15.3666, 0], [-45.7452, -15.3184, -9.95853], [-53.0341, -15.1868, -17.2487], [-62.991, -15.007, -19.9171], [-72.9479, -14.8272, -17.2487], [-80.2369, -14.6956, -9.95853]], [[-93, -16, 0], [-88.9808, -16, 15], [-78, -16, 25.9808], [-63, -16, 30], [-48, -16, 25.9808], [-37.0192, -16, 15], [-33, -16, 0], [-37.0192, -16, -15], [-48, -16, -25.9808], [-63, -16, -30], [-78, -16, -25.9808], [-88.9808, -16, -15], [-83, -16, 0], [-80.3205, -16, 10], [-73, -16, 17.3205], [-63, -16, 20], [-53, -16, 17.3205], [-45.6795, -16, 10], [-43, -16, 0], [-45.6795, -16, -10], [-53, -16, -17.3205], [-63, -16, -20], [-73, -16, -17.3205], [-80.3205, -16, -10]]]; for(i = [0:len(expected) - 1]) { - assertEqualPoints(expected[i], sections[i], float_digits = 3); + assertEqualPoints(expected[i], sections[i]); } } diff --git a/test/test_helix_extrude.scad b/test/test_helix_extrude.scad index fa5d1bc0..38ff076d 100644 --- a/test/test_helix_extrude.scad +++ b/test/test_helix_extrude.scad @@ -11,166 +11,10 @@ module test_helix_extrude_same_radius() { include ; module test_helix_extrude(sections) { - expected = [ - [[45, 0.08, -1.998], [45, -0.08, 1.998], [44, -0.08, 1.998], [44, 0, 0], [36, 0, 0], [36, -0.08, 1.998], [35, -0.08, 1.998], [35, 0.08, -1.998]] - ,[[44, 9.434, -1.665], [44.033, 9.278, 2.332], [43.055, 9.07, 2.332], [43.038, 9.148, 0.333], [35.213, 7.485, 0.333], [35.23, 7.407, 2.332], [34.252, 7.199, 2.332], [34.219, 7.355, -1.665]] - ,[[41.077, 18.376, -1.332], [41.142, 18.231, 2.665], [40.228, 17.824, 2.665], [40.196, 17.896, 0.667], [32.888, 14.643, 0.667], [32.92, 14.57, 2.665], [32.006, 14.163, 2.665], [31.942, 14.308, -1.332]] - ,[[36.359, 26.515, -0.998], [36.453, 26.386, 2.998], [35.643, 25.798, 2.998], [35.597, 25.863, 1], [29.125, 21.16, 1], [29.171, 21.096, 2.998], [28.362, 20.508, 2.998], [28.269, 20.637, -0.998]] - ,[[30.052, 33.495, -0.665], [30.17, 33.388, 3.332], [29.501, 32.645, 3.332], [29.442, 32.698, 1.333], [24.089, 26.753, 1.333], [24.148, 26.7, 3.332], [23.479, 25.957, 3.332], [23.36, 26.063, -0.665]] - ,[[22.431, 39.011, -0.332], [22.569, 38.931, 3.665], [22.069, 38.065, 3.665], [22, 38.105, 1.667], [18, 31.177, 1.667], [18.069, 31.137, 3.665], [17.569, 30.271, 3.665], [17.431, 30.351, -0.332]] - ,[[13.83, 42.822, 0.002], [13.981, 42.773, 3.998], [13.672, 41.822, 3.998], [13.597, 41.846, 2], [11.125, 34.238, 2], [11.2, 34.213, 3.998], [10.891, 33.262, 3.998], [10.74, 33.312, 0.002]] - ,[[4.625, 44.762, 0.335], [4.783, 44.745, 4.332], [4.678, 43.751, 4.332], [4.599, 43.759, 2.333], [3.763, 35.803, 2.333], [3.842, 35.794, 4.332], [3.738, 34.8, 4.332], [3.579, 34.817, 0.335]] - ,[[-4.783, 44.745, 0.668], [-4.625, 44.762, 4.665], [-4.52, 43.767, 4.665], [-4.599, 43.759, 2.667], [-3.763, 35.803, 2.667], [-3.684, 35.811, 4.665], [-3.579, 34.817, 4.665], [-3.738, 34.8, 0.668]] - ,[[-13.981, 42.773, 1.002], [-13.83, 42.822, 4.998], [-13.521, 41.871, 4.998], [-13.597, 41.846, 3], [-11.125, 34.238, 3], [-11.049, 34.263, 4.998], [-10.74, 33.312, 4.998], [-10.891, 33.262, 1.002]] - ,[[-22.569, 38.931, 1.335], [-22.431, 39.011, 5.332], [-21.931, 38.145, 5.332], [-22, 38.105, 3.333], [-18, 31.177, 3.333], [-17.931, 31.217, 5.332], [-17.431, 30.351, 5.332], [-17.569, 30.271, 1.335]] - ,[[-30.17, 33.388, 1.668], [-30.052, 33.495, 5.665], [-29.383, 32.752, 5.665], [-29.442, 32.698, 3.667], [-24.089, 26.753, 3.667], [-24.03, 26.806, 5.665], [-23.36, 26.063, 5.665], [-23.479, 25.957, 1.668]] - ,[[-36.453, 26.386, 2.002], [-36.359, 26.515, 5.998], [-35.55, 25.927, 5.998], [-35.597, 25.863, 4], [-29.125, 21.16, 4], [-29.078, 21.225, 5.998], [-28.269, 20.637, 5.998], [-28.362, 20.508, 2.002]] - ,[[-41.142, 18.231, 2.335], [-41.077, 18.376, 6.332], [-40.164, 17.969, 6.332], [-40.196, 17.896, 4.333], [-32.888, 14.643, 4.333], [-32.855, 14.715, 6.332], [-31.942, 14.308, 6.332], [-32.006, 14.163, 2.335]] - ,[[-44.033, 9.278, 2.668], [-44, 9.434, 6.665], [-43.022, 9.226, 6.665], [-43.038, 9.148, 4.667], [-35.213, 7.485, 4.667], [-35.197, 7.563, 6.665], [-34.219, 7.355, 6.665], [-34.252, 7.199, 2.668]] - ,[[-45, -0.08, 3.002], [-45, 0.08, 6.998], [-44, 0.08, 6.998], [-44, 0, 5], [-36, 0, 5], [-36, 0.08, 6.998], [-35, 0.08, 6.998], [-35, -0.08, 3.002]] - ,[[-44, -9.434, 3.335], [-44.033, -9.278, 7.332], [-43.055, -9.07, 7.332], [-43.038, -9.148, 5.333], [-35.213, -7.485, 5.333], [-35.23, -7.407, 7.332], [-34.252, -7.199, 7.332], [-34.219, -7.355, 3.335]] - ,[[-41.077, -18.376, 3.668], [-41.142, -18.231, 7.665], [-40.228, -17.824, 7.665], [-40.196, -17.896, 5.667], [-32.888, -14.643, 5.667], [-32.92, -14.57, 7.665], [-32.006, -14.163, 7.665], [-31.942, -14.308, 3.668]] - ,[[-36.359, -26.515, 4.002], [-36.453, -26.386, 7.998], [-35.643, -25.798, 7.998], [-35.597, -25.863, 6], [-29.125, -21.16, 6], [-29.171, -21.096, 7.998], [-28.362, -20.508, 7.998], [-28.269, -20.637, 4.002]] - ,[[-30.052, -33.495, 4.335], [-30.17, -33.388, 8.332], [-29.501, -32.645, 8.332], [-29.442, -32.698, 6.333], [-24.089, -26.753, 6.333], [-24.148, -26.7, 8.332], [-23.479, -25.957, 8.332], [-23.36, -26.063, 4.335]] - ,[[-22.431, -39.011, 4.668], [-22.569, -38.931, 8.665], [-22.069, -38.065, 8.665], [-22, -38.105, 6.667], [-18, -31.177, 6.667], [-18.069, -31.137, 8.665], [-17.569, -30.271, 8.665], [-17.431, -30.351, 4.668]] - ,[[-13.83, -42.822, 5.002], [-13.981, -42.773, 8.998], [-13.672, -41.822, 8.998], [-13.597, -41.846, 7], [-11.125, -34.238, 7], [-11.2, -34.213, 8.998], [-10.891, -33.262, 8.998], [-10.74, -33.312, 5.002]] - ,[[-4.625, -44.762, 5.335], [-4.783, -44.745, 9.332], [-4.678, -43.751, 9.332], [-4.599, -43.759, 7.333], [-3.763, -35.803, 7.333], [-3.842, -35.794, 9.332], [-3.738, -34.8, 9.332], [-3.579, -34.817, 5.335]] - ,[[4.783, -44.745, 5.668], [4.625, -44.762, 9.665], [4.52, -43.767, 9.665], [4.599, -43.759, 7.667], [3.763, -35.803, 7.667], [3.684, -35.811, 9.665], [3.579, -34.817, 9.665], [3.738, -34.8, 5.668]] - ,[[13.981, -42.773, 6.002], [13.83, -42.822, 9.998], [13.521, -41.871, 9.998], [13.597, -41.846, 8], [11.125, -34.238, 8], [11.049, -34.263, 9.998], [10.74, -33.312, 9.998], [10.891, -33.262, 6.002]] - ,[[22.569, -38.931, 6.335], [22.431, -39.011, 10.332], [21.931, -38.145, 10.332], [22, -38.105, 8.333], [18, -31.177, 8.333], [17.931, -31.217, 10.332], [17.431, -30.351, 10.332], [17.569, -30.271, 6.335]] - ,[[30.17, -33.388, 6.668], [30.052, -33.495, 10.665], [29.383, -32.752, 10.665], [29.442, -32.698, 8.667], [24.089, -26.753, 8.667], [24.03, -26.806, 10.665], [23.36, -26.063, 10.665], [23.479, -25.957, 6.668]] - ,[[36.453, -26.386, 7.002], [36.359, -26.515, 10.998], [35.55, -25.927, 10.998], [35.597, -25.863, 9], [29.125, -21.16, 9], [29.078, -21.225, 10.998], [28.269, -20.637, 10.998], [28.362, -20.508, 7.002]] - ,[[41.142, -18.231, 7.335], [41.077, -18.376, 11.332], [40.164, -17.969, 11.332], [40.196, -17.896, 9.333], [32.888, -14.643, 9.333], [32.855, -14.715, 11.332], [31.942, -14.308, 11.332], [32.006, -14.163, 7.335]] - ,[[44.033, -9.278, 7.668], [44, -9.434, 11.665], [43.022, -9.226, 11.665], [43.038, -9.148, 9.667], [35.213, -7.485, 9.667], [35.197, -7.563, 11.665], [34.219, -7.355, 11.665], [34.252, -7.199, 7.668]] - ,[[45, 0.08, 8.002], [45, -0.08, 11.998], [44, -0.08, 11.998], [44, 0, 10], [36, 0, 10], [36, -0.08, 11.998], [35, -0.08, 11.998], [35, 0.08, 8.002]] - ,[[44, 9.434, 8.335], [44.033, 9.278, 12.332], [43.055, 9.07, 12.332], [43.038, 9.148, 10.333], [35.213, 7.485, 10.333], [35.23, 7.407, 12.332], [34.252, 7.199, 12.332], [34.219, 7.355, 8.335]] - ,[[41.077, 18.376, 8.668], [41.142, 18.231, 12.665], [40.228, 17.824, 12.665], [40.196, 17.896, 10.667], [32.888, 14.643, 10.667], [32.92, 14.57, 12.665], [32.006, 14.163, 12.665], [31.942, 14.308, 8.668]] - ,[[36.359, 26.515, 9.002], [36.453, 26.386, 12.998], [35.643, 25.798, 12.998], [35.597, 25.863, 11], [29.125, 21.16, 11], [29.171, 21.096, 12.998], [28.362, 20.508, 12.998], [28.269, 20.637, 9.002]] - ,[[30.052, 33.495, 9.335], [30.17, 33.388, 13.332], [29.501, 32.645, 13.332], [29.442, 32.698, 11.333], [24.089, 26.753, 11.333], [24.148, 26.7, 13.332], [23.479, 25.957, 13.332], [23.36, 26.063, 9.335]] - ,[[22.431, 39.011, 9.668], [22.569, 38.931, 13.665], [22.069, 38.065, 13.665], [22, 38.105, 11.667], [18, 31.177, 11.667], [18.069, 31.137, 13.665], [17.569, 30.271, 13.665], [17.431, 30.351, 9.668]] - ,[[13.83, 42.822, 10.002], [13.981, 42.773, 13.998], [13.672, 41.822, 13.998], [13.597, 41.846, 12], [11.125, 34.238, 12], [11.2, 34.213, 13.998], [10.891, 33.262, 13.998], [10.74, 33.312, 10.002]] - ,[[4.625, 44.762, 10.335], [4.783, 44.745, 14.332], [4.678, 43.751, 14.332], [4.599, 43.759, 12.333], [3.763, 35.803, 12.333], [3.842, 35.794, 14.332], [3.738, 34.8, 14.332], [3.579, 34.817, 10.335]] - ,[[-4.783, 44.745, 10.668], [-4.625, 44.762, 14.665], [-4.52, 43.767, 14.665], [-4.599, 43.759, 12.667], [-3.763, 35.803, 12.667], [-3.684, 35.811, 14.665], [-3.579, 34.817, 14.665], [-3.738, 34.8, 10.668]] - ,[[-13.981, 42.773, 11.002], [-13.83, 42.822, 14.998], [-13.521, 41.871, 14.998], [-13.597, 41.846, 13], [-11.125, 34.238, 13], [-11.049, 34.263, 14.998], [-10.74, 33.312, 14.998], [-10.891, 33.262, 11.002]] - ,[[-22.569, 38.931, 11.335], [-22.431, 39.011, 15.332], [-21.931, 38.145, 15.332], [-22, 38.105, 13.333], [-18, 31.177, 13.333], [-17.931, 31.217, 15.332], [-17.431, 30.351, 15.332], [-17.569, 30.271, 11.335]] - ,[[-30.17, 33.388, 11.668], [-30.052, 33.495, 15.665], [-29.383, 32.752, 15.665], [-29.442, 32.698, 13.667], [-24.089, 26.753, 13.667], [-24.03, 26.806, 15.665], [-23.36, 26.063, 15.665], [-23.479, 25.957, 11.668]] - ,[[-36.453, 26.386, 12.002], [-36.359, 26.515, 15.998], [-35.55, 25.927, 15.998], [-35.597, 25.863, 14], [-29.125, 21.16, 14], [-29.078, 21.225, 15.998], [-28.269, 20.637, 15.998], [-28.362, 20.508, 12.002]] - ,[[-41.142, 18.231, 12.335], [-41.077, 18.376, 16.332], [-40.164, 17.969, 16.332], [-40.196, 17.896, 14.333], [-32.888, 14.643, 14.333], [-32.855, 14.715, 16.332], [-31.942, 14.308, 16.332], [-32.006, 14.163, 12.335]] - ,[[-44.033, 9.278, 12.668], [-44, 9.434, 16.665], [-43.022, 9.226, 16.665], [-43.038, 9.148, 14.667], [-35.213, 7.485, 14.667], [-35.197, 7.563, 16.665], [-34.219, 7.355, 16.665], [-34.252, 7.199, 12.668]] - ,[[-45, -0.08, 13.002], [-45, 0.08, 16.998], [-44, 0.08, 16.998], [-44, 0, 15], [-36, 0, 15], [-36, 0.08, 16.998], [-35, 0.08, 16.998], [-35, -0.08, 13.002]] - ,[[-44, -9.434, 13.335], [-44.033, -9.278, 17.332], [-43.055, -9.07, 17.332], [-43.038, -9.148, 15.333], [-35.213, -7.485, 15.333], [-35.23, -7.407, 17.332], [-34.252, -7.199, 17.332], [-34.219, -7.355, 13.335]] - ,[[-41.077, -18.376, 13.668], [-41.142, -18.231, 17.665], [-40.228, -17.824, 17.665], [-40.196, -17.896, 15.667], [-32.888, -14.643, 15.667], [-32.92, -14.57, 17.665], [-32.006, -14.163, 17.665], [-31.942, -14.308, 13.668]] - ,[[-36.359, -26.515, 14.002], [-36.453, -26.386, 17.998], [-35.643, -25.798, 17.998], [-35.597, -25.863, 16], [-29.125, -21.16, 16], [-29.171, -21.096, 17.998], [-28.362, -20.508, 17.998], [-28.269, -20.637, 14.002]] - ,[[-30.052, -33.495, 14.335], [-30.17, -33.388, 18.332], [-29.501, -32.645, 18.332], [-29.442, 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45], [-36, 0.08, 46.998], [-35, 0.08, 46.998], [-35, -0.08, 43.002]] - ,[[-44, -9.434, 43.335], [-44.033, -9.278, 47.332], [-43.055, -9.07, 47.332], [-43.038, -9.148, 45.333], [-35.213, -7.485, 45.333], [-35.23, -7.407, 47.332], [-34.252, -7.199, 47.332], [-34.219, -7.355, 43.335]] - ,[[-41.077, -18.376, 43.668], [-41.142, -18.231, 47.665], [-40.228, -17.824, 47.665], [-40.196, -17.896, 45.667], [-32.888, -14.643, 45.667], [-32.92, -14.57, 47.665], [-32.006, -14.163, 47.665], [-31.942, -14.308, 43.668]] - ,[[-36.359, -26.515, 44.002], [-36.453, -26.386, 47.998], [-35.643, -25.798, 47.998], [-35.597, -25.863, 46], [-29.125, -21.16, 46], [-29.171, -21.096, 47.998], [-28.362, -20.508, 47.998], [-28.269, -20.637, 44.002]] - ,[[-30.052, -33.495, 44.335], [-30.17, -33.388, 48.332], [-29.501, -32.645, 48.332], [-29.442, -32.698, 46.333], [-24.089, -26.753, 46.333], [-24.148, -26.7, 48.332], [-23.479, -25.957, 48.332], [-23.36, -26.063, 44.335]] - ,[[-22.431, -39.011, 44.668], [-22.569, 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49.998], [10.891, -33.262, 46.002]] - ,[[22.569, -38.931, 46.335], [22.431, -39.011, 50.332], [21.931, -38.145, 50.332], [22, -38.105, 48.333], [18, -31.177, 48.333], [17.931, -31.217, 50.332], [17.431, -30.351, 50.332], [17.569, -30.271, 46.335]] - ,[[30.17, -33.388, 46.668], [30.052, -33.495, 50.665], [29.383, -32.752, 50.665], [29.442, -32.698, 48.667], [24.089, -26.753, 48.667], [24.03, -26.806, 50.665], [23.36, -26.063, 50.665], [23.479, -25.957, 46.668]] - ,[[36.453, -26.386, 47.002], [36.359, -26.515, 50.998], [35.55, -25.927, 50.998], [35.597, -25.863, 49], [29.125, -21.16, 49], [29.078, -21.225, 50.998], [28.269, -20.637, 50.998], [28.362, -20.508, 47.002]] - ,[[41.142, -18.231, 47.335], [41.077, -18.376, 51.332], [40.164, -17.969, 51.332], [40.196, -17.896, 49.333], [32.888, -14.643, 49.333], [32.855, -14.715, 51.332], [31.942, -14.308, 51.332], [32.006, -14.163, 47.335]] - ,[[44.033, -9.278, 47.668], [44, -9.434, 51.665], [43.022, -9.226, 51.665], [43.038, -9.148, 49.667], 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21.0959, 42.9984], [28.3623, 20.5082, 42.9984], [28.2689, 20.6368, 39.0016]], [[30.0518, 33.4947, 39.3349], [30.17, 33.3883, 43.3318], [29.5008, 32.6452, 43.3318], [29.4417, 32.6984, 41.3333], [24.0887, 26.7532, 41.3333], [24.1478, 26.7, 43.3318], [23.4787, 25.9569, 43.3318], [23.3605, 26.0633, 39.3349]], [[22.4311, 39.0109, 39.6682], [22.5689, 38.9314, 43.6651], [22.0689, 38.0654, 43.6651], [22, 38.1051, 41.6667], [18, 31.1769, 41.6667], [18.0689, 31.1372, 43.6651], [17.5689, 30.2711, 43.6651], [17.4311, 30.3506, 39.6682]], [[13.8301, 42.8221, 40.0016], [13.9814, 42.773, 43.9984], [13.6724, 41.8219, 43.9984], [13.5967, 41.8465, 42], [11.1246, 34.238, 42], [11.2002, 34.2135, 43.9984], [10.8912, 33.2624, 43.9984], [10.74, 33.3115, 40.0016]], [[4.6247, 44.7618, 40.3349], [4.78286, 44.7452, 44.3318], [4.67833, 43.7507, 44.3318], [4.59925, 43.759, 42.3333], [3.76302, 35.8028, 42.3333], [3.8421, 35.7945, 44.3318], [3.73758, 34.8, 44.3318], [3.57942, 34.8166, 40.3349]], [[-4.78286, 44.7452, 40.6682], [-4.6247, 44.7618, 44.6651], [-4.52017, 43.7673, 44.6651], [-4.59925, 43.759, 42.6667], [-3.76302, 35.8028, 42.6667], [-3.68395, 35.8111, 44.6651], [-3.57942, 34.8166, 44.6651], [-3.73758, 34.8, 40.6682]], [[-13.9814, 42.773, 41.0016], [-13.8301, 42.8221, 44.9984], [-13.5211, 41.8711, 44.9984], [-13.5967, 41.8465, 43], [-11.1246, 34.238, 43], [-11.049, 34.2626, 44.9984], [-10.74, 33.3115, 44.9984], [-10.8912, 33.2624, 41.0016]], [[-22.5689, 38.9314, 41.3349], [-22.4311, 39.0109, 45.3318], [-21.9311, 38.1449, 45.3318], [-22, 38.1051, 43.3333], [-18, 31.1769, 43.3333], [-17.9311, 31.2167, 45.3318], [-17.4311, 30.3506, 45.3318], [-17.5689, 30.2711, 41.3349]], [[-30.17, 33.3883, 41.6682], [-30.0518, 33.4947, 45.6651], [-29.3827, 32.7516, 45.6651], [-29.4417, 32.6984, 43.6667], [-24.0887, 26.7532, 43.6667], [-24.0296, 26.8064, 45.6651], [-23.3605, 26.0633, 45.6651], [-23.4787, 25.9569, 41.6682]], [[-36.4525, 26.386, 42.0016], [-36.359, 26.5147, 45.9984], [-35.55, 25.9269, 45.9984], [-35.5967, 25.8626, 44], [-29.1246, 21.1603, 44], [-29.0779, 21.2246, 45.9984], [-28.2689, 20.6368, 45.9984], [-28.3623, 20.5082, 42.0016]], [[-41.1419, 18.2305, 42.3349], [-41.0772, 18.3758, 46.3318], [-40.1637, 17.9691, 46.3318], [-40.196, 17.8964, 44.3333], [-32.8876, 14.6425, 44.3333], [-32.8553, 14.7152, 46.3318], [-31.9417, 14.3084, 46.3318], [-32.0064, 14.1631, 42.3349]], [[-44.0332, 9.27825, 42.6682], [-44.0001, 9.4338, 46.6651], [-43.022, 9.22589, 46.6651], [-43.0385, 9.14811, 44.6667], [-35.2133, 7.48482, 44.6667], [-35.1968, 7.5626, 46.6651], [-34.2186, 7.35469, 46.6651], [-34.2517, 7.19913, 42.6682]], [[-45, -0.0795146, 43.0016], [-45, 0.0795146, 46.9984], [-44, 0.0795146, 46.9984], [-44, 0, 45], [-36, 0, 45], [-36, 0.0795146, 46.9984], [-35, 0.0795146, 46.9984], [-35, -0.0795146, 43.0016]], [[-44.0001, -9.4338, 43.3349], [-44.0332, -9.27825, 47.3318], [-43.055, -9.07034, 47.3318], [-43.0385, -9.14811, 45.3333], [-35.2133, -7.48482, 45.3333], [-35.2298, -7.40704, 47.3318], [-34.2517, -7.19913, 47.3318], [-34.2186, -7.35469, 43.3349]], [[-41.0772, -18.3758, 43.6682], [-41.1419, -18.2305, 47.6651], [-40.2283, -17.8238, 47.6651], [-40.196, -17.8964, 45.6667], [-32.8876, -14.6425, 45.6667], [-32.92, -14.5699, 47.6651], [-32.0064, -14.1631, 47.6651], [-31.9417, -14.3084, 43.6682]], [[-36.359, -26.5147, 44.0016], [-36.4525, -26.386, 47.9984], [-35.6435, -25.7982, 47.9984], [-35.5967, -25.8626, 46], [-29.1246, -21.1603, 46], [-29.1713, -21.0959, 47.9984], [-28.3623, -20.5082, 47.9984], [-28.2689, -20.6368, 44.0016]], [[-30.0518, -33.4947, 44.3349], [-30.17, -33.3883, 48.3318], [-29.5008, -32.6452, 48.3318], [-29.4417, -32.6984, 46.3333], [-24.0887, -26.7532, 46.3333], [-24.1478, -26.7, 48.3318], [-23.4787, -25.9569, 48.3318], [-23.3605, -26.0633, 44.3349]], [[-22.4311, -39.0109, 44.6682], [-22.5689, -38.9314, 48.6651], [-22.0689, -38.0654, 48.6651], [-22, -38.1051, 46.6667], [-18, -31.1769, 46.6667], [-18.0689, -31.1372, 48.6651], [-17.5689, -30.2711, 48.6651], [-17.4311, -30.3506, 44.6682]], [[-13.8301, -42.8221, 45.0016], [-13.9814, -42.773, 48.9984], [-13.6724, -41.8219, 48.9984], [-13.5967, -41.8465, 47], [-11.1246, -34.238, 47], [-11.2002, -34.2135, 48.9984], [-10.8912, -33.2624, 48.9984], [-10.74, -33.3115, 45.0016]], [[-4.6247, -44.7618, 45.3349], [-4.78286, -44.7452, 49.3318], [-4.67833, -43.7507, 49.3318], [-4.59925, -43.759, 47.3333], [-3.76302, -35.8028, 47.3333], [-3.8421, -35.7945, 49.3318], [-3.73758, -34.8, 49.3318], [-3.57942, -34.8166, 45.3349]], [[4.78286, -44.7452, 45.6682], [4.6247, -44.7618, 49.6651], [4.52017, -43.7673, 49.6651], [4.59925, -43.759, 47.6667], [3.76302, -35.8028, 47.6667], [3.68395, -35.8111, 49.6651], [3.57942, -34.8166, 49.6651], [3.73758, -34.8, 45.6682]], [[13.9814, -42.773, 46.0016], [13.8301, -42.8221, 49.9984], [13.5211, -41.8711, 49.9984], [13.5967, -41.8465, 48], [11.1246, -34.238, 48], [11.049, -34.2626, 49.9984], [10.74, -33.3115, 49.9984], [10.8912, -33.2624, 46.0016]], [[22.5689, -38.9314, 46.3349], [22.4311, -39.0109, 50.3318], [21.9311, -38.1449, 50.3318], [22, -38.1051, 48.3333], [18, -31.1769, 48.3333], [17.9311, -31.2167, 50.3318], [17.4311, -30.3506, 50.3318], [17.5689, -30.2711, 46.3349]], [[30.17, -33.3883, 46.6682], [30.0518, -33.4947, 50.6651], [29.3827, -32.7516, 50.6651], [29.4417, -32.6984, 48.6667], [24.0887, -26.7532, 48.6667], [24.0296, -26.8064, 50.6651], [23.3605, -26.0633, 50.6651], [23.4787, -25.9569, 46.6682]], [[36.4525, -26.386, 47.0016], [36.359, -26.5147, 50.9984], [35.55, -25.9269, 50.9984], [35.5967, -25.8626, 49], [29.1246, -21.1603, 49], [29.0779, -21.2246, 50.9984], [28.2689, -20.6368, 50.9984], [28.3623, -20.5082, 47.0016]], [[41.1419, -18.2305, 47.3349], [41.0772, -18.3758, 51.3318], [40.1637, -17.9691, 51.3318], [40.196, -17.8964, 49.3333], [32.8876, -14.6425, 49.3333], [32.8553, -14.7152, 51.3318], [31.9417, -14.3084, 51.3318], [32.0064, -14.1631, 47.3349]], [[44.0332, -9.27825, 47.6682], [44.0001, -9.4338, 51.6651], [43.022, -9.22589, 51.6651], [43.0385, -9.14811, 49.6667], [35.2133, -7.48482, 49.6667], [35.1968, -7.5626, 51.6651], [34.2186, -7.35469, 51.6651], [34.2517, -7.19913, 47.6682]], [[45, 0.0795146, 48.0016], [45, -0.0795146, 51.9984], [44, -0.0795146, 51.9984], [44, 0, 50], [36, 0, 50], [36, -0.0795146, 51.9984], [35, -0.0795146, 51.9984], [35, 0.0795146, 48.0016]]]; for(i = [0:len(expected) - 1]) { - assertEqualPoints(expected[i], sections[i], float_digits = 3); + assertEqualPoints(expected[i], sections[i]); } } @@ -202,162 +46,10 @@ module test_helix_extrude_diff_radius() { include ; module test_helix_extrude(sections) { - expected = [ - [[50, 0.08, -1.998], [50, -0.08, 1.998], [49, -0.08, 1.998], [49, 0, 0], [41, 0, 0], [41, -0.08, 1.998], [40, -0.08, 1.998], [40, 0.08, -1.998]] - , [[48.76, 10.446, -1.665], [48.793, 10.29, 2.332], [47.815, 10.082, 2.332], [47.799, 10.16, 0.333], [39.974, 8.497, 0.333], [39.99, 8.419, 2.332], [39.012, 8.211, 2.332], [38.979, 8.367, -1.665]] - , [[45.401, 20.301, -1.332], [45.466, 20.156, 2.665], [44.552, 19.749, 2.665], [44.52, 19.822, 0.667], [37.212, 16.568, 0.667], [37.244, 16.495, 2.665], [36.331, 16.088, 2.665], [36.266, 16.234, -1.332]] - , [[40.081, 29.218, -0.998], [40.174, 29.09, 2.998], [39.365, 28.502, 2.998], [39.318, 28.566, 1], [32.846, 23.864, 1], [32.893, 23.8, 2.998], [32.084, 23.212, 2.998], [31.99, 23.341, -0.998]] - , [[33.041, 36.814, -0.665], [33.159, 36.708, 3.332], [32.49, 35.965, 3.332], [32.431, 36.018, 1.333], [27.077, 30.073, 1.333], [27.137, 30.019, 3.332], [26.467, 29.276, 3.332], [26.349, 29.383, -0.665]] - , [[24.598, 42.764, -0.332], [24.736, 42.684, 3.665], [24.236, 41.818, 3.665], [24.167, 41.858, 1.667], [20.167, 34.93, 1.667], [20.236, 34.89, 3.665], [19.736, 34.024, 3.665], [19.598, 34.103, -0.332]] - , [[15.128, 46.817, 0.002], [15.279, 46.767, 3.998], [14.97, 45.816, 3.998], [14.895, 45.841, 2], [12.422, 38.232, 2], [12.498, 38.208, 3.998], [12.189, 37.257, 3.998], [12.038, 37.306, 0.002]] - , [[5.05, 48.806, 0.335], [5.208, 48.79, 4.332], [5.103, 47.795, 4.332], [5.024, 47.803, 2.333], [4.188, 39.847, 2.333], [4.267, 39.839, 4.332], [4.163, 38.844, 4.332], [4.004, 38.861, 0.335]] - , [[-5.194, 48.657, 0.668], [-5.036, 48.674, 4.665], [-4.931, 47.679, 4.665], [-5.01, 47.671, 2.667], [-4.174, 39.715, 2.667], [-4.095, 39.723, 4.665], [-3.991, 38.728, 4.665], [-4.149, 38.712, 0.668]] - , [[-15.156, 46.387, 1.002], [-15.004, 46.436, 4.998], [-14.695, 45.485, 4.998], [-14.771, 45.461, 3], [-12.299, 37.852, 3], [-12.223, 37.877, 4.998], [-11.914, 36.926, 4.998], [-12.065, 36.876, 1.002]] - , [[-24.402, 42.107, 1.335], [-24.264, 42.186, 5.332], [-23.764, 41.32, 5.332], [-23.833, 41.281, 3.333], [-19.833, 34.352, 3.333], [-19.764, 34.392, 5.332], [-19.264, 33.526, 5.332], [-19.402, 33.447, 1.335]] - , [[-32.534, 36.014, 1.668], [-32.416, 36.121, 5.665], [-31.747, 35.377, 5.665], [-31.806, 35.324, 3.667], [-26.453, 29.379, 3.667], [-26.394, 29.432, 5.665], [-25.725, 28.689, 5.665], [-25.843, 28.583, 1.668]] - , [[-39.203, 28.384, 2.002], [-39.11, 28.513, 5.998], [-38.301, 27.925, 5.998], [-38.347, 27.861, 4], [-31.875, 23.159, 4], [-31.829, 23.223, 5.998], [-31.02, 22.635, 5.998], [-31.113, 22.507, 2.002]] - , [[-44.126, 19.559, 2.335], [-44.061, 19.704, 6.332], [-43.148, 19.298, 6.332], [-43.18, 19.225, 4.333], [-35.872, 15.971, 4.333], [-35.84, 16.044, 6.332], [-34.926, 15.637, 6.332], [-34.991, 15.492, 2.335]] - , [[-47.098, 9.93, 2.668], [-47.065, 10.085, 6.665], [-46.087, 9.877, 6.665], [-46.103, 9.8, 4.667], [-38.278, 8.136, 4.667], [-38.262, 8.214, 6.665], [-37.283, 8.006, 6.665], [-37.317, 7.851, 2.668]] - , [[-48, -0.08, 3.002], [-48, 0.08, 6.998], [-47, 0.08, 6.998], [-47, 0, 5], [-39, 0, 5], [-39, 0.08, 6.998], [-38, 0.08, 6.998], [-38, -0.08, 3.002]] - , [[-46.804, -10.03, 3.335], [-46.837, -9.874, 7.332], [-45.859, -9.666, 7.332], [-45.843, -9.744, 5.333], [-38.017, -8.081, 5.333], [-38.034, -8.003, 7.332], [-37.056, -7.795, 7.332], [-37.023, -7.951, 3.335]] - , [[-43.574, -19.488, 3.668], [-43.639, -19.342, 7.665], [-42.725, -18.936, 7.665], [-42.693, -19.008, 5.667], [-35.385, -15.754, 5.667], [-35.417, -15.682, 7.665], [-34.503, -15.275, 7.665], [-34.439, -15.42, 3.668]] - , [[-38.462, -28.043, 4.002], [-38.556, -27.914, 7.998], [-37.747, -27.326, 7.998], [-37.7, -27.391, 6], [-31.228, -22.689, 6], [-31.275, -22.624, 7.998], [-30.466, -22.036, 7.998], [-30.372, -22.165, 4.002]] - , [[-31.702, -35.328, 4.335], [-31.82, -35.221, 8.332], [-31.151, -34.478, 8.332], [-31.092, -34.531, 6.333], [-25.739, -28.586, 6.333], [-25.798, -28.533, 8.332], [-25.129, -27.79, 8.332], [-25.011, -27.896, 4.335]] - , [[-23.598, -41.032, 4.668], [-23.736, -40.952, 8.665], [-23.236, -40.086, 8.665], [-23.167, -40.126, 6.667], [-19.167, -33.198, 6.667], [-19.236, -33.158, 8.665], [-18.736, -32.292, 8.665], [-18.598, -32.371, 4.668]] - , [[-14.51, -44.914, 5.002], [-14.661, -44.865, 8.998], [-14.352, -43.914, 8.998], [-14.277, -43.939, 7], [-11.804, -36.33, 7], [-11.88, -36.306, 8.998], [-11.571, -35.355, 8.998], [-11.42, -35.404, 5.002]] - , [[-4.841, -46.817, 5.335], [-4.999, -46.801, 9.332], [-4.894, -45.806, 9.332], [-4.815, -45.814, 7.333], [-3.979, -37.858, 7.333], [-4.058, -37.85, 9.332], [-3.954, -36.855, 9.332], [-3.795, -36.872, 5.335]] - , [[4.985, -46.668, 5.668], [4.827, -46.685, 9.665], [4.722, -45.69, 9.665], [4.801, -45.682, 7.667], [3.965, -37.726, 7.667], [3.886, -37.734, 9.665], [3.782, -36.739, 9.665], [3.94, -36.723, 5.668]] - , [[14.538, -44.485, 6.002], [14.386, -44.534, 9.998], [14.077, -43.583, 9.998], [14.153, -43.558, 8], [11.681, -35.95, 8], [11.605, -35.975, 9.998], [11.296, -35.023, 9.998], [11.447, -34.974, 6.002]] - , [[23.402, -40.375, 6.335], [23.264, -40.454, 10.332], [22.764, -39.588, 10.332], [22.833, -39.548, 8.333], [18.833, -32.62, 8.333], [18.764, -32.66, 10.332], [18.264, -31.794, 10.332], [18.402, -31.715, 6.335]] - , [[31.196, -34.528, 6.668], [31.078, -34.634, 10.665], [30.409, -33.891, 10.665], [30.468, -33.838, 8.667], [25.115, -27.893, 8.667], [25.056, -27.946, 10.665], [24.386, -27.203, 10.665], [24.505, -27.096, 6.668]] - , [[37.585, -27.209, 7.002], [37.492, -27.338, 10.998], [36.683, -26.75, 10.998], [36.729, -26.685, 9], [30.257, -21.983, 9], [30.21, -22.047, 10.998], [29.401, -21.46, 10.998], [29.495, -21.331, 7.002]] - , [[42.299, -18.746, 7.335], [42.234, -18.891, 11.332], [41.321, -18.484, 11.332], [41.353, -18.412, 9.333], [34.045, -15.158, 9.333], [34.012, -15.23, 11.332], [33.099, -14.824, 11.332], [33.164, -14.678, 7.335]] - , [[45.142, -9.514, 7.668], [45.109, -9.669, 11.665], [44.131, -9.462, 11.665], [44.147, -9.384, 9.667], [36.322, -7.72, 9.667], [36.305, -7.798, 11.665], [35.327, -7.59, 11.665], [35.36, -7.435, 7.668]] - , [[46, 0.08, 8.002], [46, -0.08, 11.998], [45, -0.08, 11.998], [45, 0, 10], [37, 0, 10], [37, -0.08, 11.998], [36, -0.08, 11.998], [36, 0.08, 8.002]] - , [[44.848, 9.614, 8.335], [44.881, 9.458, 12.332], [43.903, 9.251, 12.332], [43.886, 9.328, 10.333], [36.061, 7.665, 10.333], [36.078, 7.587, 12.332], [35.099, 7.379, 12.332], [35.066, 7.535, 8.335]] - , [[41.747, 18.674, 8.668], [41.812, 18.529, 12.665], [40.898, 18.122, 12.665], [40.866, 18.195, 10.667], [33.558, 14.941, 10.667], [33.59, 14.868, 12.665], [32.676, 14.461, 12.665], [32.612, 14.607, 8.668]] - , [[36.844, 26.867, 9.002], [36.938, 26.739, 12.998], [36.129, 26.151, 12.998], [36.082, 26.215, 11], [29.61, 21.513, 11], [29.657, 21.449, 12.998], [28.848, 20.861, 12.998], [28.754, 20.989, 9.002]] - , [[30.364, 33.842, 9.335], [30.482, 33.735, 13.332], [29.813, 32.992, 13.332], [29.754, 33.045, 11.333], [24.401, 27.1, 11.333], [24.46, 27.047, 13.332], [23.791, 26.304, 13.332], [23.673, 26.41, 9.335]] - , [[22.598, 39.3, 9.668], [22.736, 39.22, 13.665], [22.236, 38.354, 13.665], [22.167, 38.394, 11.667], [18.167, 31.466, 11.667], [18.236, 31.426, 13.665], [17.736, 30.56, 13.665], [17.598, 30.639, 9.668]] - , [[13.892, 43.012, 10.002], [14.043, 42.963, 13.998], [13.734, 42.012, 13.998], [13.659, 42.037, 12], [11.186, 34.428, 12], [11.262, 34.404, 13.998], [10.953, 33.453, 13.998], [10.802, 33.502, 10.002]] - , [[4.632, 44.828, 10.335], [4.79, 44.811, 14.332], [4.685, 43.817, 14.332], [4.606, 43.825, 12.333], [3.77, 35.869, 12.333], [3.849, 35.861, 14.332], [3.745, 34.866, 14.332], [3.586, 34.883, 10.335]] - , [[-4.776, 44.679, 10.668], [-4.618, 44.695, 14.665], [-4.513, 43.701, 14.665], [-4.592, 43.693, 12.667], [-3.756, 35.736, 12.667], [-3.677, 35.745, 14.665], [-3.572, 34.75, 14.665], [-3.731, 34.734, 10.668]] - , [[-13.92, 42.583, 11.002], [-13.768, 42.632, 14.998], [-13.459, 41.681, 14.998], [-13.535, 41.656, 13], [-11.063, 34.048, 13], [-10.987, 34.072, 14.998], [-10.678, 33.121, 14.998], [-10.829, 33.072, 11.002]] - , [[-22.402, 38.643, 11.335], [-22.264, 38.722, 15.332], [-21.764, 37.856, 15.332], [-21.833, 37.816, 13.333], [-17.833, 30.888, 13.333], [-17.764, 30.928, 15.332], [-17.264, 30.062, 15.332], [-17.402, 29.982, 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35.998], [-28.639, 20.808, 34], [-22.167, 16.105, 34], [-22.12, 16.17, 35.998], [-21.311, 15.582, 35.998], [-21.405, 15.453, 32.002]] - , [[-33.164, 14.678, 32.335], [-33.099, 14.824, 36.332], [-32.185, 14.417, 36.332], [-32.218, 14.344, 34.333], [-24.909, 11.09, 34.333], [-24.877, 11.163, 36.332], [-23.963, 10.756, 36.332], [-24.028, 10.611, 32.335]] - , [[-35.36, 7.435, 32.668], [-35.327, 7.59, 36.665], [-34.349, 7.382, 36.665], [-34.366, 7.305, 34.667], [-26.54, 5.641, 34.667], [-26.524, 5.719, 36.665], [-25.546, 5.511, 36.665], [-25.579, 5.356, 32.668]] - , [[-36, -0.08, 33.002], [-36, 0.08, 36.998], [-35, 0.08, 36.998], [-35, 0, 35], [-27, 0, 35], [-27, 0.08, 36.998], [-26, 0.08, 36.998], [-26, -0.08, 33.002]] - , [[-35.066, -7.535, 33.335], [-35.099, -7.379, 37.332], [-34.121, -7.171, 37.332], [-34.105, -7.249, 35.333], [-26.28, -5.586, 35.333], [-26.296, -5.508, 37.332], [-25.318, -5.3, 37.332], [-25.285, -5.456, 33.335]] - , [[-32.612, -14.607, 33.668], [-32.676, -14.461, 37.665], [-31.763, -14.055, 37.665], [-31.73, -14.127, 35.667], [-24.422, -10.873, 35.667], [-24.454, -10.801, 37.665], [-23.541, -10.394, 37.665], [-23.476, -10.539, 33.668]] - , [[-28.754, -20.989, 34.002], [-28.848, -20.861, 37.998], [-28.039, -20.273, 37.998], [-27.992, -20.337, 36], [-21.52, -15.635, 36], [-21.567, -15.571, 37.998], [-20.758, -14.983, 37.998], [-20.664, -15.112, 34.002]] - , [[-23.673, -26.41, 34.335], [-23.791, -26.304, 38.332], [-23.122, -25.561, 38.332], [-23.063, -25.614, 36.333], [-17.71, -19.669, 36.333], [-17.769, -19.615, 38.332], [-17.1, -18.872, 38.332], [-16.981, -18.979, 34.335]] - , [[-17.598, -30.639, 34.668], [-17.736, -30.56, 38.665], [-17.236, -29.694, 38.665], [-17.167, -29.734, 36.667], [-13.167, -22.805, 36.667], [-13.236, -22.766, 38.665], [-12.736, -21.9, 38.665], [-12.598, -21.979, 34.668]] - , [[-10.802, -33.502, 35.002], [-10.953, -33.453, 38.998], [-10.644, -32.502, 38.998], [-10.568, -32.526, 37], [-8.096, -24.918, 37], [-8.172, -24.893, 38.998], [-7.863, -23.942, 38.998], [-7.712, -23.991, 35.002]] - , [[-3.586, -34.883, 35.335], [-3.745, -34.866, 39.332], [-3.64, -33.872, 39.332], [-3.561, -33.88, 37.333], [-2.725, -25.924, 37.333], [-2.804, -25.916, 39.332], [-2.699, -24.921, 39.332], [-2.541, -24.938, 35.335]] - , [[3.731, -34.734, 35.668], [3.572, -34.75, 39.665], [3.468, -33.756, 39.665], [3.547, -33.747, 37.667], [2.711, -25.791, 37.667], [2.632, -25.8, 39.665], [2.527, -24.805, 39.665], [2.685, -24.788, 35.668]] - , [[10.829, -33.072, 36.002], [10.678, -33.121, 39.998], [10.369, -32.17, 39.998], [10.445, -32.146, 38], [7.973, -24.537, 38], [7.897, -24.562, 39.998], [7.588, -23.611, 39.998], [7.739, -23.562, 36.002]] - , [[17.402, -29.982, 36.335], [17.264, -30.062, 40.332], [16.764, -29.196, 40.332], [16.833, -29.156, 38.333], [12.833, -22.228, 38.333], [12.764, -22.268, 40.332], [12.264, -21.402, 40.332], [12.402, -21.322, 36.335]] - , [[23.166, -25.61, 36.668], [23.048, -25.716, 40.665], [22.379, -24.973, 40.665], [22.438, -24.92, 38.667], [17.085, -18.975, 38.667], [17.026, -19.028, 40.665], [16.357, -18.285, 40.665], [16.475, -18.179, 36.668]] - , [[27.877, -20.155, 37.002], [27.783, -20.284, 40.998], [26.974, -19.696, 40.998], [27.021, -19.632, 39], [20.549, -14.93, 39], [20.502, -14.994, 40.998], [19.693, -14.406, 40.998], [19.787, -14.278, 37.002]] - , [[31.336, -13.865, 37.335], [31.272, -14.01, 41.332], [30.358, -13.603, 41.332], [30.391, -13.531, 39.333], [23.082, -10.277, 39.333], [23.05, -10.35, 41.332], [22.136, -9.943, 41.332], [22.201, -9.798, 37.335]] - , [[33.404, -7.019, 37.668], [33.371, -7.174, 41.665], [32.393, -6.967, 41.665], [32.409, -6.889, 39.667], [24.584, -5.226, 39.667], [24.568, -5.303, 41.665], [23.589, -5.095, 41.665], [23.622, -4.94, 37.668]] - , [[34, 0.08, 38.002], [34, -0.08, 41.998], [33, -0.08, 41.998], [33, 0, 40], [25, 0, 40], [25, -0.08, 41.998], [24, -0.08, 41.998], [24, 0.08, 38.002]] - , [[33.11, 7.119, 38.335], [33.143, 6.963, 42.332], [32.165, 6.756, 42.332], [32.148, 6.833, 40.333], [24.323, 5.17, 40.333], [24.34, 5.092, 42.332], [23.362, 4.884, 42.332], [23.329, 5.04, 38.335]] - , [[30.785, 13.793, 38.668], [30.849, 13.648, 42.665], [29.936, 13.241, 42.665], [29.903, 13.314, 40.667], [22.595, 10.06, 40.667], [22.627, 9.987, 42.665], [21.714, 9.581, 42.665], [21.649, 9.726, 38.668]] - , [[27.136, 19.814, 39.002], [27.23, 19.685, 42.998], [26.421, 19.097, 42.998], [26.374, 19.162, 41], [19.902, 14.46, 41], [19.949, 14.395, 42.998], [19.14, 13.807, 42.998], [19.046, 13.936, 39.002]] - , [[22.334, 24.924, 39.335], [22.453, 24.817, 43.332], [21.784, 24.074, 43.332], [21.724, 24.127, 41.333], [16.371, 18.182, 41.333], [16.43, 18.129, 43.332], [15.761, 17.386, 43.332], [15.643, 17.492, 39.335]] - , [[16.598, 28.907, 39.668], [16.736, 28.828, 43.665], [16.236, 27.962, 43.665], [16.167, 28.001, 41.667], [12.167, 21.073, 41.667], [12.236, 21.034, 43.665], [11.736, 20.168, 43.665], [11.598, 20.247, 39.668]] - , [[10.184, 31.6, 40.002], [10.335, 31.551, 43.998], [10.026, 30.599, 43.998], [9.95, 30.624, 42], [7.478, 23.016, 42], [7.554, 22.991, 43.998], [7.245, 22.04, 43.998], [7.094, 22.089, 40.002]] - , [[3.377, 32.894, 40.335], [3.535, 32.877, 44.332], [3.431, 31.883, 44.332], [3.352, 31.891, 42.333], [2.516, 23.935, 42.333], [2.595, 23.927, 44.332], [2.49, 22.932, 44.332], [2.332, 22.949, 40.335]] - , [[-3.522, 32.745, 40.668], [-3.363, 32.761, 44.665], [-3.259, 31.767, 44.665], [-3.338, 31.758, 42.667], [-2.502, 23.802, 42.667], [-2.423, 23.811, 44.665], [-2.318, 22.816, 44.665], [-2.476, 22.799, 40.668]] - , [[-10.211, 31.17, 41.002], [-10.06, 31.219, 44.998], [-9.751, 30.268, 44.998], [-9.827, 30.244, 43], [-7.355, 22.635, 43], [-7.279, 22.66, 44.998], [-6.97, 21.709, 44.998], [-7.121, 21.66, 41.002]] - , [[-16.402, 28.25, 41.335], [-16.264, 28.33, 45.332], [-15.764, 27.464, 45.332], [-15.833, 27.424, 43.333], [-11.833, 20.496, 43.333], [-11.764, 20.536, 45.332], [-11.264, 19.67, 45.332], [-11.402, 19.59, 41.335]] - , [[-21.828, 24.124, 41.668], [-21.71, 24.23, 45.665], [-21.041, 23.487, 45.665], [-21.1, 23.434, 43.667], [-15.747, 17.489, 43.667], [-15.688, 17.542, 45.665], [-15.019, 16.799, 45.665], [-15.137, 16.692, 41.668]] - , [[-26.259, 18.98, 42.002], [-26.165, 19.109, 45.998], [-25.356, 18.521, 45.998], [-25.403, 18.456, 44], [-18.931, 13.754, 44], [-18.884, 13.819, 45.998], [-18.075, 13.231, 45.998], [-18.169, 13.102, 42.002]] - , [[-29.509, 13.051, 42.335], [-29.445, 13.197, 46.332], [-28.531, 12.79, 46.332], [-28.564, 12.717, 44.333], [-21.255, 9.463, 44.333], [-21.223, 9.536, 46.332], [-20.309, 9.129, 46.332], [-20.374, 8.984, 42.335]] - , [[-31.448, 6.603, 42.668], [-31.415, 6.759, 46.665], [-30.436, 6.551, 46.665], [-30.453, 6.473, 44.667], [-22.628, 4.81, 44.667], [-22.611, 4.887, 46.665], [-21.633, 4.68, 46.665], [-21.666, 4.524, 42.668]] - , [[-32, -0.08, 43.002], [-32, 0.08, 46.998], [-31, 0.08, 46.998], [-31, 0, 45], [-23, 0, 45], [-23, 0.08, 46.998], [-22, 0.08, 46.998], [-22, -0.08, 43.002]] - , [[-31.154, -6.703, 43.335], [-31.187, -6.548, 47.332], [-30.209, -6.34, 47.332], [-30.192, -6.418, 45.333], [-22.367, -4.754, 45.333], [-22.384, -4.676, 47.332], [-21.405, -4.469, 47.332], [-21.372, -4.624, 43.335]] - , [[-28.958, -12.98, 43.668], [-29.022, -12.834, 47.665], [-28.109, -12.428, 47.665], [-28.076, -12.5, 45.667], [-20.768, -9.246, 45.667], [-20.8, -9.174, 47.665], [-19.887, -8.767, 47.665], [-19.822, -8.912, 43.668]] - , [[-25.518, -18.638, 44.002], [-25.612, -18.51, 47.998], [-24.803, -17.922, 47.998], [-24.756, -17.986, 46], [-18.284, -13.284, 46], [-18.331, -13.22, 47.998], [-17.522, -12.632, 47.998], [-17.428, -12.76, 44.002]] - , [[-20.996, -23.437, 44.335], [-21.114, -23.331, 48.332], [-20.445, -22.588, 48.332], [-20.386, -22.641, 46.333], [-15.033, -16.696, 46.333], [-15.092, -16.643, 48.332], [-14.423, -15.9, 48.332], [-14.305, -16.006, 44.335]] - , [[-15.598, -27.175, 44.668], [-15.736, -27.096, 48.665], [-15.236, -26.23, 48.665], [-15.167, -26.269, 46.667], [-11.167, -19.341, 46.667], [-11.236, -19.301, 48.665], [-10.736, -18.435, 48.665], [-10.598, -18.515, 44.668]] - , [[-9.566, -29.698, 45.002], [-9.717, -29.648, 48.998], [-9.408, -28.697, 48.998], [-9.332, -28.722, 47], [-6.86, -21.113, 47], [-6.936, -21.089, 48.998], [-6.627, -20.138, 48.998], [-6.476, -20.187, 45.002]] - , [[-3.168, -30.905, 45.335], [-3.326, -30.888, 49.332], [-3.222, -29.894, 49.332], [-3.143, -29.902, 47.333], [-2.307, -21.946, 47.333], [-2.386, -21.937, 49.332], [-2.281, -20.943, 49.332], [-2.123, -20.96, 45.335]] - , [[3.312, -30.756, 45.668], [3.154, -30.772, 49.665], [3.05, -29.778, 49.665], [3.129, -29.769, 47.667], [2.293, -21.813, 47.667], [2.214, -21.821, 49.665], [2.109, -20.827, 49.665], [2.267, -20.81, 45.668]] - , [[9.593, -29.268, 46.002], [9.442, -29.317, 49.998], [9.133, -28.366, 49.998], [9.209, -28.341, 48], [6.737, -20.733, 48], [6.661, -20.758, 49.998], [6.352, -19.807, 49.998], [6.503, -19.757, 46.002]] - , [[15.402, -26.518, 46.335], [15.264, -26.598, 50.332], [14.764, -25.732, 50.332], [14.833, -25.692, 48.333], [10.833, -18.764, 48.333], [10.764, -18.804, 50.332], [10.264, -17.938, 50.332], [10.402, -17.858, 46.335]] - , [[20.49, -22.637, 46.668], [20.372, -22.744, 50.665], [19.703, -22.001, 50.665], [19.762, -21.948, 48.667], [14.409, -16.002, 48.667], [14.35, -16.056, 50.665], [13.68, -15.312, 50.665], [13.799, -15.206, 46.668]] - , [[24.641, -17.804, 47.002], [24.547, -17.933, 50.998], [23.738, -17.345, 50.998], [23.785, -17.281, 49], [17.313, -12.579, 49], [17.266, -12.643, 50.998], [16.457, -12.055, 50.998], [16.551, -11.926, 47.002]] - , [[27.682, -12.238, 47.335], [27.618, -12.383, 51.332], [26.704, -11.976, 51.332], [26.736, -11.904, 49.333], [19.428, -8.65, 49.333], [19.396, -8.723, 51.332], [18.482, -8.316, 51.332], [18.547, -8.171, 47.335]] - , [[29.491, -6.187, 47.668], [29.458, -6.343, 51.665], [28.48, -6.135, 51.665], [28.497, -6.057, 49.667], [20.672, -4.394, 49.667], [20.655, -4.472, 51.665], [19.677, -4.264, 51.665], [19.71, -4.108, 47.668]] - , [[30, 0.08, 48.002], [30, -0.08, 51.998], [29, -0.08, 51.998], [29, 0, 50], [21, 0, 50], [21, -0.08, 51.998], [20, -0.08, 51.998], [20, 0.08, 48.002]] - ]; + expected = [[[50, 0.0795146, -1.99842], [50, -0.0795146, 1.99842], [49, -0.0795146, 1.99842], [49, 0, 0], [41, 0, 0], [41, -0.0795146, 1.99842], [40, -0.0795146, 1.99842], [40, 0.0795146, -1.99842]], [[48.7604, 10.4456, -1.66509], [48.7935, 10.2901, 2.33175], [47.8153, 10.0822, 2.33175], [47.7988, 10.16, 0.333333], [39.9736, 8.49666, 0.333333], [39.9902, 8.41888, 2.33175], [39.012, 8.21097, 2.33175], [38.979, 8.36652, -1.66509]], [[45.4013, 20.301, -1.33175], [45.466, 20.1557, 2.66509], [44.5525, 19.749, 2.66509], [44.5201, 19.8216, 0.666667], [37.2118, 16.5677, 0.666667], [37.2441, 16.4951, 2.66509], [36.3305, 16.0884, 2.66509], [36.2659, 16.2336, -1.33175]], [[40.0805, 29.2185, -0.998419], [40.174, 29.0898, 2.99842], [39.365, 28.502, 2.99842], 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[2.52716, -24.8051, 39.6651], [2.68532, -24.7884, 35.6682]], [[10.8294, -33.0722, 36.0016], [10.6782, -33.1213, 39.9984], [10.3692, -32.1703, 39.9984], [10.4448, -32.1457, 38], [7.97264, -24.5373, 38], [7.89702, -24.5618, 39.9984], [7.588, -23.6108, 39.9984], [7.73924, -23.5616, 36.0016]], [[17.4022, -29.9825, 36.3349], [17.2645, -30.062, 40.3318], [16.7645, -29.1959, 40.3318], [16.8333, -29.1562, 38.3333], [12.8333, -22.228, 38.3333], [12.7645, -22.2677, 40.3318], [12.2645, -21.4017, 40.3318], [12.4022, -21.3222, 36.3349]], [[23.1664, -25.6101, 36.6682], [23.0482, -25.7165, 40.6651], [22.3791, -24.9733, 40.6651], [22.4382, -24.9201, 38.6667], [17.0851, -18.975, 38.6667], [17.026, -19.0282, 40.6651], [16.3569, -18.285, 40.6651], [16.4751, -18.1786, 36.6682]], [[27.8769, -20.1555, 37.0016], [27.7834, -20.2841, 40.9984], [26.9744, -19.6964, 40.9984], [27.0212, -19.632, 39], [20.549, -14.9297, 39], [20.5023, -14.9941, 40.9984], [19.6933, -14.4063, 40.9984], [19.7868, -14.2776, 37.0016]], [[31.3365, -13.8649, 37.3349], [31.2718, -14.0101, 41.3318], [30.3583, -13.6034, 41.3318], [30.3906, -13.5308, 39.3333], [23.0822, -10.2769, 39.3333], [23.0499, -10.3495, 41.3318], [22.1364, -9.94278, 41.3318], [22.201, -9.7975, 37.3349]], [[33.404, -7.01894, 37.6682], [33.3709, -7.1745, 41.6651], [32.3928, -6.96658, 41.6651], [32.4093, -6.88881, 39.6667], [24.5841, -5.22551, 39.6667], [24.5676, -5.30329, 41.6651], [23.5894, -5.09538, 41.6651], [23.6225, -4.93983, 37.6682]], [[34, 0.0795146, 38.0016], [34, -0.0795146, 41.9984], [33, -0.0795146, 41.9984], [33, 0, 40], [25, 0, 40], [25, -0.0795146, 41.9984], [24, -0.0795146, 41.9984], [24, 0.0795146, 38.0016]], [[33.1101, 7.11905, 38.3349], [33.1431, 6.9635, 42.3318], [32.165, 6.75559, 42.3318], [32.1485, 6.83336, 40.3333], [24.3233, 5.17007, 40.3333], [24.3398, 5.09229, 42.3318], [23.3617, 4.88438, 42.3318], [23.3286, 5.03994, 38.3349]], [[30.7846, 13.7932, 38.6682], [30.8493, 13.6479, 42.6651], [29.9357, 13.2412, 42.6651], [29.9034, 13.3138, 40.6667], [22.595, 10.06, 40.6667], [22.6274, 9.98731, 42.6651], [21.7138, 9.58058, 42.6651], [21.6491, 9.72586, 38.6682]], [[27.1362, 19.8139, 39.0016], [27.2297, 19.6853, 42.9984], [26.4207, 19.0975, 42.9984], [26.374, 19.1618, 41], [19.9018, 14.4595, 41], [19.9486, 14.3952, 42.9984], [19.1395, 13.8074, 42.9984], [19.0461, 13.9361, 39.0016]], [[22.3345, 24.9238, 39.3349], [22.4527, 24.8174, 43.3318], [21.7835, 24.0742, 43.3318], [21.7244, 24.1274, 41.3333], [16.3714, 18.1823, 41.3333], [16.4305, 18.1291, 43.3318], [15.7614, 17.3859, 43.3318], [15.6432, 17.4923, 39.3349]], [[16.5978, 28.9073, 39.6682], [16.7355, 28.8278, 43.6651], [16.2355, 27.9617, 43.6651], [16.1667, 28.0015, 41.6667], [12.1667, 21.0733, 41.6667], [12.2355, 21.0335, 43.6651], [11.7355, 20.1675, 43.6651], [11.5978, 20.247, 39.6682]], [[10.1837, 31.5996, 40.0016], [10.335, 31.5505, 43.9984], [10.026, 30.5994, 43.9984], [9.95035, 30.624, 42], [7.47821, 23.0156, 42], [7.55383, 22.991, 43.9984], [7.24482, 22.0399, 43.9984], [7.09357, 22.0891, 40.0016]], [[3.37733, 32.8938, 40.3349], [3.53549, 32.8772, 44.3318], [3.43096, 31.8827, 44.3318], [3.35188, 31.891, 42.3333], [2.51565, 23.9348, 42.3333], [2.59473, 23.9265, 44.3318], [2.4902, 22.932, 44.3318], [2.33204, 22.9486, 40.3349]], [[-3.52155, 32.7446, 40.6682], [-3.36339, 32.7612, 44.6651], [-3.25886, 31.7667, 44.6651], [-3.33794, 31.7584, 42.6667], [-2.50171, 23.8022, 42.6667], [-2.42264, 23.8105, 44.6651], [-2.31811, 22.816, 44.6651], [-2.47627, 22.7994, 40.6682]], [[-10.2114, 31.1701, 41.0016], [-10.0601, 31.2192, 44.9984], [-9.75112, 30.2682, 44.9984], [-9.82674, 30.2436, 43], [-7.3546, 22.6351, 43], [-7.27898, 22.6597, 44.9984], [-6.96996, 21.7087, 44.9984], [-7.12121, 21.6595, 41.0016]], [[-16.4022, 28.2504, 41.3349], [-16.2645, 28.3299, 45.3318], [-15.7645, 27.4639, 45.3318], [-15.8333, 27.4241, 43.3333], [-11.8333, 20.4959, 43.3333], [-11.7645, 20.5357, 45.3318], [-11.2645, 19.6697, 45.3318], [-11.4022, 19.5902, 41.3349]], [[-21.8281, 24.1238, 41.6682], [-21.71, 24.2302, 45.6651], [-21.0408, 23.487, 45.6651], [-21.0999, 23.4338, 43.6667], [-15.7469, 17.4887, 43.6667], [-15.6878, 17.5419, 45.6651], [-15.0187, 16.7987, 45.6651], [-15.1368, 16.6923, 41.6682]], [[-26.2589, 18.9799, 42.0016], [-26.1654, 19.1086, 45.9984], [-25.3564, 18.5208, 45.9984], [-25.4031, 18.4565, 44], [-18.931, 13.7542, 44], [-18.8843, 13.8185, 45.9984], [-18.0752, 13.2307, 45.9984], [-18.1687, 13.1021, 42.0016]], [[-29.5094, 13.0514, 42.3349], [-29.4447, 13.1967, 46.3318], [-28.5312, 12.7899, 46.3318], [-28.5635, 12.7173, 44.3333], [-21.2552, 9.46341, 44.3333], [-21.2228, 9.53605, 46.3318], [-20.3093, 9.12931, 46.3318], [-20.374, 8.98403, 42.3349]], [[-31.4477, 6.60312, 42.6682], [-31.4146, 6.75867, 46.6651], [-30.4365, 6.55076, 46.6651], [-30.453, 6.47298, 44.6667], [-22.6278, 4.80969, 44.6667], [-22.6113, 4.88747, 46.6651], [-21.6331, 4.67956, 46.6651], [-21.6662, 4.524, 42.6682]], [[-32, -0.0795146, 43.0016], [-32, 0.0795146, 46.9984], [-31, 0.0795146, 46.9984], [-31, 0, 45], [-23, 0, 45], [-23, 0.0795146, 46.9984], [-22, 0.0795146, 46.9984], [-22, -0.0795146, 43.0016]], [[-31.1538, -6.70323, 43.3349], [-31.1868, -6.54768, 47.3318], [-30.2087, -6.33976, 47.3318], [-30.1922, -6.41754, 45.3333], [-22.367, -4.75425, 45.3333], [-22.3835, -4.67647, 47.3318], [-21.4054, -4.46856, 47.3318], [-21.3723, -4.62411, 43.3349]], [[-28.9575, -12.9797, 43.6682], [-29.0222, -12.8345, 47.6651], [-28.1086, -12.4277, 47.6651], [-28.0763, -12.5004, 45.6667], [-20.7679, -9.24648, 45.6667], [-20.8003, -9.17384, 47.6651], [-19.8867, -8.7671, 47.6651], [-19.822, -8.91238, 43.6682]], [[-25.5182, -18.6383, 44.0016], [-25.6117, -18.5097, 47.9984], [-24.8027, -17.9219, 47.9984], [-24.7559, -17.9862, 46], [-18.2838, -13.2839, 46], [-18.3305, -13.2196, 47.9984], [-17.5215, -12.6318, 47.9984], [-17.428, -12.7605, 44.0016]], [[-20.9962, -23.4375, 44.3349], [-21.1144, -23.3311, 48.3318], [-20.4453, -22.5879, 48.3318], [-20.3862, -22.6411, 46.3333], [-15.0331, -16.696, 46.3333], [-15.0922, -16.6428, 48.3318], [-14.4231, -15.8996, 48.3318], [-14.3049, -16.006, 44.3349]], [[-15.5978, -27.1752, 44.6682], [-15.7355, -27.0957, 48.6651], [-15.2355, -26.2297, 48.6651], [-15.1667, -26.2694, 46.6667], [-11.1667, -19.3412, 46.6667], [-11.2355, -19.3015, 48.6651], [-10.7355, -18.4355, 48.6651], [-10.5978, -18.515, 44.6682]], [[-9.56571, -29.6975, 45.0016], [-9.71695, -29.6484, 48.9984], [-9.40794, -28.6973, 48.9984], [-9.33231, -28.7219, 47], [-6.86018, -21.1135, 47], [-6.9358, -21.0889, 48.9984], [-6.62678, -20.1378, 48.9984], [-6.47554, -20.187, 45.0016]], [[-3.16827, -30.9048, 45.3349], [-3.32643, -30.8882, 49.3318], [-3.2219, -29.8936, 49.3318], [-3.14282, -29.902, 47.3333], [-2.30659, -21.9458, 47.3333], [-2.38567, -21.9375, 49.3318], [-2.28115, -20.9429, 49.3318], [-2.12299, -20.9596, 45.3349]], [[3.31249, -30.7556, 45.6682], [3.15433, -30.7722, 49.6651], [3.04981, -29.7777, 49.6651], [3.12889, -29.7694, 47.6667], [2.29266, -21.8132, 47.6667], [2.21358, -21.8215, 49.6651], [2.10905, -20.827, 49.6651], [2.26721, -20.8103, 45.6682]], [[9.59335, -29.268, 46.0016], [9.4421, -29.3171, 49.9984], [9.13308, -28.3661, 49.9984], [9.20871, -28.3415, 48], [6.73657, -20.733, 48], [6.66095, -20.7576, 49.9984], [6.35193, -19.8065, 49.9984], [6.50318, -19.7574, 46.0016]], [[15.4022, -26.5184, 46.3349], [15.2645, -26.5979, 50.3318], [14.7645, -25.7318, 50.3318], [14.8333, -25.6921, 48.3333], [10.8333, -18.7639, 48.3333], [10.7645, -18.8036, 50.3318], [10.2645, -17.9376, 50.3318], [10.4022, -17.8581, 46.3349]], [[20.4899, -22.6375, 46.6682], [20.3717, -22.7439, 50.6651], [19.7026, -22.0007, 50.6651], [19.7617, -21.9475, 48.6667], [14.4086, -16.0024, 48.6667], [14.3495, -16.0556, 50.6651], [13.6804, -15.3124, 50.6651], [13.7986, -15.206, 46.6682]], [[24.6409, -17.8043, 47.0016], [24.5474, -17.933, 50.9984], [23.7384, -17.3452, 50.9984], [23.7851, -17.2809, 49], [17.313, -12.5786, 49], [17.2662, -12.6429, 50.9984], [16.4572, -12.0551, 50.9984], [16.5507, -11.9265, 47.0016]], [[27.6823, -12.2379, 47.3349], [27.6176, -12.3832, 51.3318], [26.7041, -11.9765, 51.3318], [26.7364, -11.9038, 49.3333], [19.4281, -8.64993, 49.3333], [19.3957, -8.72257, 51.3318], [18.4822, -8.31584, 51.3318], [18.5469, -8.17056, 47.3349]], [[29.4914, -6.1873, 47.6682], [29.4583, -6.34285, 51.6651], [28.4802, -6.13494, 51.6651], [28.4967, -6.05716, 49.6667], [20.6715, -4.39387, 49.6667], [20.655, -4.47164, 51.6651], [19.6768, -4.26373, 51.6651], [19.7099, -4.10818, 47.6682]], [[30, 0.0795146, 48.0016], [30, -0.0795146, 51.9984], [29, -0.0795146, 51.9984], [29, 0, 50], [21, 0, 50], [21, -0.0795146, 51.9984], [20, -0.0795146, 51.9984], [20, 0.0795146, 48.0016]]]; for(i = [0:len(sections) - 1]) { - assertEqualPoints(expected[i], sections[i], float_digits = 3); + assertEqualPoints(expected[i], sections[i]); } } diff --git a/test/test_hexagons.scad b/test/test_hexagons.scad index ed599162..2650d48d 100644 --- a/test/test_hexagons.scad +++ b/test/test_hexagons.scad @@ -10,7 +10,7 @@ module test_hexagons_lv2() { include ; module test_each_hexagon(hex_r, pts_all_lines) { - assertEqual(19, hex_r); + assertEqualNum(19, hex_r); expects = [ [[-34.641, 0], [0, 0], [34.641, 0]], @@ -40,7 +40,7 @@ module test_hexagons_lv3() { include ; module test_each_hexagon(hex_r, pts_all_lines) { - assertEqual(19, hex_r); + assertEqualNum(19, hex_r); expects = [ [[-69.282, 0], [-34.641, 0], [0, 0], [34.641, 0], [69.282, 0]], diff --git a/test/test_hull_polyline2d.scad b/test/test_hull_polyline2d.scad index f2e9b074..961d9f49 100644 --- a/test/test_hull_polyline2d.scad +++ b/test/test_hull_polyline2d.scad @@ -12,7 +12,7 @@ module test_hull_polyline2d() { module test_line_segment(index, point1, point2, radius) { assertEqualPoint(points[index - 1], point1); assertEqualPoint(points[index], point2); - assertEqual(line_width, radius * 2); + assertEqualNum(line_width, radius * 2); } hull_polyline2d( diff --git a/test/test_hull_polyline3d.scad b/test/test_hull_polyline3d.scad index 95811be6..8c6337c0 100644 --- a/test/test_hull_polyline3d.scad +++ b/test/test_hull_polyline3d.scad @@ -17,7 +17,7 @@ module test_hull_polyline3d() { module test_line_segment(index, point1, point2, radius) { assertEqualPoint(points[index - 1], point1); assertEqualPoint(points[index], point2); - assertEqual(thickness, radius * 2); + assertEqualNum(thickness, radius * 2); } hull_polyline3d( @@ -47,7 +47,7 @@ module test_hull_polyline3d_helix() { module test_line_segment(index, point1, point2, radius) { assertEqualPoint(points[index - 1], point1); assertEqualPoint(points[index], point2); - assertEqual(thickness, radius * 2); + assertEqualNum(thickness, radius * 2); } for(i = [0:7]) { diff --git a/test/test_in_polyline.scad b/test/test_in_polyline.scad new file mode 100644 index 00000000..6a247a9c --- /dev/null +++ b/test/test_in_polyline.scad @@ -0,0 +1,31 @@ +include ; + +module test_in_polyline() { + + + echo("==== test_in_polyline ===="); + + pts = [ + [0, 0], + [10, 0], + [10, 10] + ]; + + assert(!in_polyline(pts, [-2, -3])); + assert(in_polyline(pts, [5, 0])); + assert(in_polyline(pts, [10, 5])); + assert(!in_polyline(pts, [10, 15])); + + pts2 = [ + [10, 0, 10], + [20, 0, 10], + [20, 10, 10] + ]; + + assert(in_polyline(pts2, [10, 0, 10])); + assert(in_polyline(pts2, [15, 0, 10])); + assert(!in_polyline(pts2, [15, 1, 10])); + assert(!in_polyline(pts2, [20, 11, 10])); +} + +test_in_polyline(); \ No newline at end of file diff --git a/test/test_line2d.scad b/test/test_line2d.scad index 0cda2d9b..a5e70b3b 100644 --- a/test/test_line2d.scad +++ b/test/test_line2d.scad @@ -12,17 +12,17 @@ module test_line2d() { include ; module test_line2d_cap(point, style) { - assertTrue( + assert( (point == p1 && style == "CAP_SQUARE") || (point == p2 && style == "CAP_SQUARE") ); } module test_line2d_line(angle, length, width, frags) { - assertEqual(0, angle); - assertEqual(5, length); - assertEqual(1, width); - assertEqual(24, frags); + assertEqualNum(0, angle); + assertEqualNum(5, length); + assertEqualNum(1, width); + assertEqualNum(24, frags); } line2d(p1 = p1, p2 = p2, width = width); @@ -34,17 +34,17 @@ module test_line2d() { include ; module test_line2d_cap(point, style) { - assertTrue( + assert( (point == p1 && style == "CAP_ROUND") || (point == p2 && style == "CAP_ROUND") ); } module test_line2d_line(angle, length, width, frags) { - assertEqual(0, angle); - assertEqual(5, length); - assertEqual(1, width); - assertEqual(24, frags); + assertEqualNum(0, angle); + assertEqualNum(5, length); + assertEqualNum(1, width); + assertEqualNum(24, frags); } line2d(p1 = p1, p2 = p2, width = width, @@ -57,17 +57,17 @@ module test_line2d() { include ; module test_line2d_cap(point, style) { - assertTrue( + assert( (point == p1 && style == "CAP_BUTT") || (point == p2 && style == "CAP_BUTT") ); } module test_line2d_line(angle, length, width, frags) { - assertEqual(0, angle); - assertEqual(5, length); - assertEqual(1, width); - assertEqual(24, frags); + assertEqualNum(0, angle); + assertEqualNum(5, length); + assertEqualNum(1, width); + assertEqualNum(24, frags); } line2d(p1 = p1, p2 = p2, width = width, diff --git a/test/test_line3d.scad b/test/test_line3d.scad index fc0ab185..53ccd07d 100644 --- a/test/test_line3d.scad +++ b/test/test_line3d.scad @@ -13,17 +13,17 @@ module test_line3d() { module test_line3d_butt(p, r, frags, length, angles) { assertEqualPoint(p1, p); - assertEqual(thickness / 2, r); - assertEqual(fn, frags); - assertEqual(14.2829, length); + assertEqualNum(thickness / 2, r); + assertEqualNum(fn, frags); + assertEqualNum(14.2829, length); assertEqualPoint([0, 45.5618, 11.3099], angles); } module test_line3d_cap(p, r, frags, cap_leng, angles) { - assertTrue(p == p1 || p == p2); - assertEqual(thickness / 2, r); - assertEqual(fn, frags); - assertEqual(0.3536, cap_leng); + assert(p == p1 || p == p2); + assertEqualNum(thickness / 2, r); + assertEqualNum(fn, frags); + assertEqualNum(0.3536, cap_leng); assertEqualPoint([0, 45.5618, 11.3099], angles); } @@ -43,9 +43,9 @@ module test_line3d() { module test_line3d_butt(p, r, frags, length, angles) { assertEqualPoint(p1, p); - assertEqual(thickness / 2, r); - assertEqual(fn, frags); - assertEqual(14.2829, length); + assertEqualNum(thickness / 2, r); + assertEqualNum(fn, frags); + assertEqualNum(14.2829, length); assertEqualPoint([0, 45.5618, 11.3099], angles); } @@ -70,17 +70,17 @@ module test_line3d() { module test_line3d_butt(p, r, frags, length, angles) { assertEqualPoint(p1, p); - assertEqual(thickness / 2, r); - assertEqual(fn, frags); - assertEqual(14.2829, length); + assertEqualNum(thickness / 2, r); + assertEqualNum(fn, frags); + assertEqualNum(14.2829, length); assertEqualPoint([0, 45.5618, 11.3099], angles); } module test_line3d_cap(p, r, frags, cap_leng, angles) { - assertTrue(p == p1 || p == p2); - assertEqual(thickness / 2, r); - assertEqual(fn, frags); - assertEqual(0.5043, cap_leng); + assert(p == p1 || p == p2); + assertEqualNum(thickness / 2, r); + assertEqualNum(fn, frags); + assertEqualNum(0.5043, cap_leng); assertEqualPoint([0, 45.5618, 11.3099], angles); } diff --git a/test/test_midpt_smooth.scad b/test/test_midpt_smooth.scad new file mode 100644 index 00000000..3e509c23 --- /dev/null +++ b/test/test_midpt_smooth.scad @@ -0,0 +1,17 @@ +module test_midpt_smooth() { + echo("==== test_midpt_smooth ===="); + + include ; + include ; + include ; + include ; + + taiwan = shape_taiwan(50); + + expected = [[10.63, 22.383], [10.1322, 22.6054], [9.65611, 22.8175], [9.26491, 23.013], [8.97805, 23.1879], [8.77136, 23.3444], [8.59924, 23.4932], [8.41804, 23.652], [8.19789, 23.835], [7.924, 24.0385], [7.59413, 24.2351], [7.21713, 24.3828], [6.81247, 24.4453], [6.40816, 24.4087], [6.03497, 24.2851], [5.71872, 24.1048], [5.47485, 23.9026], [5.3079, 23.7055], [5.21391, 23.5269], [5.18172, 23.3679], [5.19229, 23.2254], [5.2195, 23.1], [5.23557, 22.9985], [5.21927, 22.9287], [5.16157, 22.891], [5.06439, 22.8749], [4.93268, 22.862], [4.76432, 22.8332], [4.54436, 22.7749], [4.24956, 22.6813], [3.86392, 22.5547], [3.39557, 22.4027], [2.88008, 22.2349], [2.36299, 22.0574], [1.87426, 21.8686], [1.41628, 21.658], [0.974894, 21.4098], [0.541119, 21.1111], [0.123546, 20.7617], [-0.256239, 20.3801], [-0.57757, 19.9999], [-0.831844, 19.6571], [-1.02464, 19.3735], [-1.17023, 19.1499], [-1.28387, 18.9706], [-1.37709, 18.815], [-1.45723, 18.6666], [-1.52922, 18.5148], [-1.59737, 18.3511], [-1.66659, 18.1661], [-1.74309, 17.9513], [-1.8336, 17.7034], [-1.94287, 17.4279], [-2.07092, 17.1387], [-2.2128, 16.8525], [-2.36146, 16.5833], [-2.51212, 16.3396], [-2.66534, 16.1248], [-2.82654, 15.9391], [-3.00181, 15.7792], [-3.19204, 15.6373], [-3.39004, 15.5036], [-3.5836, 15.3697], [-3.76283, 15.232], [-3.92588, 15.0903], [-4.0786, 14.9424], [-4.22925, 14.7803], [-4.38325, 14.5908], [-4.54247, 14.3608], [-4.70892, 14.0825], [-4.88942, 13.7542], [-5.09632, 13.3761], [-5.34192, 12.9479], [-5.62904, 12.4699], [-5.94531, 11.9488], [-6.26697, 11.4003], [-6.57004, 10.8482], [-6.8408, 10.319], [-7.07929, 9.83461], [-7.29556, 9.40499], [-7.50157, 9.02568], [-7.70299, 8.68327], [-7.8959, 8.36475], [-8.07105, 8.0638], [-8.22214, 7.78104], [-8.35063, 7.52096], [-8.46345, 7.28875], [-8.56764, 7.0879], [-8.66778, 6.91778], [-8.76767, 6.77148], [-8.8725, 6.63422], [-8.98878, 6.48373], [-9.12206, 6.29465], [-9.27463, 6.04779], [-9.44449, 5.74017], [-9.62607, 5.38879], [-9.8122, 5.0234], [-9.99627, 4.67235], [-10.1735, 4.35116], [-10.3417, 4.06058], [-10.5018, 3.79242], [-10.6578, 3.53644], [-10.815, 3.28328], [-10.9767, 3.02401], [-11.1434, 2.74885], [-11.3138, 2.44761], [-11.4874, 2.11172], [-11.6632, 1.73693], [-11.8362, 1.32482], [-11.9945, 0.882597], [-12.1214, 0.421669], [-12.2029, -0.0435495], [-12.2351, -0.496003], [-12.2265, -0.917097], [-12.1943, -1.29055], [-12.1569, -1.60857], [-12.1266, -1.87687], [-12.1073, -2.1145], [-12.0967, -2.34759], [-12.0909, -2.59901], [-12.0875, -2.87817], [-12.0856, -3.17605], [-12.0861, -3.46997], [-12.0925, -3.73656], [-12.1112, -3.9645], [-12.1497, -4.15813], [-12.2116, -4.33142], [-12.2942, -4.49885], [-12.3892, -4.66958], [-12.4867, -4.84605], [-12.5789, -5.02531], [-12.6606, -5.20235], [-12.7288, -5.37373], [-12.7815, -5.53935], [-12.8185, -5.70088], [-12.8435, -5.85884], [-12.8642, -6.0113], [-12.8893, -6.1556], [-12.9224, -6.29146], [-12.9583, -6.42228], [-12.9864, -6.5533], [-12.9974, -6.68803], [-12.988, -6.82606], [-12.9604, -6.96409], [-12.9194, -7.09841], [-12.8724, -7.22642], [-12.831, -7.34645], [-12.8093, -7.45742], [-12.8148, -7.55961], [-12.8398, -7.65585], [-12.861, -7.75107], [-12.8495, -7.84998], [-12.7854, -7.95458], [-12.6653, -8.06416], [-12.5022, -8.17808], [-12.3198, -8.29903], [-12.1459, -8.43379], [-12.0041, -8.59081], [-11.906, -8.77737], [-11.8454, -8.99865], [-11.8024, -9.2581], [-11.7546, -9.55546], [-11.6892, -9.88234], [-11.6065, -10.2202], [-11.5161, -10.5458], [-11.4302, -10.8414], [-11.3573, -11.1035], [-11.2972, -11.3431], [-11.2405, -11.58], [-11.1731, -11.8332], [-11.0851, -12.1128], [-10.9782, -12.4156], [-10.866, -12.7285], [-10.7644, -13.0358], [-10.6807, -13.3279], [-10.6062, -13.6054], [-10.5197, -13.877], [-10.3986, -14.1556], [-10.231, -14.4518], [-10.019, -14.7696], [-9.7739, -15.1036], [-9.50815, -15.4379], [-9.23223, -15.7506], [-8.95555, -16.0226], [-8.68614, -16.2465], [-8.42687, -16.4312], [-8.17294, -16.5961], [-7.91555, -16.7611], [-7.64966, -16.9383], [-7.37826, -17.1308], [-7.10939, -17.3374], [-6.84962, -17.559], [-6.59971, -17.8041], [-6.35454, -18.091], [-6.10578, -18.4465], [-5.84646, -18.8977], [-5.57751, -19.4544], [-5.31332, -20.0928], [-5.07946, -20.7551], [-4.9004, -21.3738], [-4.78492, -21.9043], [-4.72093, -22.3411], [-4.6835, -22.7074], [-4.64854, -23.0316], [-4.60187, -23.3294], [-4.53922, -23.5999], [-4.46074, -23.8303], [-4.36578, -24.0055], [-4.25089, -24.1171], [-4.11027, -24.1713], [-3.93791, -24.1902], [-3.73176, -24.2033], [-3.49915, -24.2312], [-3.25921, -24.2714], [-3.03757, -24.2961], [-2.85466, -24.2676], [-2.71541, -24.1588], [-2.60844, -23.9622], [-2.5152, -23.6777], [-2.42195, -23.2904], [-2.32518, -22.7628], [-2.22734, -22.0581], [-2.12804, -21.1793], [-2.01909, -20.1875], [-1.88796, -19.1792], [-1.72615, -18.24], [-1.53476, -17.4131], [-1.32269, -16.7014], [-1.1003, -16.0884], [-0.874376, -15.5549], [-0.646564, -15.0844], [-0.412728, -14.6623], [-0.162371, -14.2745], [0.118432, -13.9069], [0.437826, -13.5483], [0.78743, -13.195], [1.13984, -12.8535], [1.45894, -12.5358], [1.71665, -12.2513], [1.90496, -11.9993], [2.03782, -11.7689], [2.14479, -11.5435], [2.26081, -11.3054], [2.41465, -11.0385], [2.61883, -10.731], [2.86575, -10.3772], [3.13293, -9.98036], [3.39433, -9.55373], [3.63087, -9.11958], [3.83492, -8.7049], [4.00901, -8.33342], [4.16189, -8.01644], [4.30401, -7.74663], [4.44318, -7.49923], [4.58137, -7.24097], [4.71483, -6.94304], [4.83826, -6.59181], [4.95091, -6.19061], [5.06067, -5.74888], [5.18352, -5.26098], [5.3388, -4.68715], [5.54274, -3.95538], [5.80235, -2.99549], [6.11142, -1.79066], [6.45018, -0.408993], [6.78998, 1.01337], [7.10169, 2.32818], [7.36418, 3.43108], [7.56883, 4.28566], [7.71799, 4.91335], [7.81921, 5.36711], [7.88006, 5.70627], [7.90757, 5.98122], [7.91202, 6.22881], [7.91038, 6.47525], [7.92429, 6.74011], [7.97288, 7.03653], [8.06507, 7.36705], [8.19695, 7.72015], [8.35563, 8.07296], [8.52631, 8.40133], [8.69826, 8.69143], [8.86757, 8.94609], [9.03639, 9.18305], [9.20865, 9.42694], [9.38396, 9.6985], [9.55407, 10.005], [9.70582, 10.3361], [9.82882, 10.6691], [9.92175, 10.9806], [9.9928, 11.2592], [10.0561, 11.5091], [10.1272, 11.7438], [10.2186, 11.9752], [10.3341, 12.206], [10.4653, 12.4299], [10.5932, 12.6382], [10.699, 12.8267], [10.7744, 12.9985], [10.8261, 13.1626], [10.8682, 13.3307], [10.9112, 13.512], [10.9562, 13.7092], [10.9981, 13.9164], [11.0333, 14.1208], [11.0602, 14.3088], [11.0751, 14.4742], [11.068, 14.6227], [11.0282, 14.7706], [10.9539, 14.9379], [10.8577, 15.1407], [10.7606, 15.3877], [10.6798, 15.6804], [10.6216, 16.0162], [10.5851, 16.3894], [10.5709, 16.7903], [10.5883, 17.2078], [10.6555, 17.6348], [10.7948, 18.0721], [11.0224, 18.5236], [11.3355, 18.9861], [11.7031, 19.441], [12.068, 19.8573], [12.3644, 20.2048], [12.5429, 20.4677], [12.5893, 20.6501], [12.5242, 20.7735], [12.3886, 20.8694], [12.2256, 20.9704], [12.0668, 21.1008], [11.9255, 21.2704], [11.7926, 21.4735], [11.6355, 21.6961], [11.4076, 21.9256], [11.0719, 22.1554]]; + actual = midpt_smooth(taiwan, 20, true); + + assertEqualPoints(expected, actual); +} + +test_midpt_smooth(); \ No newline at end of file diff --git a/test/test_parse_number.scad b/test/test_parse_number.scad deleted file mode 100644 index e07e4b95..00000000 --- a/test/test_parse_number.scad +++ /dev/null @@ -1,13 +0,0 @@ -module test_parse_number() { - echo("==== test_parse_number ===="); - - include ; - include ; - include ; - include ; - - assertEqual(11, parse_number("10") + 1); - assertEqual(-0.1, parse_number("-1.1") + 1); -} - -test_parse_number(); diff --git a/test/test_path_extrude.scad b/test/test_path_extrude.scad new file mode 100644 index 00000000..45374a5e --- /dev/null +++ b/test/test_path_extrude.scad @@ -0,0 +1,74 @@ +include ; + +include ; +include ; +include ; +include ; + +module test_path_extrude_euler_angle() { + echo("==== test_path_extrude_euler_angle ===="); + + include ; + + module test_path_extrude(sections) { + + expected = [[[2.95434, 0.520746, 0.297969], [2.85599, 0.35729, -0.0111818], [2.4941, 0.325562, -0.0111818], [2.7952, 0.256268, -0.202247], [2.69684, 0.0928122, -0.511398], [2.98129, 0.213443, -0.320332], [3.28238, 0.144149, -0.511398], [3.15708, 0.287996, -0.202247], [3.44153, 0.408627, -0.0111818], [3.07964, 0.376899, -0.0111818]], [[2.83958, 0.799164, 0.153715], [2.77043, 0.623587, -0.156699], [2.41955, 0.529518, -0.156699], [2.7277, 0.515074, -0.348545], [2.65855, 0.339496, -0.658959], [2.91814, 0.506147, -0.467113], [3.22628, 0.491702, -0.658959], [3.07858, 0.609142, -0.348545], [3.33817, 0.775793, -0.156699], [2.98729, 0.681724, -0.156699]], [[2.68151, 1.04943, 0.0178389], [2.64148, 0.869239, -0.295041], [2.31207, 0.716097, -0.295041], [2.61675, 0.757873, -0.488412], [2.57672, 0.577678, -0.801292], [2.80505, 0.783691, -0.607921], [3.10973, 0.825467, -0.801292], [2.94616, 0.911014, -0.488412], [3.17449, 1.11703, -0.295041], [2.84507, 0.963886, -0.295041]], [[2.48791, 1.26518, -0.106704], [2.47471, 1.08723, -0.423132], [2.17621, 0.880208, -0.423132], [2.46656, 0.977256, -0.618695], [2.45336, 0.799308, -0.935122], [2.646, 1.03723, -0.739559], [2.93635, 1.13428, -0.935122], [2.76506, 1.18428, -0.618695], [2.95771, 1.42221, -0.423132], [2.6592, 1.21518, -0.423132]], [[2.26759, 1.44211, -0.217276], [2.27699, 1.27204, -0.538143], [2.01742, 1.0179, -0.538143], [2.2828, 1.16693, -0.736449], [2.29221, 0.99687, -1.05732], [2.44682, 1.25904, -0.85901], [2.7122, 1.40808, -1.05732], [2.54238, 1.42108, -0.736449], [2.69699, 1.68325, -0.538143], [2.43742, 1.42911, -0.538143]], [[2.02981, 1.57809, -0.311625], [2.05611, 1.41985, -0.637563], [1.84182, 1.12652, -0.637563], [2.07237, 1.32206, -0.839004], [2.09867, 1.16382, -1.16494], [2.21485, 1.44291, -0.963501], [2.4454, 1.63845, -1.16494], [2.28666, 1.61539, -0.839004], [2.40284, 1.89448, -0.637563], [2.18855, 1.60115, -0.637563]], [[1.78378, 1.6732, -0.387964], [1.82034, 1.52873, -0.719262], [1.65586, 1.20483, -0.719262], [1.84294, 1.43945, -0.924016], [1.8795, 1.29498, -1.25531], [1.95855, 1.58445, -1.05056], [2.14563, 1.81907, -1.25531], [2.00741, 1.76335, -0.924016], [2.08647, 2.05282, -0.719262], [1.92199, 1.72892, -0.719262]], [[1.53815, 1.72956, -0.445029], [1.57798, 1.59865, -0.781545], [1.46599, 1.25307, -0.781545], [1.60259, 1.51774, -0.989523], [1.64242, 1.38683, -1.32604], [1.68701, 1.68132, -1.11806], [1.82361, 1.94599, -1.32604], [1.71458, 1.86332, -0.989523], [1.75918, 2.15781, -0.781545], [1.64719, 1.81223, -0.781545]], [[1.30056, 1.75109, -0.48214], [1.3369, 1.6314, -0.823198], [1.27831, 1.27288, -0.823198], [1.35936, 1.55743, -1.03398], [1.3957, 1.43774, -1.37504], [1.40946, 1.73329, -1.16426], [1.49051, 2.01783, -1.37504], [1.41795, 1.91595, -1.03398], [1.4317, 2.21149, -0.823198], [1.37311, 1.85297, -0.823198]], [[1.0772, 1.74315, -0.499231], [1.10413, 1.63043, -0.843523], [1.09819, 1.26721, -0.843523], [1.12077, 1.56077, -1.05631], [1.1477, 1.44806, -1.4006], [1.13472, 1.74221, -1.18781], [1.1573, 2.03577, -1.4006], [1.12671, 1.924, -1.05631], [1.11373, 2.21814, -0.843523], [1.10779, 1.85492, -0.843523]], [[0.872557, 1.71206, -0.496867], [0.885448, 1.60054, -0.842357], [0.929966, 1.24001, -0.842357], [0.893415, 1.53162, -1.05588], [0.906305, 1.4201, -1.40137], [0.870825, 1.71184, -1.18785], [0.834273, 2.00345, -1.40137], [0.848896, 1.89215, -1.05588], [0.813415, 2.18389, -0.842357], [0.857934, 1.82336, -0.842357]], [[0.68925, 1.66452, -0.476198], [0.685146, 1.54745, -0.820065], [0.776653, 1.19589, -0.820065], [0.682609, 1.4751, -1.03259], [0.678504, 1.35803, -1.37645], [0.624487, 1.64766, -1.16393], [0.530443, 1.92686, -1.37645], [0.591102, 1.82666, -1.03259], [0.537084, 2.11628, -0.820065], [0.628591, 1.76472, -0.820065]], [[0.528059, 1.60696, -0.438872], [0.505828, 1.47737, -0.777514], [0.639793, 1.1397, -0.777514], [0.492088, 1.39728, -0.986807], [0.469857, 1.26769, -1.32545], [0.400802, 1.55647, -1.11616], [0.253097, 1.81405, -1.32545], [0.358123, 1.73495, -0.986807], [0.289068, 2.02373, -0.777514], [0.423033, 1.68606, -0.777514]], [[0.388193, 1.54493, -0.386859], [0.3484, 1.39646, -0.716009], [0.519408, 1.07596, -0.716009], [0.323806, 1.3047, -0.919435], [0.284013, 1.15624, -1.24858], [0.202918, 1.44608, -1.04516], [0.0073171, 1.67482, -1.24858], [0.152799, 1.62521, -0.919435], [0.0717037, 1.91505, -0.716009], [0.242712, 1.59454, -0.716009]], [[0.267797, 1.48254, -0.322209], [0.212192, 1.31034, -0.637203], [0.414076, 1.00833, -0.637203], [0.177826, 1.20391, -0.831881], [0.122221, 1.03171, -1.14688], [0.0318154, 1.32479, -0.952198], [-0.204435, 1.52037, -1.14688], [-0.0240582, 1.50592, -0.831881], [-0.114464, 1.799, -0.637203], [0.0874206, 1.49699, -0.637203]], [[0.164626, 1.42205, -0.246739], [0.0952018, 1.22359, -0.54298], [0.321094, 0.939094, -0.54298], [0.0522951, 1.10094, -0.726067], [-0.0171294, 0.902473, -1.02231], [-0.113831, 1.20096, -0.839221], [-0.382629, 1.3628, -1.02231], [-0.173596, 1.38543, -0.726067], [-0.270299, 1.68392, -0.54298], [-0.0444068, 1.39942, -0.54298]], [[0.0767633, 1.36372, -0.161682], [-0.00559166, 1.13943, -0.435312], [0.236618, 0.868684, -0.435312], [-0.0564899, 1.0008, -0.604425], [-0.138845, 0.776502, -0.878056], [-0.23764, 1.08245, -0.708943], [-0.530747, 1.21457, -0.878056], [-0.298699, 1.27154, -0.604425], [-0.397495, 1.57749, -0.435312], [-0.155285, 1.30675, -0.435312]], [[0.00305186, 1.30565, -0.0673166], [-0.0939741, 1.05937, -0.316114], [0.155642, 0.795445, -0.316114], [-0.153939, 0.907166, -0.46988], [-0.250965, 0.66089, -0.718677], [-0.345271, 0.976213, -0.564912], [-0.654853, 1.08793, -0.718677], [-0.403555, 1.17109, -0.46988], [-0.497862, 1.48642, -0.316114], [-0.248245, 1.22249, -0.316114]], [[-0.0574023, 1.24379, 0.0373803], [-0.174492, 0.983272, -0.187091], [0.0716547, 0.716105, -0.187091], [-0.246858, 0.822264, -0.325822], [-0.363948, 0.561749, -0.550294], [-0.443709, 0.887874, -0.411563], [-0.762221, 0.994032, -0.550294], [-0.493004, 1.08943, -0.325822], [-0.572766, 1.41556, -0.187091], [-0.326619, 1.14839, -0.187091]], [[-0.107744, 1.17276, 0.154856], [-0.252867, 0.90993, -0.0496585], [-0.0235737, 0.628166, -0.0496585], [-0.342558, 0.747492, -0.176055], [-0.487682, 0.484663, -0.380569], [-0.539702, 0.82124, -0.254173], [-0.858686, 0.940566, -0.380569], [-0.571852, 1.02926, -0.176055], [-0.623872, 1.36583, -0.0496585], [-0.394578, 1.08407, -0.0496585]], [[-0.157788, 1.08965, 0.288185], [-0.336278, 0.839185, 0.0948634], [-0.137798, 0.534929, 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-1.05264], [-2.25504, -0.436855, -0.839173], [-1.97181, -0.20937, -0.839173]], [[-1.7565, -0.262182, -0.469212], [-1.64914, -0.20959, -0.812248], [-1.39778, 0.0526804, -0.812248], [-1.58279, -0.177086, -1.02426], [-1.47542, -0.124493, -1.36729], [-1.69713, -0.319089, -1.15528], [-1.88213, -0.548855, -1.36729], [-1.83414, -0.439356, -1.02426], [-2.05584, -0.633952, -0.812248], [-1.80449, -0.371682, -0.812248]], [[-1.62726, -0.368039, -0.428415], [-1.49868, -0.324135, -0.765319], [-1.28078, -0.0334733, -0.765319], [-1.41921, -0.297002, -0.973538], [-1.29063, -0.253099, -1.31044], [-1.50477, -0.459871, -1.10222], [-1.6432, -0.723399, -1.31044], [-1.63711, -0.587664, -0.973538], [-1.85125, -0.794436, -0.765319], [-1.63335, -0.503774, -0.765319]], [[-1.50556, -0.45402, -0.373394], [-1.35092, -0.414989, -0.699782], [-1.16616, -0.102212, -0.699782], [-1.25535, -0.390866, -0.901501], [-1.10071, -0.351834, -1.22789], [-1.31047, -0.569263, -1.02617], [-1.39966, -0.857916, -1.22789], [-1.44011, -0.703642, -0.901501], [-1.64987, -0.921071, -0.699782], [-1.46511, -0.608295, -0.699782]], [[-1.39361, -0.523727, -0.306174], [-1.21006, -0.485721, -0.61735], [-1.05601, -0.15673, -0.61735], [-1.09662, -0.462231, -0.809667], [-0.913071, -0.424225, -1.12084], [-1.12172, -0.651041, -0.928526], [-1.16233, -0.956543, -1.12084], [-1.25067, -0.791222, -0.809667], [-1.45932, -1.01804, -0.61735], [-1.30527, -0.689048, -0.61735]], [[-1.2919, -0.580006, -0.228475], [-1.07871, -0.540443, -0.519941], [-0.950505, -0.200548, -0.519941], [-0.946957, -0.515992, -0.700076], [-0.73377, -0.476429, -0.991541], [-0.944764, -0.710947, -0.811406], [-0.941216, -1.02639, -0.991541], [-1.07517, -0.855887, -0.700076], [-1.28616, -1.09041, -0.519941], [-1.15795, -0.75051, -0.519941]], [[-1.19934, -0.624272, -0.141349], [-0.957732, -0.58336, -0.409527], [-0.847562, -0.237197, -0.409527], [-0.808412, -0.558075, -0.57527], [-0.566808, -0.517163, -0.843448], [-0.784216, -0.756388, -0.677705], [-0.745067, -1.07727, -0.843448], [-0.918582, -0.904237, -0.57527], [-1.13599, -1.14346, -0.409527], [-1.02582, -0.7973, -0.409527]], [[-1.11335, -0.656197, -0.044808], [-0.846136, -0.618455, -0.287987], [-0.742712, -0.270217, -0.287987], [-0.680986, -0.595129, -0.438281], [-0.413769, -0.557387, -0.68146], [-0.642837, -0.795936, -0.531167], [-0.581111, -1.12085, -0.68146], [-0.78441, -0.943367, -0.438281], [-1.01348, -1.18192, -0.287987], [-0.910055, -0.833678, -0.287987]], [[-1.02953, -0.674488, 0.0624958], [-0.741119, -0.649606, -0.156966], [-0.629552, -0.303891, -0.156966], [-0.562869, -0.634229, -0.2926], [-0.274453, -0.609347, -0.512062], [-0.521656, -0.838388, -0.376427], [-0.454973, -1.16873, -0.512062], [-0.674436, -0.979943, -0.2926], [-0.921639, -1.20898, -0.156966], [-0.810072, -0.86327, -0.156966]], [[-0.941149, -0.680164, 0.183273], [-0.638617, -0.681463, -0.0178214], [-0.502375, -0.344708, -0.0178214], [-0.451643, -0.682267, -0.142105], [-0.149111, -0.683567, -0.343199], [-0.420288, -0.89089, -0.218916], [-0.369555, -1.22845, -0.343199], [-0.587885, -1.01902, -0.142105], [-0.859062, -1.22635, -0.0178214], [-0.72282, -0.88959, -0.0178214]], [[-0.841129, -0.682668, 0.320454], [-0.535334, -0.720642, 0.128064], [-0.362312, -0.401221, 0.128064], [-0.346343, -0.744111, 0.00916022], [-0.040549, -0.782084, -0.18323], [-0.336474, -0.956028, -0.0643262], [-0.320505, -1.29892, -0.18323], [-0.519365, -1.06353, 0.00916022], [-0.815291, -1.23747, 0.128064], [-0.642268, -0.918054, 0.128064]], [[-0.728356, -0.701405, 0.474311], [-0.431276, -0.774534, 0.27845], [-0.221075, -0.478253, 0.27845], [-0.24767, -0.81973, 0.157402], [0.0494106, -0.892859, -0.0384589], [-0.264106, -1.03077, 0.0825896], [-0.2907, -1.37225, -0.0384589], [-0.45787, -1.11601, 0.157402], [-0.771387, -1.25392, 0.27845], [-0.561187, -0.957645, 0.27845]], [[-0.609066, -0.753814, 0.639991], [-0.328039, -0.847063, 0.429528], [-0.0914566, -0.571391, 0.429528], [-0.154355, -0.904694, 0.299455], [0.126672, -0.997943, 0.0889923], [-0.193228, -1.11069, 0.219066], [-0.256126, -1.44399, 0.0889923], [-0.390937, -1.18037, 0.299455], [-0.710837, -1.29311, 0.429528], [-0.474255, -1.01744, 0.429528]], [[-0.487096, -0.84401, 0.808722], [-0.223881, -0.937201, 0.576345], [0.0248025, -0.672394, 0.576345], [-0.0612057, -0.994796, 0.432727], [0.202009, -1.08799, 0.200349], [-0.114361, -1.19405, 0.343967], [-0.200369, -1.51645, 0.200349], [-0.309889, -1.2596, 0.432727], [-0.62626, -1.36567, 0.576345], [-0.377576, -1.10086, 0.576345]], [[-0.358119, -0.965594, 0.971127], [-0.11303, -1.04121, 0.713875], [0.135194, -0.775975, 0.713875], [0.0384441, -1.08795, 0.554884], [0.283534, -1.16357, 0.297632], [-0.0213502, -1.28076, 0.456622], [-0.118099, -1.59273, 0.297632], [-0.209779, -1.35319, 0.554884], [-0.514663, -1.47038, 0.713875], [-0.26644, -1.20514, 0.713875]], [[-0.213379, -1.10807, 1.1193], [0.0114663, -1.15412, 0.837714], [0.24911, -0.879362, 0.837714], [0.150428, -1.18258, 0.663685], [0.375273, -1.22863, 0.3821], [0.0894397, -1.36998, 0.556129], [-0.00924145, -1.6732, 0.3821], [-0.0872149, -1.45734, 0.663685], [-0.373049, -1.59869, 0.837714], [-0.135405, -1.32393, 0.837714]], [[-0.0446229, -1.25963, 1.24731], [0.155461, -1.26985, 0.944277], [0.374091, -0.979738, 0.944277], [0.279119, -1.27617, 0.756994], [0.479203, -1.28639, 0.453962], [0.220423, -1.45937, 0.641246], [0.125452, -1.7558, 0.453962], [0.060489, -1.56628, 0.756994], [-0.198291, -1.73927, 0.944277], [0.0203398, -1.44915, 0.944277]], [[0.153404, -1.40806, 1.35108], [0.322733, -1.38136, 1.0308], [0.514965, -1.07312, 1.0308], [0.427383, -1.36486, 0.832856], [0.596711, -1.33816, 0.512573], [0.373255, -1.54516, 0.710519], [0.285674, -1.83691, 0.512573], [0.235151, -1.6731, 0.832856], [0.0116946, -1.8801, 1.0308], [0.203927, -1.57186, 1.0308]], [[0.382253, -1.54128, 1.42815], [0.514685, -1.48096, 1.0953], [0.673888, -1.15444, 1.0953], [0.596532, -1.44368, 0.889586], [0.728964, -1.38336, 0.556736], [0.548723, -1.62245, 0.762448], [0.471367, -1.9117, 0.556736], [0.437329, -1.77021, 0.889586], [0.257088, -2.0093, 1.0953], [0.416292, -1.68277, 1.0953]], [[0.639908, -1.64814, 1.47734], [0.730347, -1.56091, 1.1365], [0.850598, -1.21811, 1.1365], [0.786242, -1.50699, 0.925841], [0.876681, -1.41975, 0.584995], [0.746468, -1.68552, 0.79565], [0.682112, -1.9744, 0.584995], [0.665992, -1.84978, 0.925841], [0.535778, -2.11555, 1.1365], [0.656029, -1.77276, 1.1365]], [[0.921297, -1.71899, 1.49855], [0.966539, -1.61389, 1.15378], [1.0427, -1.25869, 1.15378], [0.994501, -1.54893, 0.940691], [1.03974, -1.44382, 0.595914], [0.964711, -1.7283, 0.808998], [0.916511, -2.01854, 0.595914], [0.918339, -1.90412, 0.940691], [0.843307, -2.18861, 1.15378], [0.919469, -1.83341, 1.15378]], [[1.21894, -1.74622, 1.49247], [1.21814, -1.63357, 1.14711], [1.24602, -1.27137, 1.14711], [1.21764, -1.56395, 0.933664], [1.21684, -1.4513, 0.588302], [1.20011, -1.74477, 0.801748], [1.17173, -2.03735, 0.588302], [1.18976, -1.92615, 0.933664], [1.17303, -2.21962, 1.14711], [1.20091, -1.85742, 1.14711]], [[1.5236, -1.72457, 1.4604], [1.47842, -1.615, 1.11701], [1.45495, -1.25249, 1.11701], [1.45049, -1.54729, 0.904781], [1.4053, -1.43772, 0.561387], [1.44773, -1.72948, 0.773616], [1.44327, -2.02428, 0.561387], [1.47395, -1.9098, 0.904781], [1.51638, -2.20156, 1.11701], [1.49292, -1.83905, 1.11701]], [[1.825, -1.65132, 1.40412], [1.73947, -1.55493, 1.06448], [1.66292, -1.19981, 1.06448], [1.6866, -1.49535, 0.854565], [1.60107, -1.39895, 0.514922], [1.70124, -1.678, 0.724833], [1.72492, -1.97354, 0.514922], [1.76315, -1.85046, 0.854565], [1.86332, -2.12952, 1.06448], [1.78677, -1.7744, 1.06448]], [[2.11238, -1.52639, 1.32577], [1.99264, -1.45202, 0.990962], [1.86281, -1.11274, 0.990962], [1.91864, -1.40605, 0.784039], [1.79889, -1.33167, 0.449231], [1.95314, -1.58733, 0.656154], [2.00896, -1.88064, 0.449231], [2.04846, -1.74533, 0.784039], [2.2027, -2.00098, 0.990962], [2.07288, -1.6617, 0.990962]], [[2.37518, -1.35225, 1.22783], [2.22905, -1.307, 0.898339], [2.04743, -0.992384, 0.898339], [2.13873, -1.27902, 0.694704], [1.9926, -1.23377, 0.365216], [2.19516, -1.45618, 0.568851], [2.28646, -1.74282, 0.365216], [2.32035, -1.59364, 0.694704], [2.52292, -1.81605, 0.898339], [2.3413, -1.50144, 0.898339]], [[2.6036, -1.13382, 1.11304], [2.44006, -1.12263, 0.788856], [2.20994, -0.841535, 0.788856], [2.33898, -1.11571, 0.588501], [2.17544, -1.10452, 0.26432], [2.41873, -1.28516, 0.464675], [2.54777, -1.55934, 0.26432], [2.5691, -1.39681, 0.588501], [2.81239, -1.57745, 0.788856], [2.58228, -1.29635, 0.788856]], [[2.78916, -0.878157, 0.984388], [2.61778, -0.903613, 0.665099], [2.34432, -0.66448, 0.665099], [2.51186, -0.919346, 0.467768], [2.34047, -0.944801, 0.148479], [2.6154, -1.07686, 0.34581], [2.78294, -1.33173, 0.148479], [2.78532, -1.15848, 0.467768], [3.06025, -1.29054, 0.665099], [2.78679, -1.05141, 0.665099]], [[2.92519, -0.594112, 0.845061], [2.75551, -0.656344, 0.529937], [2.44564, -0.466754, 0.529937], [2.65065, -0.694805, 0.33518], [2.48097, -0.757037, 0.0200556], [2.77735, -0.835748, 0.214813], [2.98236, -1.0638, 0.0200556], [2.96052, -0.884395, 0.33518], [3.2569, -0.963106, 0.529937], [2.94702, -0.773517, 0.529937]], [[3.00719, -0.291798, 0.698393], [2.84812, -0.388579, 0.38647], [2.51037, -0.254813, 0.38647], [2.74981, -0.448393, 0.193691], [2.59074, -0.545174, -0.118232], [2.89779, -0.568032, 0.074547], [3.13722, -0.761611, -0.118232], [3.08756, -0.582158, 0.193691], [3.39461, -0.605016, 0.38647], [3.05686, -0.471251, 0.38647]], [[3.03312, 0.0179831, 0.547811], [2.89231, -0.109027, 0.237961], [2.53653, -0.0356621, 0.237961], [2.80529, -0.187524, 0.0464628], [2.66448, -0.314534, -0.263388], [2.97139, -0.281379, -0.0718896], [3.24015, -0.43324, -0.263388], [3.16107, -0.260888, 0.0464628], [3.46799, -0.227734, 0.237961], [3.1122, -0.154369, 0.237961]], [[3.01297, 0.22306, 0.447299], [2.89194, 0.0754433, 0.138223], [2.52928, 0.096523, 0.138223], [2.81714, -0.0157888, -0.0527965], [2.69611, -0.163405, -0.361872], [2.99505, -0.0852013, -0.170853], [3.28291, -0.197513, -0.361872], [3.1798, -0.0368685, -0.0527965], [3.47873, 0.0413356, 0.138223], [3.11607, 0.0624153, 0.138223]], [[2.95434, 0.520746, 0.297969], [2.85599, 0.35729, -0.0111818], [2.4941, 0.325562, -0.0111818], [2.7952, 0.256268, -0.202247], [2.69684, 0.0928122, -0.511398], [2.98129, 0.213443, -0.320332], [3.28238, 0.144149, -0.511398], [3.15708, 0.287996, -0.202247], [3.44153, 0.408627, -0.0111818], [3.07964, 0.376899, -0.0111818]]]; + + for(i = [0:len(expected) - 1]) { + assertEqualPoints(expected[i], sections[i]); + } + } + + + p = 2; + q = 3; + phi_step = 0.05; + star_radius = 0.5; + + pts = torus_knot(p, q, phi_step); + + shape_pentagram_pts = shape_pentagram(star_radius); + + path_extrude( + shape_pentagram_pts, + concat(pts, [pts[0]]), + closed = true, + method = "EULER_ANGLE" + ); +} + +module test_path_extrude_axis_angle() { + echo("==== test_path_extrude_axis_angle ===="); + + include ; + + module test_path_extrude(sections) { + + expected = [[[2.9805, 0.222367, 0.447407], [2.88215, 0.0589106, 0.138256], [2.52026, 0.0271826, 0.138256], [2.82136, -0.0421108, -0.0528092], [2.723, -0.205567, -0.36196], [3.00745, -0.0849366, -0.170894], [3.30854, -0.15423, -0.36196], [3.18324, -0.0103828, -0.0528092], [3.46769, 0.110248, 0.138256], [3.1058, 0.0785196, 0.138256]], [[2.95434, 0.520746, 0.297969], [2.85599, 0.35729, -0.0111818], [2.4941, 0.325562, -0.0111818], [2.7952, 0.256268, -0.202247], [2.69684, 0.0928122, -0.511398], [2.98129, 0.213443, -0.320332], [3.28238, 0.144149, -0.511398], [3.15708, 0.287996, -0.202247], [3.44153, 0.408627, -0.0111818], [3.07964, 0.376899, -0.0111818]], [[2.86455, 0.805557, 0.153118], [2.77764, 0.628055, -0.151684], [2.42509, 0.542053, -0.134859], [2.72392, 0.518352, -0.340062], [2.637, 0.34085, -0.644864], [2.9086, 0.503705, -0.466885], [3.20742, 0.480005, -0.672088], [3.07646, 0.604355, -0.356887], [3.34806, 0.767209, -0.178908], [2.99552, 0.681207, -0.162083]], [[2.72752, 1.06964, 0.015547], [2.6542, 0.880061, -0.285534], [2.31993, 0.741734, -0.252475], [2.60889, 0.762895, -0.471612], [2.53557, 0.573315, -0.772693], [2.78747, 0.775973, -0.607046], [3.07643, 0.797134, -0.826183], [2.94316, 0.901222, -0.504671], [3.19507, 1.10388, -0.339024], [2.86079, 0.965553, -0.305965]], [[2.54875, 1.30479, -0.111553], [2.49076, 1.10553, -0.409708], [2.18335, 0.918084, -0.361421], [2.45492, 0.982373, -0.593979], [2.39693, 0.783108, -0.892134], [2.62276, 1.02211, -0.737707], [2.89433, 1.08639, -0.970265], [2.76233, 1.16981, -0.642266], [2.98816, 1.40881, -0.487839], [2.68075, 1.22137, -0.439552]], [[2.33552, 1.50419, -0.2252], [2.294, 1.29804, -0.521414], [2.02152, 1.06593, -0.459353], [2.26833, 1.17063, -0.704484], [2.22681, 0.964474, -1.0007], [2.42087, 1.23533, -0.855983], [2.66769, 1.34002, -1.10111], [2.54081, 1.40273, -0.766544], [2.73487, 1.67359, -0.62183], [2.4624, 1.44148, -0.559769]], [[2.09654, 1.66282, -0.322716], [2.07181, 1.4529, -0.618161], [1.84159, 1.18178, -0.544283], [2.05653, 1.32317, -0.800756], [2.0318, 1.11324, -1.0962], [2.18937, 1.41054, -0.959265], [2.4043, 1.55193, -1.21574], [2.28675, 1.59428, -0.874634], [2.44432, 1.89158, -0.737698], [2.21409, 1.62046, -0.66382]], [[1.84149, 1.7778, -0.401834], [1.83287, 1.56739, -0.697844], [1.6512, 1.264, -0.614663], [1.82753, 1.43736, -0.880788], [1.8189, 1.22695, -1.1768], [1.93651, 1.5445, -1.04526], [2.11284, 1.71785, -1.31139], [2.00919, 1.74075, -0.963969], [2.1268, 2.05829, -0.832433], [1.94514, 1.7549, -0.749252]], [[1.58057, 1.84855, -0.460816], [1.5861, 1.64086, -0.75881], [1.45798, 1.31289, -0.669451], [1.58952, 1.5125, -0.94298], [1.59505, 1.30481, -1.24097], [1.67081, 1.63587, -1.11203], [1.80235, 1.83548, -1.38556], [1.71764, 1.84047, -1.03234], [1.7934, 2.17153, -0.903395], [1.66528, 1.84356, -0.814036]], [[1.32382, 1.87694, -0.498575], [1.34016, 1.67472, -0.799918], [1.26887, 1.33054, -0.708146], [1.35027, 1.54974, -0.986157], [1.36661, 1.34752, -1.2875], [1.40057, 1.68522, -1.15798], [1.48196, 1.90442, -1.43599], [1.42156, 1.89392, -1.07793], [1.45552, 2.23162, -0.948407], [1.38422, 1.88744, -0.856635]], [[1.08053, 1.86715, -0.514808], [1.10289, 1.6723, -0.820584], [1.08964, 1.32055, -0.730775], [1.11672, 1.55188, -1.00956], [1.13909, 1.35703, -1.31534], [1.13345, 1.69484, -1.18187], [1.16053, 1.92616, -1.46065], [1.12997, 1.90362, -1.09937], [1.12434, 2.24144, -0.965898], [1.11108, 1.88969, -0.876089]], [[0.858524, 1.82543, -0.510091], [0.880812, 1.63853, -0.820796], [0.924361, 1.28755, -0.737801], [0.894586, 1.52302, -1.01282], [0.916874, 1.33612, -1.32353], [0.876184, 1.66854, -1.1828], [0.84641, 1.904, -1.45782], [0.851037, 1.87399, -1.09582], [0.810348, 2.20641, -0.955086], [0.853897, 1.85544, -0.872091]], [[0.663547, 1.7595, -0.485931], [0.678721, 1.57947, -0.801084], [0.775139, 1.23653, -0.729928], [0.688099, 1.4682, -0.99586], [0.703272, 1.28816, -1.31101], [0.634305, 1.61137, -1.16022], [0.547265, 1.84304, -1.42615], [0.59168, 1.81113, -1.06702], [0.522713, 2.13435, -0.916218], [0.619131, 1.79141, -0.845062]], [[0.498677, 1.67784, -0.444675], [0.49943, 1.50177, -0.762425], [0.642074, 1.17217, -0.707793], [0.499896, 1.39295, -0.958806], [0.500648, 1.21688, -1.27656], [0.412024, 1.5294, -1.11394], [0.269846, 1.75018, -1.36495], [0.357252, 1.72255, -1.01344], [0.268628, 2.03506, -0.850822], [0.411272, 1.70547, -0.79619]], [[0.364059, 1.58856, -0.389233], [0.34368, 1.41204, -0.70608], [0.523547, 1.09831, -0.671575], [0.331085, 1.30294, -0.901902], [0.310706, 1.12643, -1.21875], [0.212137, 1.42941, -1.04425], [0.0196751, 1.63404, -1.27458], [0.151218, 1.61667, -0.936407], [0.0526489, 1.91966, -0.76191], [0.232516, 1.60593, -0.727405]], [[0.256985, 1.49844, -0.322546], [0.210279, 1.31631, -0.633372], [0.416785, 1.01771, -0.620634], [0.181413, 1.20374, -0.825472], [0.134707, 1.02161, -1.1363], [0.0359454, 1.31872, -0.952069], [-0.199426, 1.50475, -1.15691], [-0.0250928, 1.50234, -0.83821], [-0.123855, 1.79944, -0.653981], [0.0826512, 1.50085, -0.641244]], [[0.172449, 1.41207, -0.246877], [0.0964491, 1.21962, -0.545465], [0.318554, 0.932268, -0.553367], [0.0494783, 1.10069, -0.730002], [-0.0265218, 0.90824, -1.02859], [-0.116819, 1.20477, -0.839169], [-0.385895, 1.37319, -1.0158], [-0.172626, 1.38804, -0.7221], [-0.262924, 1.68457, -0.532678], [-0.0408192, 1.39722, -0.540581]], [[0.104051, 1.33159, -0.163091], [-0.0017305, 1.12594, -0.443241], [0.225686, 0.843701, -0.46749], [-0.0671073, 0.998844, -0.616384], [-0.172889, 0.793194, -0.896534], [-0.248063, 1.09473, -0.708405], [-0.540856, 1.24987, -0.857298], [-0.294523, 1.28108, -0.592135], [-0.369698, 1.58262, -0.404005], [-0.142281, 1.30038, -0.428254]], [[0.0449523, 1.25719, -0.070278], [-0.0889033, 1.03822, -0.327376], [0.135222, 0.754295, -0.360859], [-0.171631, 0.902887, -0.486271], [-0.305486, 0.683914, -0.743369], [-0.361276, 0.994721, -0.563781], [-0.668128, 1.14331, -0.689193], [-0.395755, 1.18681, -0.452789], [-0.451545, 1.49762, -0.2732], [-0.22742, 1.21369, -0.306683]], [[-0.0114836, 1.18809, 0.0339872], [-0.170144, 0.958587, -0.198654], [0.044155, 0.667238, -0.232678], [-0.268202, 0.816747, -0.342434], [-0.426862, 0.587245, -0.575075], [-0.461248, 0.909149, -0.410267], [-0.773605, 1.05866, -0.520023], [-0.4825, 1.1081, -0.30841], [-0.516887, 1.43, -0.143602], [-0.302588, 1.13865, -0.177626]], [[-0.0715622, 1.12352, 0.152643], [-0.250781, 0.888396, -0.0584525], [-0.0509185, 0.586184, -0.0846979], [-0.361545, 0.743079, -0.188917], [-0.540763, 0.507951, -0.400012], [-0.553522, 0.840046, -0.253328], [-0.864148, 0.99694, -0.357546], [-0.561407, 1.04529, -0.162671], [-0.574165, 1.37739, -0.0159866], [-0.374303, 1.07517, -0.042232]], [[-0.141465, 1.06316, 0.287643], [-0.336201, 0.828018, 0.0907882], [-0.153793, 0.514118, 0.0781423], [-0.456554, 0.682692, -0.030875], [-0.651289, 0.447549, -0.22773], [-0.64367, 0.786877, -0.0982515], [-0.94643, 0.955451, -0.207269], [-0.638961, 0.996592, -0.0182292], [-0.631342, 1.33592, 0.11125], [-0.448935, 1.02202, 0.0986037]], [[-0.227322, 1.00662, 0.438508], [-0.431473, 0.776466, 0.245332], [-0.268022, 0.452055, 0.248007], [-0.557645, 0.634223, 0.125943], [-0.761796, 0.404067, -0.0672326], [-0.736642, 0.746808, 0.0505039], [-1.02626, 0.928976, -0.0715595], [-0.721096, 0.958634, 0.123269], [-0.695942, 1.30138, 0.241006], [-0.532491, 0.976964, 0.24368]], [[-0.334717, 0.952491, 0.601513], [-0.54076, 0.731084, 0.400289], [-0.395847, 0.398311, 0.415397], [-0.668102, 0.594248, 0.275925], [-0.874145, 0.372841, 0.0747005], [-0.836364, 0.715343, 0.189726], [-1.10862, 0.911279, 0.0502542], [-0.813014, 0.927021, 0.260816], [-0.775234, 1.26952, 0.375842], [-0.630321, 0.93675, 0.390951]], [[-0.467604, 0.897449, 0.769873], [-0.66664, 0.687552, 0.550115], [-0.537234, 0.34875, 0.570944], [-0.789651, 0.557828, 0.414297], [-0.988686, 0.34793, 0.194538], [-0.945653, 0.687045, 0.317483], [-1.19807, 0.896122, 0.160835], [-0.919056, 0.896629, 0.393467], [-0.876023, 1.23574, 0.516412], [-0.746617, 0.896942, 0.537241]], [[-0.627051, 0.836133, 0.93488], [-0.809598, 0.640306, 0.689331], [-0.689596, 0.297889, 0.707124], [-0.922418, 0.519278, 0.537574], [-1.10496, 0.323451, 0.292025], [-1.06631, 0.656103, 0.432786], [-1.29913, 0.877492, 0.263236], [-1.04242, 0.861694, 0.519781], [-1.00376, 1.19435, 0.660542], [-0.883762, 0.851931, 0.678335]], [[-0.810465, 0.761897, 1.08756], [-0.967893, 0.583272, 0.813201], [-0.848404, 0.240269, 0.819318], [-1.06519, 0.472875, 0.643635], [-1.22262, 0.29425, 0.369272], [-1.19917, 0.616634, 0.535057], [-1.41595, 0.84924, 0.359374], [-1.18468, 0.815878, 0.637518], [-1.16123, 1.13826, 0.803303], [-1.04174, 0.795259, 0.80942]], [[-1.01175, 0.668128, 1.22027], [-1.13784, 0.510654, 0.918165], [-1.00836, 0.171462, 0.905942], [-1.21577, 0.413329, 0.731453], [-1.34186, 0.255855, 0.429346], [-1.34396, 0.562811, 0.623613], [-1.55137, 0.804678, 0.449124], [-1.34525, 0.752521, 0.743676], [-1.34735, 1.05948, 0.937943], [-1.21787, 0.720285, 0.92572]], [[-1.22231, 0.549492, 1.32765], [-1.31435, 0.417546, 1.00195], [-1.16452, 0.0883814, 0.967753], [-1.37123, 0.335999, 0.800647], [-1.46326, 0.204053, 0.474938], [-1.49898, 0.489035, 0.697369], [-1.70568, 0.736652, 0.530262], [-1.52105, 0.665163, 0.834839], [-1.55677, 0.950145, 1.05727], [-1.40694, 0.620981, 1.02308]], [[-1.4325, 0.402678, 1.40689], [-1.49147, 0.300283, 1.06337], [-1.31289, -0.0109598, 1.00678], [-1.52791, 0.237, 0.851064], [-1.58688, 0.134605, 0.507546], [-1.6608, 0.390247, 0.754828], [-1.87583, 0.638206, 0.599116], [-1.70649, 0.548242, 0.907657], [-1.78042, 0.803884, 1.15494], [-1.60184, 0.492642, 1.09835]], [[-1.63279, 0.226528, 1.45726], [-1.66282, 0.156577, 1.10206], [-1.45027, -0.127848, 1.0253], [-1.68137, 0.113345, 0.882526], [-1.7114, 0.0433938, 0.52732], [-1.8242, 0.26241, 0.794289], [-2.05531, 0.503603, 0.651518], [-1.89392, 0.39777, 0.959285], [-2.00673, 0.616786, 1.22625], [-1.79418, 0.332361, 1.1495]], [[-1.81459, 0.0217734, 1.47952], [-1.82182, -0.0144367, 1.11813], [-1.57381, -0.263086, 1.02523], [-1.8263, -0.0368156, 0.894778], [-1.83354, -0.0730256, 0.533388], [-1.98234, 0.103027, 0.814152], [-2.23483, 0.329296, 0.683695], [-2.07431, 0.211833, 0.987673], [-2.22312, 0.387886, 1.26844], [-1.9751, 0.139237, 1.17554]], [[-1.9704, -0.20932, 1.47518], [-1.96188, -0.212155, 1.11202], [-1.68044, -0.416903, 1.00793], [-1.95662, -0.213907, 0.887578], [-1.9481, -0.216741, 0.524417], [-2.12731, -0.0884478, 0.813196], [-2.40348, 0.114549, 0.692843], [-2.23806, -0.00915799, 0.99167], [-2.41726, 0.119136, 1.28045], [-2.13582, -0.0856129, 1.17636]], [[-2.09387, -0.463212, 1.44612], [-2.07654, -0.434452, 1.0844], [-1.76663, -0.588669, 0.974248], [-2.06584, -0.416677, 0.860851], [-2.04851, -0.387917, 0.499135], [-2.25076, -0.31038, 0.790768], [-2.54997, -0.138388, 0.677371], [-2.37575, -0.26246, 0.971007], [-2.578, -0.184923, 1.26264], [-2.26808, -0.33914, 1.15248]], [[-2.17964, -0.73522, 1.3943], [-2.15975, -0.677651, 1.03617], [-1.82841, -0.776563, 0.924806], [-2.14745, -0.642072, 0.814835], [-2.12756, -0.584504, 0.456707], [-2.34463, -0.558952, 0.746869], [-2.66366, -0.42446, 0.636898], [-2.47878, -0.54316, 0.9262], [-2.69585, -0.517608, 1.21636], [-2.36452, -0.61652, 1.105]], [[-2.22336, -1.01958, 1.32174], [-2.20615, -0.936568, 0.968495], [-1.8618, -0.977369, 0.860238], [-2.19552, -0.885265, 0.75018], [-2.17831, -0.802255, 0.396939], [-2.40177, -0.828341, 0.68216], [-2.73549, -0.736237, 0.572102], [-2.53988, -0.844463, 0.858436], [-2.76334, -0.870549, 1.14366], [-2.41898, -0.911351, 1.0354]], [[-2.22183, -1.30951, 1.23052], [-2.21151, -1.20466, 0.88286], [-1.86318, -1.18645, 0.781384], [-2.20514, -1.13985, 0.667996], [-2.19483, -1.035, 0.320339], [-2.41649, -1.11105, 0.597918], [-2.75845, -1.06446, 0.48453], [-2.55348, -1.15806, 0.769472], [-2.77513, -1.23411, 1.04705], [-2.4268, -1.21591, 0.945576]], [[-2.17313, -1.59738, 1.12287], [-2.17299, -1.47427, 0.781089], [-1.82987, -1.39792, 0.689415], [-2.17291, -1.39819, 0.569859], [-2.17276, -1.27509, 0.228083], [-2.38491, -1.39836, 0.49597], [-2.72795, -1.39862, 0.376415], [-2.51603, -1.47454, 0.661534], [-2.72818, -1.59781, 0.929421], [-2.38505, -1.52146, 0.837747]], [[-2.07693, -1.87495, 1.00119], [-2.08945, -1.73705, 0.665344], [-1.7605, -1.60498, 0.585882], [-2.09719, -1.65182, 0.45778], [-2.10972, -1.51392, 0.121935], [-2.30528, -1.68077, 0.378609], [-2.64197, -1.72761, 0.250506], [-2.42615, -1.78389, 0.537242], [-2.62171, -1.95074, 0.793915], [-2.29276, -1.81867, 0.714454]], [[-1.93457, -2.13374, 0.868113], [-1.96164, -1.98431, 0.538105], [-1.65532, -1.80032, 0.472717], [-1.97837, -1.89196, 0.334149], [-2.00545, -1.74254, 0.00414212], [-2.17804, -1.9486, 0.24851], [-2.50109, -2.04024, 0.109943], [-2.2847, -2.07596, 0.399538], [-2.45729, -2.28202, 0.643906], [-2.15097, -2.09803, 0.578517]], [[-1.74924, -2.36542, 0.726483], [-1.79225, -2.20758, 0.402133], [-1.51631, -1.97666, 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[-0.697387, -1.31697, 0.409751], [-0.476109, -1.02926, 0.424695]], [[-0.512348, -0.872465, 0.807748], [-0.236513, -0.941906, 0.581786], [-0.00345302, -0.66387, 0.600369], [-0.0660372, -0.984823, 0.442134], [0.209798, -1.05426, 0.216171], [-0.104716, -1.18318, 0.344339], [-0.1673, -1.50414, 0.186103], [-0.299097, -1.26286, 0.42355], [-0.613611, -1.39178, 0.551718], [-0.380551, -1.11374, 0.570301]], [[-0.374583, -0.983774, 0.970679], [-0.120893, -1.04442, 0.717836], [0.118348, -0.771373, 0.731103], [0.0358961, -1.0819, 0.56157], [0.289586, -1.14254, 0.308727], [-0.0150616, -1.27382, 0.456793], [-0.0975128, -1.58434, 0.287261], [-0.203344, -1.35494, 0.548303], [-0.507992, -1.48622, 0.696369], [-0.268752, -1.21317, 0.709636]], [[-0.212961, -1.10759, 1.1193], [0.0116581, -1.15403, 0.837597], [0.249504, -0.879443, 0.837219], [0.15048, -1.18273, 0.663496], [0.375099, -1.22917, 0.381795], [0.0892802, -1.37017, 0.556129], [-0.00974368, -1.67345, 0.382406], [-0.0873657, -1.45731, 0.663874], [-0.373185, -1.59831, 0.838209], [-0.135339, -1.32373, 0.837831]], [[-0.0253282, -1.23482, 1.24644], [0.163996, -1.2644, 0.93782], [0.390953, -0.981462, 0.917792], [0.281005, -1.28269, 0.747082], [0.47033, -1.31227, 0.43846], [0.213054, -1.46885, 0.641577], [0.103106, -1.77007, 0.470867], [0.0540483, -1.56563, 0.76711], [-0.203228, -1.72221, 0.970227], [0.0237291, -1.43927, 0.950199]], [[0.188083, -1.35529, 1.34738], [0.337483, -1.36863, 1.01652], [0.54277, -1.07195, 0.973998], [0.429817, -1.37687, 0.812035], [0.579217, -1.39021, 0.481176], [0.360009, -1.56532, 0.711936], [0.247057, -1.87024, 0.549972], [0.224531, -1.67355, 0.854553], [0.00532206, -1.84866, 1.08531], [0.210609, -1.55198, 1.04279]], [[0.424851, -1.45919, 1.41984], [0.532001, -1.45977, 1.07273], [0.704643, -1.14677, 1.00801], [0.598223, -1.46013, 0.858207], [0.705373, -1.46072, 0.511098], [0.532452, -1.65381, 0.765622], [0.426033, -1.96717, 0.615815], [0.425582, -1.77314, 0.922926], [0.252661, -1.96623, 1.17745], [0.425303, -1.65322, 1.11273]], [[0.680925, -1.53812, 1.46355], [0.746048, -1.53129, 1.10623], [0.876091, -1.2027, 1.02208], [0.786297, -1.52707, 0.885395], [0.85142, -1.52025, 0.528074], [0.730801, -1.72755, 0.800917], [0.641007, -2.05192, 0.664228], [0.656254, -1.85567, 0.969543], [0.535635, -2.06297, 1.24239], [0.665678, -1.73438, 1.15824]], [[0.951191, -1.58543, 1.4795], [0.976809, -1.57722, 1.11722], [1.05631, -1.23693, 1.01799], [0.992641, -1.57214, 0.893326], [1.01826, -1.56393, 0.531052], [0.953293, -1.77932, 0.816277], [0.889625, -2.11454, 0.69161], [0.913141, -1.91244, 0.992556], [0.848174, -2.12782, 1.27778], [0.927675, -1.78753, 1.17855]], [[1.22985, -1.59619, 1.46932], [1.22019, -1.59232, 1.10619], [1.2438, -1.24667, 0.996943], [1.21422, -1.58993, 0.881772], [1.20456, -1.58607, 0.51865], [1.19594, -1.80208, 0.810593], [1.16636, -2.14534, 0.695422], [1.19061, -1.93558, 0.991023], [1.18199, -2.15159, 1.28297], [1.2056, -1.80595, 1.17371]], [[1.51058, -1.567, 1.43491], [1.47086, -1.57231, 1.07386], [1.43599, -1.22921, 0.959704], [1.44632, -1.57559, 0.850713], [1.40661, -1.5809, 0.489658], [1.45271, -1.78967, 0.783353], [1.46304, -2.13605, 0.674362], [1.4812, -1.91869, 0.964866], [1.52729, -2.12746, 1.25856], [1.49242, -1.78436, 1.14441]], [[1.78657, -1.4959, 1.37826], [1.7224, -1.51406, 1.02116], [1.62906, -1.18211, 0.906864], [1.68274, -1.52528, 0.800466], [1.61857, -1.54343, 0.443369], [1.71592, -1.73737, 0.734709], [1.7696, -2.08053, 0.628311], [1.77608, -1.85722, 0.914767], [1.87343, -2.05116, 1.20611], [1.78009, -1.71921, 1.09181]], [[2.05061, -1.38233, 1.30138], [1.96747, -1.41588, 0.94935], [1.81795, -1.10371, 0.839077], [1.91608, -1.43661, 0.731781], [1.83294, -1.47015, 0.379747], [1.97673, -1.64235, 0.665468], [2.07486, -1.97526, 0.558172], [2.0656, -1.74878, 0.842054], [2.20939, -1.92098, 1.12778], [2.05987, -1.60881, 1.0175]], [[2.2952, -1.22724, 1.20638], [2.19819, -1.27774, 0.859968], [1.99667, -0.993479, 0.757242], [2.13823, -1.30895, 0.645872], [2.04121, -1.35946, 0.299458], [2.22571, -1.50393, 0.577042], [2.36727, -1.81941, 0.465672], [2.33974, -1.59322, 0.748598], [2.52424, -1.73769, 1.02618], [2.32273, -1.45343, 0.923456]], [[2.51284, -1.03314, 1.09551], [2.40653, -1.10142, 0.754915], [2.1587, -0.852377, 0.66261], [2.34083, -1.14362, 0.544418], [2.23453, -1.2119, 0.203825], [2.4534, -1.32362, 0.471371], [2.63554, -1.61486, 0.353178], [2.58867, -1.39266, 0.636723], [2.80754, -1.50438, 0.904269], [2.55971, -1.25534, 0.811963]], [[2.69632, -0.804209, 0.971208], [2.58481, -0.890524, 0.636425], [2.29748, -0.682984, 0.556815], [2.51588, -0.94387, 0.429518], [2.40437, -1.03019, 0.0947355], [2.65086, -1.10511, 0.350844], [2.86927, -1.36599, 0.223547], [2.80321, -1.15141, 0.509128], [3.04971, -1.22633, 0.765237], [2.76238, -1.01879, 0.685627]], [[2.8392, -0.546199, 0.836151], [2.72609, -0.650404, 0.507043], [2.40698, -0.489507, 0.441867], [2.65618, -0.714807, 0.303643], [2.54306, -0.819012, -0.0254647], [2.81019, -0.85405, 0.218216], [3.05939, -1.07935, 0.0799924], [2.97529, -0.875704, 0.368819], [3.24242, -0.910741, 0.6125], [2.92331, -0.749844, 0.547324]], [[2.93615, -0.266308, 0.693225], [2.82468, -0.387946, 0.369582], [2.48212, -0.277622, 0.320099], [2.75579, -0.463122, 0.169559], [2.64432, -0.584761, -0.154084], [2.92492, -0.577768, 0.0765208], [3.19859, -0.763268, -0.0740189], [3.09835, -0.573446, 0.219042], [3.37895, -0.566454, 0.449647], [3.03639, -0.45613, 0.400164]], [[2.98335, 0.027088, 0.54551], [2.87648, -0.11125, 0.227064], [2.51924, -0.0541853, 0.194101], [2.81044, -0.196748, 0.0302532], [2.70357, -0.335086, -0.288193], [2.9904, -0.284857, -0.0710107], [3.2816, -0.427419, -0.234859], [3.16768, -0.253813, 0.0632155], [3.45451, -0.203583, 0.280398], [3.09727, -0.146518, 0.247436]], [[2.98177, 0.224436, 0.446426], [2.88233, 0.0727283, 0.131681], [2.51979, 0.0836457, 0.111385], [2.82088, -0.0210325, -0.0628413], [2.72145, -0.172741, -0.377586], [3.00696, -0.0857271, -0.170519], [3.30805, -0.190405, -0.344746], [3.18342, -0.0319498, -0.0425455], [3.46894, 0.0550637, 0.164521], [3.1064, 0.065981, 0.144225]]]; + + for(i = [0:len(expected) - 1]) { + assertEqualPoints(expected[i], sections[i]); + } + } + + p = 2; + q = 3; + phi_step = 0.05; + star_radius = 0.5; + + pts = torus_knot(p, q, phi_step); + + shape_pentagram_pts = shape_pentagram(star_radius); + + // adjust it + path_extrude( + shape_pentagram_pts, + concat(pts, [pts[0]]), + closed = true, + twist = 188, + method = "AXIS_ANGLE" + ); +} + +test_path_extrude_euler_angle(); +test_path_extrude_axis_angle(); \ No newline at end of file diff --git a/test/test_polyline2d.scad b/test/test_polyline2d.scad index fc0bc635..508a7fd6 100644 --- a/test/test_polyline2d.scad +++ b/test/test_polyline2d.scad @@ -11,7 +11,7 @@ module test_polyline2d() { module assertCorrectSegment(index, point1, point2, width) { assertEqualPoint(points[index - 1], point1); assertEqualPoint(points[index], point2); - assertEqual(line_width, width); + assertEqualNum(line_width, width); } module assertCorrectCaps(startStyle, endStyle, index, p1Style, p2Style) { diff --git a/test/test_polyline3d.scad b/test/test_polyline3d.scad index a455e80b..71c43f72 100644 --- a/test/test_polyline3d.scad +++ b/test/test_polyline3d.scad @@ -17,7 +17,7 @@ module test_polyline3d() { module assertCorrectSegment(expected, actual, thickness) { assertEqualPoint(expected[0], actual[0]); assertEqualPoint(expected[1], actual[1]); - assertEqual(line_thickness, thickness); + assertEqualNum(line_thickness, thickness); } module assertCorrectCaps(leng_pts, startStyle, endStyle, index, p1Style, p2Style) { diff --git a/test/test_polysections.scad b/test/test_polysections.scad index bc3793d6..6f7b7a01 100644 --- a/test/test_polysections.scad +++ b/test/test_polysections.scad @@ -35,7 +35,7 @@ module test_polysections_solid_sections() { assertEqualPoints(expected_pts, points); for(i = [0:len(expected_faces) - 1]) { - assertTrue(expected_faces[i] == faces[i]); + assert(expected_faces[i] == faces[i]); } } @@ -78,7 +78,7 @@ module test_polysections_hollow_sections() { assertEqualPoints(expected_pts, points); for(i = [0:len(expected_faces) - 1]) { - assertTrue(expected_faces[i] == faces[i]); + assert(expected_faces[i] == faces[i]); } } diff --git a/test/test_ring_extrude.scad b/test/test_ring_extrude.scad index bd3cd96b..918e5e9f 100644 --- a/test/test_ring_extrude.scad +++ b/test/test_ring_extrude.scad @@ -9,42 +9,10 @@ module test_ring_extrude_closed() { include ; module test_ring_extrude(sections) { - expected = [ - [[52, 0, -10], [52, 0, 10], [48, 0, 10], [48, 0, -10]] - , [[51.875, 11.026, -9.736], [49.831, 10.592, 10.154], [45.939, 9.765, 9.736], [47.984, 10.199, -10.154]] - , [[49.364, 21.978, -9.366], [45.565, 20.287, 10.197], [41.991, 18.695, 9.366], [45.789, 20.387, -10.197]] - , [[44.49, 32.324, -8.893], [39.49, 28.691, 10.129], [36.412, 26.455, 8.893], [41.412, 30.088, -10.129]] - , [[37.401, 41.538, -8.322], [31.957, 35.492, 9.949], [29.512, 32.777, 8.322], [34.956, 38.822, -9.949]] - , [[28.366, 49.131, -7.66], [23.366, 40.471, 9.66], [21.634, 37.471, 7.66], [26.634, 46.131, -9.66]] - , [[17.767, 54.682, -6.915], [14.134, 43.501, 9.266], [13.134, 40.424, 6.915], [16.767, 51.604, -9.266]] - , [[6.081, 57.859, -6.093], [4.682, 44.55, 8.77], [4.372, 41.593, 6.093], [5.77, 54.903, -8.77]] - , [[-6.143, 58.448, -5.205], [-4.59, 43.666, 8.178], [-4.31, 41.004, 5.205], [-5.863, 55.786, -8.178]] - , [[-18.314, 56.365, -4.26], [-13.314, 40.977, 7.496], [-12.588, 38.741, 4.26], [-17.588, 54.129, -7.496]] - , [[-29.83, 51.667, -3.268], [-21.17, 36.667, 6.732], [-20.17, 34.935, 3.268], [-28.83, 49.935, -6.732]] - , [[-40.114, 44.551, -2.24], [-27.888, 30.973, 5.894], [-26.799, 29.764, 2.24], [-39.025, 43.342, -5.894]] - , [[-48.645, 35.343, -1.188], [-33.257, 24.162, 4.992], [-32.257, 23.436, 1.188], [-47.645, 34.616, -4.992]] - , [[-54.993, 24.484, -0.123], [-37.121, 16.527, 4.035], [-36.362, 16.189, 0.123], [-54.233, 24.146, -4.035]] - , [[-58.84, 12.507, 0.944], [-39.384, 8.371, 3.034], [-38.975, 8.284, -0.944], [-58.431, 12.42, -3.034]] - , [[-60, 0, 2], [-40, 0, 2], [-40, 0, -2], [-60, 0, -2]] - , [[-58.431, -12.42, 3.034], [-38.975, -8.284, 0.944], [-39.384, -8.371, -3.034], [-58.84, -12.507, -0.944]] - , [[-54.233, -24.146, 4.035], [-36.362, -16.189, -0.123], [-37.121, -16.527, -4.035], [-54.993, -24.484, 0.123]] - , [[-47.645, -34.616, 4.992], [-32.257, -23.436, -1.188], [-33.257, -24.162, -4.992], [-48.645, -35.343, 1.188]] - , [[-39.025, -43.342, 5.894], [-26.799, -29.764, -2.24], [-27.888, -30.973, -5.894], [-40.114, -44.551, 2.24]] - , [[-28.83, -49.935, 6.732], [-20.17, -34.935, -3.268], [-21.17, -36.667, -6.732], [-29.83, -51.667, 3.268]] - , [[-17.588, -54.129, 7.496], [-12.588, -38.741, -4.26], [-13.314, -40.977, -7.496], [-18.314, -56.365, 4.26]] - , [[-5.863, -55.786, 8.178], [-4.31, -41.004, -5.205], [-4.59, -43.666, -8.178], [-6.143, -58.448, 5.205]] - , [[5.77, -54.903, 8.77], [4.372, -41.593, -6.093], [4.682, -44.55, -8.77], [6.081, -57.859, 6.093]] - , [[16.767, -51.604, 9.266], [13.134, -40.424, -6.915], [14.134, -43.501, -9.266], [17.767, -54.682, 6.915]] - , [[26.634, -46.131, 9.66], [21.634, -37.471, -7.66], [23.366, -40.471, -9.66], [28.366, -49.131, 7.66]] - , [[34.956, -38.822, 9.949], [29.512, -32.777, -8.322], [31.957, -35.492, -9.949], [37.401, -41.538, 8.322]] - , [[41.412, -30.088, 10.129], [36.412, -26.455, -8.893], [39.49, -28.691, -10.129], [44.49, -32.324, 8.893]] - , [[45.789, -20.387, 10.197], [41.991, -18.695, -9.366], [45.565, -20.287, -10.197], [49.364, -21.978, 9.366]] - , [[47.984, -10.199, 10.154], [45.939, -9.765, -9.736], [49.831, -10.592, -10.154], [51.875, -11.026, 9.736]] - , [[48, 0, 10], [48, 0, -10], [52, 0, -10], [52, 0, 10]] - ]; - + expected = [[[52, 0, -10], [52, 0, 10], [48, 0, 10], [48, 0, -10]], [[51.8754, 11.0265, -9.73616], [49.8305, 10.5918, 10.1543], [45.9394, 9.76471, 9.73616], [47.9842, 10.1994, -10.1543]], [[49.3638, 21.9782, -9.36565], [45.5651, 20.2869, 10.1973], [41.9907, 18.6955, 9.36565], [45.7895, 20.3868, -10.1973]], [[44.4897, 32.3237, -8.89253], [39.4897, 28.6909, 10.1286], [36.412, 26.4549, 8.89253], [41.412, 30.0876, -10.1286]], [[37.4007, 41.5377, -8.32198], [31.9575, 35.4924, 9.94893], [29.5124, 32.7768, 8.32198], [34.9556, 38.8221, -9.94893]], [[28.366, 49.1314, -7.66025], [23.366, 40.4711, 9.66025], [21.634, 37.4711, 7.66025], [26.634, 46.1314, -9.66025]], [[17.7672, 54.6818, -6.9146], [14.1345, 43.5015, 9.26574], [13.1345, 40.4238, 6.9146], [16.7672, 51.6042, -9.26574]], [[6.08121, 57.8589, -6.09319], [4.68235, 44.5496, 8.76971], [4.37163, 41.5933, 6.09319], [5.7705, 54.9026, -8.76971]], [[-6.14311, 58.4478, -5.20502], [-4.58951, 43.6663, 8.1776], [-4.30974, 41.0044, 5.20502], [-5.86333, 55.7859, -8.1776]], [[-18.3141, 56.3651, -4.25982], [-13.3141, 40.9767, 7.49589], [-12.5876, 38.7406, 4.25982], [-17.5876, 54.129, -7.49589]], [[-29.8301, 51.6673, -3.26795], [-21.1699, 36.6673, 6.73205], [-20.1699, 34.9352, 3.26795], [-28.8301, 49.9352, -6.73205]], [[-40.1137, 44.5507, -2.24028], [-27.888, 30.9728, 5.89446], [-26.7994, 29.7637, 2.24028], [-39.025, 43.3417, -5.89446]], [[-48.6451, 35.3427, -1.18806], [-33.2566, 24.1624, 4.99228], [-32.2566, 23.4358, 1.18806], [-47.6451, 34.6162, -4.99228]], [[-54.993, 24.4844, -0.122822], [-37.1213, 16.5275, 4.03541], [-36.3616, 16.1892, 0.122822], [-54.2332, 24.1462, -4.03541]], [[-58.8398, 12.5068, 0.943759], [-39.384, 8.37132, 3.03433], [-38.975, 8.28439, -0.943759], [-58.4308, 12.4198, -3.03433]], [[-60, 0, 2], [-40, 0, 2], [-40, 0, -2], [-60, 0, -2]], [[-58.4308, -12.4198, 3.03433], [-38.975, -8.28439, 0.943759], [-39.384, -8.37132, -3.03433], [-58.8398, -12.5068, -0.943759]], [[-54.2332, -24.1462, 4.03541], [-36.3616, -16.1892, -0.122822], [-37.1213, -16.5275, -4.03541], [-54.993, -24.4844, 0.122822]], [[-47.6451, -34.6162, 4.99228], [-32.2566, -23.4358, -1.18806], [-33.2566, -24.1624, -4.99228], [-48.6451, -35.3427, 1.18806]], [[-39.025, -43.3417, 5.89446], [-26.7994, -29.7637, -2.24028], [-27.888, -30.9728, -5.89446], [-40.1137, -44.5507, 2.24028]], [[-28.8301, -49.9352, 6.73205], [-20.1699, -34.9352, -3.26795], [-21.1699, -36.6673, -6.73205], [-29.8301, -51.6673, 3.26795]], [[-17.5876, -54.129, 7.49589], [-12.5876, -38.7406, -4.25982], [-13.3141, -40.9767, -7.49589], [-18.3141, -56.3651, 4.25982]], [[-5.86333, -55.7859, 8.1776], [-4.30974, -41.0044, -5.20502], [-4.58951, -43.6663, -8.1776], [-6.14311, -58.4478, 5.20502]], [[5.7705, -54.9026, 8.76971], [4.37163, -41.5933, -6.09319], [4.68235, -44.5496, -8.76971], [6.08121, -57.8589, 6.09319]], [[16.7672, -51.6042, 9.26574], [13.1345, -40.4238, -6.9146], [14.1345, -43.5015, -9.26574], [17.7672, -54.6818, 6.9146]], [[26.634, -46.1314, 9.66025], [21.634, -37.4711, -7.66025], [23.366, -40.4711, -9.66025], [28.366, -49.1314, 7.66025]], [[34.9556, -38.8221, 9.94893], [29.5124, -32.7768, -8.32198], [31.9575, -35.4924, -9.94893], [37.4007, -41.5377, 8.32198]], [[41.412, -30.0876, 10.1286], [36.412, -26.4549, -8.89253], [39.4897, -28.6909, -10.1286], [44.4897, -32.3237, 8.89253]], [[45.7895, -20.3868, 10.1973], [41.9907, -18.6955, -9.36565], [45.5651, -20.2869, -10.1973], [49.3638, -21.9782, 9.36565]], [[47.9842, -10.1994, 10.1543], [45.9394, -9.76471, -9.73616], [49.8305, -10.5918, -10.1543], [51.8754, -11.0265, 9.73616]], [[48, 0, 10], [48, 0, -10], [52, 0, -10], [52, 0, 10]]]; + for(i = [0:len(expected) - 1]) { - assertEqualPoints(expected[i], sections[i], float_digits = 3); + assertEqualPoints(expected[i], sections[i]); } } @@ -64,27 +32,10 @@ module test_ring_extrude_not_closed() { include ; module test_ring_extrude(sections) { - expected = [ - [[52, 0, -10], [52, 0, 10], [48, 0, 10], [48, 0, -10]] - , [[50.994, 10.839, -10.667], [50.994, 10.839, 10.667], [46.821, 9.952, 10.667], [46.821, 9.952, -10.667]] - , [[47.748, 21.259, -11.333], [47.748, 21.259, 11.333], [43.607, 19.415, 11.333], [43.607, 19.415, -11.333]] - , [[42.392, 30.8, -12], [42.392, 30.8, 12], [38.509, 27.979, 12], [38.509, 27.979, -12]] - , [[35.152, 39.04, -12.667], [35.152, 39.04, 12.667], [31.761, 35.275, 12.667], [31.761, 35.275, -12.667]] - , [[26.333, 45.611, -13.333], [26.333, 45.611, 13.333], [23.667, 40.992, 13.333], [23.667, 40.992, -13.333]] - , [[16.316, 50.216, -14], [16.316, 50.216, 14], [14.586, 44.89, 14], [14.586, 44.89, -14]] - , [[5.533, 52.643, -14.667], [5.533, 52.643, 14.667], [4.92, 46.809, 14.667], [4.92, 46.809, -14.667]] - , [[-5.547, 52.776, -15.333], [-5.547, 52.776, 15.333], [-4.906, 46.676, 15.333], [-4.906, 46.676, -15.333]] - , [[-16.44, 50.596, -16], [-16.44, 50.596, 16], [-14.462, 44.509, 16], [-14.462, 44.509, -16]] - , [[-26.667, 46.188, -16.667], [-26.667, 46.188, 16.667], [-23.333, 40.415, 16.667], [-23.333, 40.415, -16.667]] - , [[-35.776, 39.733, -17.333], [-35.776, 39.733, 17.333], [-31.137, 34.581, 17.333], [-31.137, 34.581, -17.333]] - , [[-43.363, 31.505, -18], [-43.363, 31.505, 18], [-37.538, 27.273, 18], [-37.538, 27.273, -18]] - , [[-49.088, 21.855, -18.667], [-49.088, 21.855, 18.667], [-42.267, 18.818, 18.667], [-42.267, 18.818, -18.667]] - , [[-52.69, 11.2, -19.333], [-52.69, 11.2, 19.333], [-45.125, 9.592, 19.333], [-45.125, 9.592, -19.333]] - , [[-54, 0, -20], [-54, 0, 20], [-46, 0, 20], [-46, 0, -20]] - ]; + expected = [[[52, 0, -10], [52, 0, 10], [48, 0, 10], [48, 0, -10]], [[50.9941, 10.8391, -10.6667], [50.9941, 10.8391, 10.6667], [46.8207, 9.95204, 10.6667], [46.8207, 9.95204, -10.6667]], [[47.748, 21.2588, -11.3333], [47.748, 21.2588, 11.3333], [43.6066, 19.4149, 11.3333], [43.6066, 19.4149, -11.3333]], [[42.3925, 30.7999, -12], [42.3925, 30.7999, 12], [38.5092, 27.9786, 12], [38.5092, 27.9786, -12]], [[35.1517, 39.0399, -12.6667], [35.1517, 39.0399, 12.6667], [31.7614, 35.2746, 12.6667], [31.7614, 35.2746, -12.6667]], [[26.3333, 45.6107, -13.3333], [26.3333, 45.6107, 13.3333], [23.6667, 40.9919, 13.3333], [23.6667, 40.9919, -13.3333]], [[16.3161, 50.2158, -14], [16.3161, 50.2158, 14], [14.5856, 44.8899, 14], [14.5856, 44.8899, -14]], [[5.53304, 52.6434, -14.6667], [5.53304, 52.6434, 14.6667], [4.91981, 46.8088, 14.6667], [4.91981, 46.8088, -14.6667]], [[-5.54698, 52.776, -15.3333], [-5.54698, 52.776, 15.3333], [-4.90587, 46.6762, 15.3333], [-4.90587, 46.6762, -15.3333]], [[-16.4397, 50.5962, -16], [-16.4397, 50.5962, 16], [-14.462, 44.5094, 16], [-14.462, 44.5094, -16]], [[-26.6667, 46.188, -16.6667], [-26.6667, 46.188, 16.6667], [-23.3333, 40.4145, 16.6667], [-23.3333, 40.4145, -16.6667]], [[-35.7762, 39.7335, -17.3333], [-35.7762, 39.7335, 17.3333], [-31.1369, 34.581, 17.3333], [-31.1369, 34.581, -17.3333]], [[-43.3633, 31.5053, -18], [-43.3633, 31.5053, 18], [-37.5384, 27.2732, 18], [-37.5384, 27.2732, -18]], [[-49.0878, 21.8553, -18.6667], [-49.0878, 21.8553, 18.6667], [-42.2667, 18.8183, 18.6667], [-42.2667, 18.8183, -18.6667]], [[-52.6896, 11.1995, -19.3333], [-52.6896, 11.1995, 19.3333], [-45.1252, 9.59166, 19.3333], [-45.1252, 9.59166, -19.3333]], [[-54, 0, -20], [-54, 0, 20], [-46, 0, 20], [-46, 0, -20]]]; for(i = [0:len(expected) - 1]) { - assertEqualPoints(expected[i], sections[i], float_digits = 3); + assertEqualPoints(expected[i], sections[i]); } } @@ -95,6 +46,7 @@ module test_ring_extrude_not_closed() { [-2, -10] ]; + ring_extrude(shape_pts, radius = 50, angle = 180); ring_extrude(shape_pts, radius = 50, angle = 180, scale = 2); } diff --git a/test/test_rounded_cube.scad b/test/test_rounded_cube.scad index 4ae311df..9500da78 100644 --- a/test/test_rounded_cube.scad +++ b/test/test_rounded_cube.scad @@ -11,7 +11,7 @@ module test_rounded_cube_size_corner() { module test_rounded_edge_corner_center(corner_frags, corners, center_pts) { half_size = size / 2; - assertTrue(corner_frags % 4 == 0); + assert(corner_frags % 4 == 0); expected_corners = [[5.0961, 5.0961, 5.0961], [-5.0961, 5.0961, 5.0961], [5.0961, -5.0961, 5.0961], [-5.0961, -5.0961, 5.0961], [5.0961, 5.0961, -5.0961], [-5.0961, 5.0961, -5.0961], [5.0961, -5.0961, -5.0961], [-5.0961, -5.0961, -5.0961]]; @@ -36,7 +36,7 @@ module test_rounded_cube_size_center() { module test_rounded_edge_corner_center(corner_frags, corners, center_pts) { - assertTrue(corner_frags % 4 == 0); + assert(corner_frags % 4 == 0); expected_corners = [[20.0961, 7.5961, 2.5961], [-20.0961, 7.5961, 2.5961], [20.0961, -7.5961, 2.5961], [-20.0961, -7.5961, 2.5961], [20.0961, 7.5961, -2.5961], [-20.0961, 7.5961, -2.5961], [20.0961, -7.5961, -2.5961], [-20.0961, -7.5961, -2.5961]]; @@ -63,7 +63,7 @@ module test_rounded_cube_size_center_fn() { module test_rounded_edge_corner_center(corner_frags, corners, center_pts) { - assertTrue(corner_frags == $fn); + assert(corner_frags == $fn); expected_corners = [[20.3806, 7.8806, 2.8806], [-20.3806, 7.8806, 2.8806], [20.3806, -7.8806, 2.8806], [-20.3806, -7.8806, 2.8806], [20.3806, 7.8806, -2.8806], [-20.3806, 7.8806, -2.8806], [20.3806, -7.8806, -2.8806], [-20.3806, -7.8806, -2.8806]]; diff --git a/test/test_shape_arc.scad b/test/test_shape_arc.scad new file mode 100644 index 00000000..6e8fc276 --- /dev/null +++ b/test/test_shape_arc.scad @@ -0,0 +1,14 @@ +include ; +include ; + +module test_shape_arc() { + echo("==== test_shape_arc ===="); + + expected = [[0, -12.4315], [1.3066, -12.4315], [3.8627, -11.8882], [6.25, -10.8253], [8.3641, -9.2893], [10.1127, -7.3473], [11.4193, -5.0842], [12.2268, -2.5989], [12.5, 0], [12.2268, 2.5989], [11.4193, 5.0842], [10.1127, 7.3473], [8.3641, 9.2893], [6.25, 10.8253], [3.8627, 11.8882], [1.3066, 12.4315], [0, 12.4315], [0, 7.4589], [0.784, 7.4589], [2.3176, 7.1329], [3.75, 6.4952], [5.0185, 5.5736], [6.0676, 4.4084], [6.8516, 3.0505], [7.3361, 1.5593], [7.5, 0], [7.3361, -1.5593], [6.8516, -3.0505], [6.0676, -4.4084], [5.0185, -5.5736], [3.75, -6.4952], [2.3176, -7.1329], [0.784, -7.4589], [0, -7.4589]]; + + actual = shape_arc(radius = 10, angle = [-90, 90], width = 5); + + assertEqualPoints(expected, actual); +} + +test_shape_arc(); \ No newline at end of file diff --git a/test/test_shape_glued2circles.scad b/test/test_shape_glued2circles.scad new file mode 100644 index 00000000..6707695d --- /dev/null +++ b/test/test_shape_glued2circles.scad @@ -0,0 +1,22 @@ +include ; +include ; +include ; +include ; +include ; + +module test_shape_glued2circles() { + echo("==== test_shape_glued2circles ===="); + + $fn = 36; + + radius = 10; + centre_dist = 30; + + expected = [[0, -6.49519], [2.24, -6.58179], [4.42, -6.8416], [6.48, -7.27461], [8.36, -7.88083], [10, -8.66025], [10, -8.66025], [11.5798, -9.39693], [13.2635, -9.84808], [15, -10], [16.7365, -9.84808], [18.4202, -9.39693], [20, -8.66025], [21.4279, -7.66044], [22.6604, -6.42788], [23.6603, -5], [24.3969, -3.4202], [24.8481, -1.73648], [25, 0], [24.8481, 1.73648], [24.3969, 3.4202], [23.6603, 5], [22.6604, 6.42788], [21.4279, 7.66044], [20, 8.66025], [18.4202, 9.39693], [16.7365, 9.84808], [15, 10], [13.2635, 9.84808], [11.5798, 9.39693], [10, 8.66025], [10, 8.66025], [8.36, 7.88083], [6.48, 7.27461], [4.42, 6.8416], [2.24, 6.58179], [0, 6.49519], [0, 6.49519], [-2.24, 6.58179], [-4.42, 6.8416], [-6.48, 7.27461], [-8.36, 7.88083], [-10, 8.66025], [-10, 8.66025], [-11.5798, 9.39693], [-13.2635, 9.84808], [-15, 10], [-16.7365, 9.84808], [-18.4202, 9.39693], [-20, 8.66025], [-21.4279, 7.66044], [-22.6604, 6.42788], [-23.6603, 5], [-24.3969, 3.4202], [-24.8481, 1.73648], [-25, 0], [-24.8481, -1.73648], [-24.3969, -3.4202], [-23.6603, -5], [-22.6604, -6.42788], [-21.4279, -7.66044], [-20, -8.66025], [-18.4202, -9.39693], [-16.7365, -9.84808], [-15, -10], [-13.2635, -9.84808], [-11.5798, -9.39693], [-10, -8.66025], [-10, -8.66025], [-8.36, -7.88083], [-6.48, -7.27461], [-4.42, -6.8416], [-2.24, -6.58179], [0, -6.49519]]; + + actual = shape_glued2circles(radius, centre_dist); + + assertEqualPoints(expected, actual); +} + +test_shape_glued2circles(); \ No newline at end of file diff --git a/test/test_shape_path_extend.scad b/test/test_shape_path_extend.scad index 6cd43257..3e6aac0f 100644 --- a/test/test_shape_path_extend.scad +++ b/test/test_shape_path_extend.scad @@ -31,13 +31,13 @@ module test_shape_path_extend_stroke2() { num_of_points = 85 ); - expected = [[-4.5011, 0.0947], [-8.4053, -3.9989], [-12.4989, -0.0947], [-12.3643, -5.7817], [-8.5243, -12.4798], [-2.2566, -16.2117], [4.7338, -16.8348], [11.2185, -14.7228], [16.3807, -10.5003], [19.7496, -4.8836], [21.1346, 1.4176], [20.5617, 7.7614], [18.2156, 13.6081], [14.389, 18.5362], [9.4388, 22.2465], [3.7507, 24.5569], [-2.2893, 25.3921], [-8.317, 24.7693], [-14.0056, 22.7825], [-19.0767, 19.5862], [-23.3068, 15.3794], [-26.5297, 10.3903], [-28.6366, 4.8631], [-29.5737, -0.9545], [-29.3373, -6.8213], [-27.9691, -12.511], [-25.5494, -17.819], [-22.1903, -22.5671], [-18.0291, -26.6074], [-13.221, -29.8235], [-7.9329, -32.1319], [-2.3372, -33.4815], [3.394, -33.8522], [9.0933, -33.2528], [14.6026, -31.7189], [19.7766, -29.3093], [24.4855, -26.1033], [28.6173, -22.1964], [32.0793, -17.6978], [34.7988, -12.726], [36.7237, -7.4055], [37.8222, -1.8642], [38.0821, 3.7706], [37.5103, 9.3741], [36.1309, 14.8272], [33.984, 20.018], [31.124, 24.8443], [27.6176, 29.2145], [23.5417, 33.0491], [18.9816, 36.2816], [14.0288, 38.859], [8.7792, 40.7418], [3.3307, 41.9044], [-2.2179, 42.3347], [-7.7694, 42.0336], [-13.2293, 41.0145], [-18.5073, 39.3023], [-23.519, 36.9325], [-28.1862, 33.9503], [-32.4387, 30.4092], [-36.2144, 26.3702], [-39.4604, 21.9], [-42.1328, 17.0702], [-44.1976, 11.9559], [-45.6306, 6.6344], [-46.4169, 1.1839], [-46.5514, -4.3173], [-46.0381, -9.7921], [-44.8898, -15.1657], [-43.1276, -20.3663], [-40.7801, -25.3262], [-37.8833, -29.9823], [-34.479, -34.2768], [-30.6151, -38.1579], [-26.3437, -41.5801], [-21.7212, -44.5045], [-16.8071, -46.8992], [-11.663, -48.7393], [-6.352, -50.0072], [-0.9381, -50.6921], [4.5151, -50.7904], [9.9446, -50.3053], [15.2889, -49.2466], [20.4888, -47.6301], [25.4876, -45.4777], [30.2321, -42.8167], [34.6727, -39.6793], [35.6093, -34.1005], [30.0305, -33.1639], [30.0305, -33.1639], [26.2907, -35.855], [22.294, -38.1428], [18.0826, -40.0005], [13.7017, -41.4056], [9.1992, -42.3401], [4.6253, -42.7912], [0.0318, -42.7511], [-4.5284, -42.2178], [-9.0017, -41.195], [-13.3348, -39.6921], [-17.4748, -37.7246], [-21.3703, -35.3139], [-24.972, -32.4873], [-28.2333, -29.2777], [-31.1109, -25.7237], [-33.5658, -21.8689], [-35.5634, -17.7618], [-37.0749, -13.455], [-38.0769, -9.0052], [-38.5529, -4.4719], [-38.493, 0.0827], [-37.8948, 4.5951], [-36.7635, 9.0007], [-35.1119, 13.2352], [-32.9611, 17.2353], [-30.3397, 20.9399], [-27.2846, 24.2908], [-23.8397, 27.234], [-20.0566, 29.7206], [-15.9932, 31.7076], [-11.7134, 33.1594], [-7.2866, 34.0482], [-2.786, 34.3549], [1.7117, 34.0699], [6.1279, 33.1939], [10.3834, 31.7378], [14.3997, 29.7237], [18.1006, 27.1845], [21.4135, 24.1638], [24.2714, 20.7162], [26.6141, 16.9059], [28.3902, 12.8067], [29.5581, 8.5005], [30.0879, 4.0761], [29.9625, -0.3721], [29.1786, -4.7462], [27.7479, -8.9466], [25.6972, -12.8741], [23.0694, -16.4328], [19.9228, -19.532], [16.3312, -22.0893], [12.3824, -24.0332], [8.1775, -25.3054], [3.8285, -25.864], [-0.5437, -25.6851], [-4.8124, -24.7656], [-8.8484, -23.1242], [-12.5235, -20.8032], [-15.7156, -17.8685], [-18.3121, -14.4099], [-20.2157, -10.5398], [-21.3488, -6.3913], [-21.6583, -2.1154], [-21.1203, 2.1236], [-19.7441, 6.153], [-17.5751, 9.7984], [-14.6973, 12.8913], [-11.2338, 15.278], [-7.3453, 16.8285], [-3.2269, 17.4472], [0.898, 17.0828], [4.7872, 15.7378], [8.1917, 13.4772], [10.8722, 10.4342], [12.618, 6.8134], [13.2708, 2.8875], [12.749, -1.0117], [11.0749, -4.5129], [8.3989, -7.2362], [5.0179, -8.8399], [1.3786, -9.0853], [-1.9491, -7.9227]]; + expected = [[-4.50112, 0.0946668], [-8.40532, -3.99889], [-12.4989, -0.0946859], [-12.3642, -5.78176], [-8.52426, -12.4798], [-2.25652, -16.2117], [4.73389, -16.8348], [11.2186, -14.7228], [16.3807, -10.5002], [19.7496, -4.88353], [21.1345, 1.41768], [20.5616, 7.76153], [18.2155, 13.6082], [14.3889, 18.5363], [9.43865, 22.2465], [3.75054, 24.5569], [-2.2895, 25.3921], [-8.31717, 24.7692], [-14.0057, 22.7824], [-19.0769, 19.586], [-23.3069, 15.3792], [-26.5298, 10.3901], [-28.6367, 4.86291], [-29.5736, -0.954708], [-29.3372, -6.82151], [-27.969, -12.5112], [-25.5492, -17.8192], [-22.1901, -22.5673], [-18.0289, -26.6075], [-13.2208, -29.8236], [-7.93264, -32.132], [-2.33684, -33.4815], [3.39434, -33.8521], [9.09361, -33.2527], [14.6029, -31.7188], [19.7769, -29.3091], [24.4858, -26.103], [28.6176, -22.1962], [32.0795, -17.6975], [34.799, -12.7256], [36.7238, -7.40514], [37.8222, -1.86377], [38.0821, 3.77099], [37.5102, 9.37453], [36.1307, 14.8276], [33.9838, 20.0184], [31.1237, 24.8447], [27.6173, 29.2148], [23.5413, 33.0494], [18.9812, 36.2819], [14.0284, 38.8591], [8.7787, 40.7419], [3.33025, 41.9044], [-2.21838, 42.3346], [-7.76988, 42.0335], [-13.2298, 41.0143], [-18.5078, 39.302], [-23.5194, 36.9322], [-28.1866, 33.9499], [-32.4391, 30.4088], [-36.2148, 26.3697], [-39.4606, 21.8995], [-42.133, 17.0697], [-44.1978, 11.9554], [-45.6306, 6.63376], [-46.4169, 1.18325], [-46.5513, -4.31793], [-46.038, -9.79273], [-44.8896, -15.1663], [-43.1273, -20.3669], [-40.7798, -25.3268], [-37.8829, -29.9828], [-34.4786, -34.2773], [-30.6145, -38.1583], [-26.3431, -41.5805], [-21.7206, -44.5048], [-16.8064, -46.8994], [-11.6623, -48.7395], [-6.35131, -50.0073], [-0.937338, -50.6921], [4.51586, -50.7903], [9.94533, -50.3052], [15.2896, -49.2463], [20.4895, -47.6298], [25.4883, -45.4773], [30.2327, -42.8162], [34.6733, -39.6788], [35.6098, -34.1], [30.031, -33.1634], [30.031, -33.1634], [26.2913, -35.8546], [22.2946, -38.1424], [18.0832, -40.0002], [13.7023, -41.4054], [9.19983, -42.34], [4.62594, -42.7911], [0.032421, -42.7511], [-4.52778, -42.2179], [-9.00115, -41.1951], [-13.3342, -39.6922], [-17.4742, -37.7248], [-21.3698, -35.3142], [-24.9715, -32.4876], [-28.2329, -29.2781], [-31.1106, -25.7242], [-33.5655, -21.8694], [-35.5632, -17.7623], [-37.0747, -13.4555], [-38.0768, -9.0057], [-38.5528, -4.47244], [-38.493, 0.082213], [-37.8949, 4.59457], [-36.7636, 9.00019], [-35.1121, 13.2347], [-32.9613, 17.2349], [-30.34, 20.9395], [-27.2849, 24.2905], [-23.8401, 27.2337], [-20.057, 29.7203], [-15.9936, 31.7074], [-11.7138, 33.1593], [-7.28699, 34.0481], [-2.78643, 34.3548], [1.71125, 34.0699], [6.12748, 33.1939], [10.383, 31.7379], [14.3994, 29.7239], [18.1003, 27.1847], [21.4132, 24.1641], [24.2711, 20.7165], [26.6139, 16.9062], [28.3901, 12.8071], [29.558, 8.50082], [30.0879, 4.07644], [29.9625, -0.3718], [29.1787, -4.74591], [27.748, -8.94627], [25.6973, -12.8738], [23.0695, -16.4325], [19.923, -19.5318], [16.3314, -22.0891], [12.3826, -24.033], [8.17771, -25.3053], [3.82872, -25.8639], [-0.543495, -25.6851], [-4.81221, -24.7656], [-8.84815, -23.1243], [-12.5234, -20.8033], [-15.7154, -17.8686], [-18.312, -14.41], [-20.2157, -10.5399], [-21.3488, -6.3915], [-21.6583, -2.11558], [-21.1204, 2.12341], [-19.7441, 6.15281], [-17.5752, 9.79825], [-14.6974, 12.8912], [-11.2339, 15.2779], [-7.34541, 16.8284], [-3.22705, 17.4472], [0.897907, 17.0828], [4.78711, 15.7378], [8.19166, 13.4772], [10.8721, 10.4343], [12.618, 6.81346], [13.2708, 2.8876], [12.749, -1.01163], [11.0749, -4.51283], [8.39894, -7.23614], [5.01789, -8.83984], [1.37862, -9.08532], [-1.9491, -7.92267]]; actual = shape_path_extend( stroke2, [for(pa = pts_angles) pa[0]] ); - + assertEqualPoints(expected, actual); } diff --git a/test/test_shape_starburst.scad b/test/test_shape_starburst.scad new file mode 100644 index 00000000..8c7646ed --- /dev/null +++ b/test/test_shape_starburst.scad @@ -0,0 +1,14 @@ +include ; +include ; + +module test_shape_starburst() { + echo("==== test_shape_starburst ===="); + + expected = [[30, 0], [10.3923, 6], [15, 25.9808], [0, 12], [-15, 25.9808], [-10.3923, 6], [-30, 0], [-10.3923, -6], [-15, -25.9808], [0, -12], [15, -25.9808], [10.3923, -6]]; + + actual = shape_starburst(30, 12, 6); + + assertEqualPoints(expected, actual); +} + +test_shape_starburst(); \ No newline at end of file diff --git a/test/test_shape_superformula.scad b/test/test_shape_superformula.scad index fd249fa3..fe273b2c 100644 --- a/test/test_shape_superformula.scad +++ b/test/test_shape_superformula.scad @@ -6,53 +6,16 @@ module test_shape_superformula() { phi_step = 0.05; + assertEqualPoints( - [[1, 0], [1.0003, 0.0501], [1.0012, 0.1005], [1.0028, 0.1516], [1.005, 0.2037], [1.0077, 0.2573], [1.0111, 0.3128], [1.015, 0.3705], [1.0195, 0.431], [1.0245, 0.4949], [1.0299, 0.5626], [1.0357, 0.635], [1.0418, 0.7127], [1.0479, 0.7966], [1.0538, 0.8876], [1.0589, 0.9865], [1.0621, 1.0936], [1.0614, 1.2083], [1.0533, 1.3273], [1.0318, 1.4429], [0.9897, 1.5413], [0.9213, 1.6062], [0.8287, 1.6281], [0.7213, 1.6117], [0.6105, 1.5704], [0.5041, 1.5171], [0.4054, 1.4602], [0.3152, 1.4041], [0.2329, 1.3506], [0.1578, 1.3004], [0.0889, 1.2534], [0.0252, 1.2097], [-0.0341, 1.1688], [-0.0897, 1.1305], [-0.1422, 1.0945], [-0.1921, 1.0606], [-0.24, 1.0285], [-0.2861, 0.998], [-0.331, 0.969], [-0.375, 0.9412], [-0.4185, 0.9144], [-0.4616, 0.8885], [-0.5049, 0.8632], [-0.5484, 0.8385], [-0.5926, 0.8142], [-0.6378, 0.79], [-0.6842, 0.7657], [-0.7322, 0.7413], [-0.7821, 0.7164], [-0.8344, 0.6909], [-0.8893, 0.6644], [-0.9475, 0.6366], [-1.0093, 0.6072], [-1.0754, 0.5758], [-1.1463, 0.5419], [-1.2227, 0.5049], [-1.3052, 0.464], [-1.3941, 0.4184], [-1.4891, 0.3669], [-1.5883, 0.3081], [-1.6868, 0.2404], [-1.7743, 0.163], [-1.8345, 0.0763], [-1.851, -0.0156], [-1.8184, -0.1063], [-1.747, -0.1901], [-1.6543, -0.2643], [-1.5547, -0.3288], [-1.4565, -0.385], [-1.3634, -0.4344], [-1.2767, -0.4782], [-1.1964, -0.5177], [-1.1219, -0.5536], [-1.0527, -0.5866], [-0.9881, -0.6173], [-0.9276, -0.6461], [-0.8705, -0.6734], [-0.8165, -0.6996], [-0.7651, -0.7249], [-0.7158, -0.7496], [-0.6684, -0.7739], [-0.6225, -0.7981], [-0.5777, -0.8223], [-0.5337, -0.8468], [-0.4903, -0.8716], [-0.4471, -0.8971], [-0.4039, -0.9233], [-0.3603, -0.9504], [-0.3161, -0.9786], [-0.2708, -1.0081], [-0.2241, -1.0391], [-0.1756, -1.0718], [-0.1249, -1.1064], [-0.0714, -1.1431], [-0.0146, -1.1822], [0.0461, -1.2241], [0.1115, -1.2689], [0.1824, -1.3169], [0.2598, -1.3682], [0.3446, -1.4227], [0.4376, -1.4794], [0.5391, -1.5357], [0.6476, -1.5862], [0.7583, -1.6207], [0.8621, -1.6255], [0.9473, -1.589], [1.0066, -1.5112], [1.041, -1.4051], [1.0572, -1.2871], [1.0623, -1.169], [1.0613, -1.0566], [1.0573, -0.9523], [1.0519, -0.8562], [1.0458, -0.7676], [1.0397, -0.6859], [1.0337, -0.6101], [1.028, -0.5394], [1.0227, -0.473], [1.0179, -0.4103], [1.0136, -0.3508], [1.0099, -0.2939], [1.0067, -0.2391], [1.0042, -0.186], [1.0022, -0.1343], [1.0009, -0.0834], [1.0001, -0.0332]], + [[1, 0], [1.00031, 0.0500573], [1.00125, 0.10046], [1.0028, 0.151559], [1.00497, 0.203718], [1.00774, 0.257319], [1.0111, 0.31277], [1.01503, 0.370514], [1.01949, 0.431035], [1.02447, 0.494873], [1.02989, 0.562631], [1.03569, 0.634988], [1.04176, 0.712707], [1.04791, 0.796625], [1.05382, 0.887618], [1.05891, 0.986477], [1.06212, 1.09359], [1.06143, 1.20826], [1.05327, 1.32729], [1.03183, 1.4429], [0.989681, 1.54134], [0.921341, 1.60619], [0.828655, 1.62811], [0.721278, 1.61169], [0.61053, 1.57037], [0.50409, 1.51709], [0.405381, 1.46023], [0.315158, 1.4041], [0.232947, 1.3506], [0.157848, 1.30036], [0.0888879, 1.25345], [0.0251604, 1.20967], [-0.0341423, 1.16878], [-0.0897256, 1.13048], [-0.142206, 1.0945], [-0.192123, 1.06059], [-0.239956, 1.02851], [-0.286133, 0.998049], [-0.331044, 0.968998], [-0.375046, 0.941168], [-0.418473, 0.91438], [-0.461641, 0.888456], [-0.504856, 0.863226], [-0.548417, 0.838518], [-0.592622, 0.814157], [-0.637774, 0.789965], [-0.684186, 0.765751], [-0.732186, 0.741314], [-0.782123, 0.716436], [-0.834372, 0.690875], [-0.889346, 0.664361], [-0.947497, 0.63659], [-1.00933, 0.607209], [-1.0754, 0.575806], [-1.14631, 0.541894], [-1.22271, 0.504878], [-1.30517, 0.464026], [-1.39405, 0.418422], [-1.48905, 0.366911], [-1.58832, 0.30809], [-1.68684, 0.240453], [-1.77429, 0.162968], [-1.8345, 0.076346], [-1.85103, -0.0155626], [-1.81842, -0.10633], [-1.74702, -0.190135], [-1.6543, -0.264268], [-1.55469, -0.328782], [-1.45649, -0.384975], [-1.36344, -0.434355], [-1.27673, -0.478245], [-1.19637, -0.517714], [-1.12188, -0.553613], [-1.05267, -0.586621], [-0.988091, -0.617293], [-0.927557, -0.64609], [-0.870528, -0.673402], [-0.816518, -0.699563], [-0.765091, -0.724866], [-0.715846, -0.74957], [-0.668418, -0.773908], [-0.622465, -0.798093], [-0.577665, -0.822322], [-0.533711, -0.84678], [-0.490299, -0.871644], [-0.447134, -0.897088], [-0.403913, -0.923283], [-0.360329, -0.950402], [-0.316059, -0.978622], [-0.270764, -1.00813], [-0.224075, -1.03911], [-0.175591, -1.07178], [-0.124868, -1.10636], [-0.0714085, -1.14308], [-0.0146473, -1.18223], [0.0460598, -1.22406], [0.111452, -1.26886], [0.18237, -1.31688], [0.259752, -1.36824], [0.344568, -1.42274], [0.437631, -1.47942], [0.53912, -1.53573], [0.647576, -1.58617], [0.758281, -1.62073], [0.862053, -1.62552], [0.947326, -1.58897], [1.00661, -1.5112], [1.04098, -1.40513], [1.05716, -1.28714], [1.06228, -1.16898], [1.06135, -1.05666], [1.05734, -0.952316], [1.05189, -0.856175], [1.04585, -0.767657], [1.0397, -0.685922], [1.0337, -0.610096], [1.02802, -0.539367], [1.02274, -0.472999], [1.01793, -0.41034], [1.01364, -0.35081], [1.00991, -0.293889], [1.00674, -0.239108], [1.00417, -0.186036], [1.00221, -0.134275], [1.00086, -0.0834498], [1.00014, -0.0332021]], shape_superformula(phi_step, 3, 3, 4.5, 10, 10) ); - - assertEqualPoints( - [[1, 0], [1.0003, 0.0501], [1.0013, 0.1005], [1.0028, 0.1516], [1.005, 0.2037], [1.0079, 0.2574], [1.0115, 0.3129], [1.0158, 0.3708], [1.0208, 0.4316], [1.0266, 0.4959], [1.0332, 0.5644], [1.0406, 0.638], [1.0489, 0.7176], [1.0572, 0.8037], [1.0628, 0.8952], [1.0548, 0.9827], [1.0124, 1.0424], [0.9331, 1.0622], [0.8414, 1.0602], [0.7526, 1.0524], [0.6703, 1.044], [0.5944, 1.0362], [0.5238, 1.0292], [0.4579, 1.0231], [0.3957, 1.0178], [0.3367, 1.0132], [0.2802, 1.0093], [0.2258, 1.0062], [0.1731, 1.0037], [0.1216, 1.0018], [0.071, 1.0006], [0.0208, 1.0001], [-0.0292, 1.0001], [-0.0794, 1.0008], [-0.1302, 1.0021], [-0.1819, 1.004], [-0.2349, 1.0066], [-0.2895, 1.0099], [-0.3464, 1.0139], [-0.4059, 1.0186], [-0.4687, 1.0241], [-0.5354, 1.0303], [-0.6067, 1.0374], [-0.6837, 1.0454], [-0.7671, 1.0538], [-0.8568, 1.0612], [-0.948, 1.061], [-1.0226, 1.0353], [-1.058, 0.9691], [-1.0624, 0.8796], [-1.0559, 0.7888], [-1.0474, 0.7037], [-1.0393, 0.6253], [-1.032, 0.5526], [-1.0255, 0.4848], [-1.0199, 0.4211], [-1.015, 0.3609], [-1.0108, 0.3034], [-1.0074, 0.2482], [-1.0046, 0.1949], [-1.0025, 0.1429], [-1.0011, 0.0919], [-1.0002, 0.0416], [-1, -0.0084], [-1.0004, -0.0585], [-1.0015, -0.109], [-1.0032, -0.1603], [-1.0055, -0.2126], [-1.0085, -0.2666], [-1.0122, -0.3224], [-1.0165, -0.3808], [-1.0217, -0.4421], [-1.0276, -0.5071], [-1.0344, -0.5764], [-1.042, -0.651], [-1.0503, -0.7316], [-1.0585, -0.8188], [-1.0629, -0.9106], [-1.0506, -0.9954], [-1.0011, -1.0483], [-0.9179, -1.0628], [-0.826, -1.0591], [-0.7383, -1.051], [-0.6571, -1.0426], [-0.5822, -1.0349], [-0.5124, -1.0281], [-0.4472, -1.0221], [-0.3855, -1.0169], [-0.327, -1.0125], [-0.2709, -1.0087], [-0.2169, -1.0057], [-0.1644, -1.0033], [-0.113, -1.0016], [-0.0625, -1.0005], [-0.0124, -1], [0.0376, -1.0002], [0.0879, -1.001], [0.1388, -1.0024], [0.1907, -1.0044], [0.2439, -1.0072], [0.2989, -1.0105], [0.3562, -1.0146], [0.4162, -1.0195], [0.4796, -1.0251], [0.547, -1.0315], [0.6193, -1.0387], [0.6973, -1.0468], [0.7818, -1.0552], [0.8723, -1.0621], [0.9625, -1.0591], [1.0315, -1.027], [1.0602, -0.9549], [1.0617, -0.8641], [1.0545, -0.774], [1.046, -0.6901], [1.038, -0.6126], [1.0309, -0.5408], [1.0245, -0.4738], [1.019, -0.4108], [1.0142, -0.351], [1.0102, -0.294], [1.0069, -0.2391], [1.0042, -0.186], [1.0022, -0.1343], [1.0009, -0.0834], [1.0001, -0.0332]], + [[1, 0], [1.00031, 0.0500574], [1.00125, 0.10046], [1.00283, 0.151562], [1.00505, 0.203733], [1.00793, 0.257366], [1.01149, 0.31289], [1.01576, 0.370781], [1.02077, 0.431575], [1.02656, 0.495886], [1.03317, 0.564426], [1.04064, 0.638021], [1.04887, 0.717569], [1.05724, 0.803717], [1.0628, 0.89518], [1.05482, 0.982667], [1.01242, 1.04243], [0.933118, 1.0622], [0.841354, 1.06024], [0.752593, 1.05241], [0.670333, 1.04398], [0.594371, 1.03618], [0.523835, 1.02921], [0.457858, 1.02308], [0.395681, 1.01775], [0.336652, 1.01318], [0.280204, 1.00932], [0.225839, 1.00616], [0.17311, 1.00367], [0.121609, 1.00183], [0.0709593, 1.00063], [0.0208004, 1.00005], [-0.0292151, 1.00011], [-0.079432, 1.00079], [-0.1302, 1.00209], [-0.18188, 1.00404], [-0.234854, 1.00665], [-0.289537, 1.00992], [-0.346382, 1.01389], [-0.405899, 1.01859], [-0.468666, 1.02405], [-0.535354, 1.03032], [-0.606739, 1.03743], [-0.683704, 1.04537], [-0.767083, 1.05384], [-0.856786, 1.06124], [-0.948011, 1.06103], [-1.02259, 1.03534], [-1.05797, 0.969119], [-1.06236, 0.879651], [-1.05589, 0.788775], [-1.04744, 0.703741], [-1.03932, 0.625254], [-1.032, 0.552572], [-1.02553, 0.484797], [-1.01987, 0.421124], [-1.01499, 0.360859], [-1.01084, 0.303402], [-1.0074, 0.248228], [-1.00463, 0.19487], [-1.00252, 0.142905], [-1.00105, 0.0919462], [-1.00022, 0.0416257], [-1.00001, -0.00840762], [-1.00043, -0.0584988], [-1.00147, -0.108994], [-1.00315, -0.16025], [-1.00548, -0.212638], [-1.00848, -0.266558], [-1.01216, -0.322445], [-1.01655, -0.380784], [-1.02169, -0.442124], [-1.02761, -0.507094], [-1.03437, -0.576423], [-1.04197, -0.650956], [-1.0503, -0.731587], [-1.05852, -0.818825], [-1.06289, -0.910641], [-1.05065, -0.995413], [-1.00113, -1.04829], [-0.917916, -1.06278], [-0.826033, -1.0591], [-0.738293, -1.05098], [-0.657142, -1.04261], [-0.582156, -1.03494], [-0.512444, -1.02812], [-0.447156, -1.02213], [-0.385551, -1.01693], [-0.326994, -1.01248], [-0.27093, -1.00874], [-0.21687, -1.0057], [-0.164375, -1.00332], [-0.113043, -1.00158], [-0.0625005, -1.00049], [-0.0123899, -1.00002], [0.0376354, -1.00018], [0.0879203, -1.00096], [0.138816, -1.00238], [0.190686, -1.00444], [0.243918, -1.00715], [0.298931, -1.01054], [0.356188, -1.01463], [0.416209, -1.01946], [0.479586, -1.02505], [0.547006, -1.03146], [0.619266, -1.03871], [0.697257, -1.04677], [0.78176, -1.05524], [0.872294, -1.06205], [0.962466, -1.05915], [1.03154, -1.02698], [1.06023, -0.95492], [1.06165, -0.864124], [1.0545, -0.774011], [1.04603, -0.6901], [1.03803, -0.612652], [1.03086, -0.540856], [1.02452, -0.473824], [1.019, -0.41077], [1.01424, -0.351017], [1.01021, -0.293978], [1.00688, -0.239141], [1.00423, -0.186045], [1.00223, -0.134277], [1.00087, -0.0834499], [1.00014, -0.0332021]], shape_superformula(phi_step, 4, 4, 12, 15, 15) ); - - - assertEqualPoints( - [[1, 0], [1.001, 0.0501], [1.0042, 0.1008], [1.0096, 0.1526], [1.0173, 0.2062], [1.0271, 0.2623], [1.0381, 0.3211], [1.0476, 0.3824], [1.0493, 0.4436], [1.0343, 0.4996], [0.9989, 0.5457], [0.9496, 0.5822], [0.8957, 0.6128], [0.843, 0.6408], [0.7932, 0.6681], [0.7466, 0.6956], [0.7029, 0.7237], [0.6614, 0.7528], [0.6216, 0.7833], [0.5832, 0.8155], [0.5456, 0.8497], [0.5084, 0.8863], [0.4713, 0.9259], [0.4335, 0.9687], [0.3942, 1.0141], [0.3521, 1.0596], [0.305, 1.0985], [0.2516, 1.1208], [0.1933, 1.1208], [0.1341, 1.1044], [0.0767, 1.0812], [0.022, 1.0575], [-0.0303, 1.0357], [-0.0807, 1.0165], [-0.1299, 1], [-0.1786, 0.9858], [-0.2272, 0.9739], [-0.2764, 0.9639], [-0.3266, 0.9559], [-0.3785, 0.9499], [-0.4327, 0.9456], [-0.4899, 0.9428], [-0.55, 0.9403], [-0.6119, 0.9355], [-0.6714, 0.9224], [-0.7215, 0.8937], [-0.7571, 0.8474], [-0.7808, 0.7905], [-0.7983, 0.7312], [-0.8138, 0.6738], [-0.8294, 0.6196], [-0.8459, 0.5683], [-0.8637, 0.5196], [-0.8831, 0.4728], [-0.9041, 0.4274], [-0.9271, 0.3828], [-0.9523, 0.3386], [-0.98, 0.2941], [-1.0106, 0.249], [-1.0442, 0.2025], [-1.0798, 0.1539], [-1.1144, 0.1024], [-1.1407, 0.0475], [-1.1484, -0.0097], [-1.1334, -0.0663], [-1.1033, -0.1201], [-1.0677, -0.1706], [-1.0326, -0.2184], [-1, -0.2643], [-0.9704, -0.3091], [-0.9435, -0.3534], [-0.9191, -0.3977], [-0.8968, -0.4426], [-0.8764, -0.4884], [-0.8576, -0.5358], [-0.8402, -0.5852], [-0.8241, -0.6375], [-0.8086, -0.6928], [-0.7928, -0.7511], [-0.7738, -0.8103], [-0.7468, -0.8646], [-0.7061, -0.9054], [-0.6521, -0.9282], [-0.591, -0.9377], [-0.5294, -0.9412], [-0.4703, -0.9436], [-0.4142, -0.9468], [-0.3608, -0.9517], [-0.3095, -0.9584], [-0.2597, -0.9671], [-0.2108, -0.9777], [-0.1622, -0.9903], [-0.1135, -1.0053], [-0.0639, -1.0227], [-0.0129, -1.0427], [0.0401, -1.0653], [0.0957, -1.0893], [0.1539, -1.1111], [0.2132, -1.1231], [0.2702, -1.1157], [0.3215, -1.0867], [0.3667, -1.0445], [0.4077, -0.9986], [0.4463, -0.9539], [0.4838, -0.9122], [0.5209, -0.8737], [0.5581, -0.8379], [0.596, -0.8045], [0.6348, -0.7729], [0.6751, -0.7429], [0.7173, -0.7141], [0.762, -0.6863], [0.8096, -0.6589], [0.8604, -0.6315], [0.9139, -0.6029], [0.9671, -0.5708], [1.0129, -0.5314], [1.0417, -0.4817], [1.0501, -0.4233], [1.0449, -0.3616], [1.0344, -0.301], [1.0236, -0.2431], [1.0145, -0.1879], [1.0076, -0.135], [1.0029, -0.0836], [1.0005, -0.0332]], - shape_superformula(phi_step, 7, 7, 10, 6, 6) - ); - - - assertEqualPoints( - [[1, 0], [1.0007, 0.0501], [1.0028, 0.1006], [1.0061, 0.1521], [1.0104, 0.2048], [1.0155, 0.2593], [1.0206, 0.3157], [1.025, 0.3742], [1.0274, 0.4344], [1.0261, 0.4957], [1.0192, 0.5568], [1.0045, 0.6158], [0.9803, 0.6706], [0.946, 0.7192], [0.9025, 0.7601], [0.8516, 0.7934], [0.7961, 0.8197], [0.7383, 0.8405], [0.6802, 0.8572], [0.6231, 0.8714], [0.5676, 0.884], [0.514, 0.8961], [0.4623, 0.9082], [0.4121, 0.9209], [0.3633, 0.9344], [0.3153, 0.949], [0.2679, 0.965], [0.2205, 0.9824], [0.1727, 1.0012], [0.124, 1.0215], [0.074, 1.043], [0.0222, 1.0652], [-0.0318, 1.0875], [-0.088, 1.1087], [-0.1464, 1.127], [-0.2065, 1.1401], [-0.2673, 1.1456], [-0.3271, 1.141], [-0.3843, 1.1249], [-0.4374, 1.0976], [-0.4854, 1.0606], [-0.5282, 1.0166], [-0.5664, 0.9685], [-0.6007, 0.9185], [-0.6322, 0.8685], [-0.6616, 0.8194], [-0.6897, 0.7719], [-0.7173, 0.7262], [-0.7448, 0.6822], [-0.7726, 0.6398], [-0.8013, 0.5986], [-0.8309, 0.5583], [-0.8619, 0.5185], [-0.8944, 0.4789], [-0.9285, 0.4389], [-0.9642, 0.3981], [-1.0013, 0.356], [-1.0391, 0.3119], [-1.0767, 0.2653], [-1.1126, 0.2158], [-1.1444, 0.1631], [-1.1694, 0.1074], [-1.185, 0.0493], [-1.189, -0.01], [-1.181, -0.0691], [-1.1619, -0.1265], [-1.1343, -0.1812], [-1.1008, -0.2328], [-1.0642, -0.2813], [-1.0263, -0.327], [-0.9887, -0.3703], [-0.9521, -0.412], [-0.9169, -0.4525], [-0.8833, -0.4922], [-0.8513, -0.5319], [-0.8208, -0.5717], [-0.7915, -0.6123], [-0.7632, -0.6539], [-0.7355, -0.6968], [-0.708, -0.7414], [-0.6803, -0.7877], [-0.6518, -0.8358], [-0.6219, -0.8852], [-0.5896, -0.9354], [-0.554, -0.985], [-0.5144, -1.032], [-0.4698, -1.074], [-0.4201, -1.108], [-0.3655, -1.1316], [-0.3072, -1.1438], [-0.2469, -1.1448], [-0.1862, -1.1364], [-0.1265, -1.1213], [-0.0688, -1.1018], [-0.0134, -1.0801], [0.0398, -1.0577], [0.091, -1.0356], [0.1405, -1.0145], [0.1888, -0.9947], [0.2365, -0.9763], [0.2838, -0.9595], [0.3314, -0.944], [0.3796, -0.9297], [0.4288, -0.9165], [0.4795, -0.9041], [0.5318, -0.8921], [0.5861, -0.8799], [0.6422, -0.8668], [0.6997, -0.8519], [0.7579, -0.834], [0.8151, -0.8115], [0.8694, -0.783], [0.9181, -0.7472], [0.9586, -0.7036], [0.9895, -0.6528], [1.0104, -0.5963], [1.0223, -0.5364], [1.0271, -0.475], [1.0269, -0.414], [1.0237, -0.3543], [1.0189, -0.2965], [1.0137, -0.2408], [1.0089, -0.1869], [1.0048, -0.1346], [1.0019, -0.0835], [1.0003, -0.0332]], - shape_superformula(phi_step, 5, 5, 4, 4, 4) - ); - - - assertEqualPoints( - [[1, 0], [1.0056, 0.0503], [1.0227, 0.1026], [1.0519, 0.159], [1.0946, 0.2219], [1.1526, 0.2943], [1.2283, 0.38], [1.3248, 0.4836], [1.4443, 0.6106], [1.5862, 0.7662], [1.7408, 0.951], [1.8778, 1.1513], [1.9418, 1.3285], [1.8814, 1.4302], [1.7043, 1.4355], [1.4736, 1.3728], [1.247, 1.2839], [1.0505, 1.1958], [0.8884, 1.1195], [0.7565, 1.0579], [0.6488, 1.0105], [0.5599, 0.9761], [0.4853, 0.9535], [0.4214, 0.9417], [0.3656, 0.9403], [0.3154, 0.9491], [0.2689, 0.9685], [0.2243, 0.9993], [0.1798, 1.0427], [0.1336, 1.1007], [0.0834, 1.1757], [0.0264, 1.2712], [-0.0406, 1.3913], [-0.1222, 1.5402], [-0.2234, 1.7195], [-0.3482, 1.922], [-0.4943, 2.1189], [-0.6448, 2.2491], [-0.7666, 2.2438], [-0.8339, 2.0925], [-0.8507, 1.8587], [-0.8385, 1.6137], [-0.8158, 1.3949], [-0.793, 1.2124], [-0.7744, 1.0639], [-0.7617, 0.9435], [-0.7556, 0.8457], [-0.7562, 0.7657], [-0.7638, 0.6997], [-0.7787, 0.6448], [-0.8015, 0.5988], [-0.8331, 0.5597], [-0.8747, 0.5262], [-0.9281, 0.4969], [-0.9954, 0.4705], [-1.0797, 0.4458], [-1.185, 0.4213], [-1.3162, 0.395], [-1.4785, 0.3643], [-1.6756, 0.325], [-1.9038, 0.2714], [-2.1389, 0.1965], [-2.3222, 0.0966], [-2.376, -0.02], [-2.2714, -0.1328], [-2.0619, -0.2244], [-1.8245, -0.2915], [-1.6054, -0.3395], [-1.4201, -0.3754], [-1.2688, -0.4042], [-1.147, -0.4296], [-1.0492, -0.454], [-0.971, -0.4792], [-0.9087, -0.5064], [-0.8595, -0.537], [-0.8214, -0.5722], [-0.7929, -0.6134], [-0.7729, -0.6622], [-0.7605, -0.7205], [-0.7553, -0.7908], [-0.7569, -0.8764], [-0.7653, -0.9812], [-0.78, -1.1104], [-0.8003, -1.2698], [-0.8238, -1.4646], [-0.8445, -1.6943], [-0.8494, -1.9416], [-0.8177, -2.1567], [-0.7309, -2.2632], [-0.5956, -2.2175], [-0.4434, -2.0564], [-0.3035, -1.8525], [-0.1869, -1.6559], [-0.0929, -1.4867], [-0.0167, -1.3479], [0.0465, -1.2365], [0.1009, -1.1483], [0.1495, -1.0794], [0.1949, -1.0266], [0.2392, -0.9876], [0.2842, -0.9608], [0.3317, -0.945], [0.3836, -0.9396], [0.4419, -0.9445], [0.509, -0.9598], [0.588, -0.9863], [0.6827, -1.0249], [0.7979, -1.077], [0.9393, -1.1436], [1.1127, -1.2244], [1.3205, -1.3147], [1.5529, -1.3987], [1.7734, -1.4435], [1.9167, -1.4069], [1.9324, -1.2748], [1.8367, -1.084], [1.6887, -0.886], [1.5363, -0.7105], [1.4014, -0.5649], [1.2899, -0.4464], [1.2007, -0.3494], [1.1312, -0.2687], [1.0786, -0.1998], [1.0406, -0.1394], [1.0156, -0.0847], [1.0025, -0.0333]], - shape_superformula(phi_step, 5, 5, 2, 7, 7) - ); - - - - assertEqualPoints( - [[1, 0], [1.0115, 0.0506], [1.047, 0.105], [1.1092, 0.1676], [1.2034, 0.2439], [1.3379, 0.3416], [1.5257, 0.472], [1.7868, 0.6522], [2.152, 0.9098], [2.6685, 1.289], [3.4016, 1.8583], [4.3853, 2.6887], [5.318, 3.6382], [5.2197, 3.968], [4.0782, 3.4351], [2.9443, 2.7429], [2.136, 2.1994], [1.5884, 1.8082], [1.2129, 1.5284], [0.9491, 1.3273], [0.7594, 1.1826], [0.6196, 1.0801], [0.5142, 1.0103], [0.4328, 0.9672], [0.3683, 0.9474], [0.3154, 0.9492], [0.2701, 0.9728], [0.2289, 1.02], [0.1888, 1.0945], [0.146, 1.2025], [0.096, 1.3539], [0.0325, 1.5636], [-0.0542, 1.8545], [-0.1796, 2.2622], [-0.3693, 2.8422], [-0.6657, 3.6751], [-1.1265, 4.8286], [-1.7383, 6.0632], [-2.1478, 6.2868], [-2.0438, 5.1287], [-1.7389, 3.7996], [-1.4633, 2.8161], [-1.2524, 2.1414], [-1.0962, 1.676], [-0.9816, 1.3486], [-0.899, 1.1136], [-0.8417, 0.9421], [-0.8053, 0.8154], [-0.7872, 0.7211], [-0.7861, 0.6509], [-0.8019, 0.599], [-0.8358, 0.5615], [-0.8903, 0.5356], [-0.9698, 0.5193], [-1.081, 0.511], [-1.2338, 0.5095], [-1.4437, 0.5133], [-1.7341, 0.5205], [-2.1414, 0.5276], [-2.7227, 0.5281], [-3.5642, 0.5081], [-4.7564, 0.4369], [-6.1478, 0.2558], [-6.7005, -0.0564], [-5.6982, -0.3332], [-4.3144, -0.4696], [-3.2456, -0.5185], [-2.5031, -0.5293], [-1.9883, -0.5256], [-1.6255, -0.5179], [-1.3655, -0.5115], [-1.1769, -0.5093], [-1.0395, -0.513], [-0.9399, -0.5238], [-0.8694, -0.5432], [-0.8222, -0.5727], [-0.7946, -0.6147], [-0.7846, -0.6722], [-0.7914, -0.7498], [-0.8155, -0.8539], [-0.8585, -0.994], [-0.9237, -1.1844], [-1.0162, -1.4466], [-1.1435, -1.8143], [-1.3165, -2.3405], [-1.5487, -3.1073], [-1.8435, -4.2141], [-2.1216, -5.5961], [-2.0671, -6.4005], [-1.5279, -5.6887], [-0.9502, -4.4063], [-0.5506, -3.361], [-0.2961, -2.6234], [-0.1317, -2.1091], [-0.0216, -1.7457], [0.0559, -1.4853], [0.114, -1.2974], [0.1609, -1.1619], [0.2024, -1.066], [0.2425, -1.0013], [0.2847, -0.9624], [0.3322, -0.9462], [0.3885, -0.9516], [0.458, -0.979], [0.5465, -1.0305], [0.6621, -1.1106], [0.8167, -1.226], [1.0281, -1.3877], [1.3243, -1.6124], [1.7496, -1.9253], [2.3738, -2.3633], [3.2908, -2.9639], [4.5032, -3.6653], [5.416, -3.9753], [5.0622, -3.3397], [4.0315, -2.3794], [3.1266, -1.6404], [2.4741, -1.1442], [2.015, -0.8122], [1.6892, -0.5846], [1.4555, -0.4236], [1.2875, -0.3058], [1.1677, -0.2163], [1.085, -0.1454], [1.0322, -0.0861], [1.0051, -0.0334]], - shape_superformula(phi_step, 5, 5, 2, 13, 13) - ); - - - assertEqualPoints( - [[1, 0], [0.9523, 0.0477], [0.9088, 0.0912], [0.8687, 0.1313], [0.8315, 0.1685], [0.7966, 0.2034], [0.7637, 0.2363], [0.7326, 0.2674], [0.7028, 0.2972], [0.6743, 0.3257], [0.6467, 0.3533], [0.6199, 0.3801], [0.5938, 0.4062], [0.5681, 0.4319], [0.5428, 0.4572], [0.5177, 0.4823], [0.4927, 0.5073], [0.4677, 0.5323], [0.4424, 0.5576], [0.4169, 0.5831], [0.391, 0.609], [0.3645, 0.6355], [0.3373, 0.6627], [0.3092, 0.6908], [0.2799, 0.7201], [0.2494, 0.7506], [0.2173, 0.7827], [0.1833, 0.8167], [0.1471, 0.8529], [0.1082, 0.8918], [0.0662, 0.9338], [0.0204, 0.9796], [-0.0284, 0.9716], [-0.0735, 0.9265], [-0.115, 0.885], [-0.1534, 0.8466], [-0.1892, 0.8108], [-0.2228, 0.7772], [-0.2546, 0.7454], [-0.2849, 0.7151], [-0.314, 0.686], [-0.3419, 0.6581], [-0.369, 0.631], [-0.3954, 0.6046], [-0.4213, 0.5787], [-0.4467, 0.5533], [-0.4719, 0.5281], [-0.4969, 0.5031], [-0.5219, 0.4781], [-0.547, 0.453], [-0.5724, 0.4276], [-0.5981, 0.4019], [-0.6244, 0.3756], [-0.6513, 0.3487], [-0.679, 0.321], [-0.7078, 0.2922], [-0.7377, 0.2623], [-0.7691, 0.2309], [-0.8023, 0.1977], [-0.8375, 0.1625], [-0.8752, 0.1248], [-0.9159, 0.0841], [-0.96, 0.04], [-0.9917, -0.0083], [-0.9448, -0.0552], [-0.9018, -0.0982], [-0.8623, -0.1377], [-0.8254, -0.1746], [-0.7909, -0.2091], [-0.7584, -0.2416], [-0.7275, -0.2725], [-0.698, -0.302], [-0.6696, -0.3304], [-0.6421, -0.3579], [-0.6155, -0.3845], [-0.5894, -0.4106], [-0.5638, -0.4362], [-0.5386, -0.4614], [-0.5135, -0.4865], [-0.4885, -0.5115], [-0.4634, -0.5366], [-0.4382, -0.5618], [-0.4126, -0.5874], [-0.3866, -0.6134], [-0.36, -0.64], [-0.3326, -0.6674], [-0.3043, -0.6957], [-0.2749, -0.7251], [-0.2441, -0.7559], [-0.2117, -0.7883], [-0.1774, -0.8226], [-0.1408, -0.8592], [-0.1014, -0.8986], [-0.0588, -0.9412], [-0.0122, -0.9878], [0.0363, -0.9637], [0.0807, -0.9193], [0.1216, -0.8784], [0.1596, -0.8404], [0.195, -0.805], [0.2283, -0.7717], [0.2598, -0.7402], [0.2899, -0.7101], [0.3187, -0.6813], [0.3465, -0.6535], [0.3735, -0.6265], [0.3998, -0.6002], [0.4256, -0.5744], [0.451, -0.549], [0.4761, -0.5239], [0.5011, -0.4989], [0.5261, -0.4739], [0.5513, -0.4487], [0.5767, -0.4233], [0.6025, -0.3975], [0.6289, -0.3711], [0.6559, -0.3441], [0.6838, -0.3162], [0.7127, -0.2873], [0.7429, -0.2571], [0.7746, -0.2254], [0.8081, -0.1919], [0.8437, -0.1563], [0.8819, -0.1181], [0.923, -0.077], [0.9679, -0.0321]], - shape_superformula(phi_step, 4, 4, 1, 1, 1) - ); - - assertEqualPoints( - [[1, 0], [1.0075, 0.0504], [1.0305, 0.1034], [1.0701, 0.1617], [1.1284, 0.2287], [1.2086, 0.3086], [1.3153, 0.4069], [1.4549, 0.5311], [1.6363, 0.6918], [1.8711, 0.9038], [2.174, 1.1877], [2.5611, 1.5702], [3.0433, 2.0821], [3.6083, 2.743], [4.1846, 3.5246], [4.6053, 4.2903], [4.6507, 4.7886], [4.2298, 4.815], [3.4997, 4.4102], [2.7159, 3.7978], [2.0403, 3.1776], [1.5167, 2.644], [1.1286, 2.2175], [0.8445, 1.887], [0.6354, 1.6343], [0.4792, 1.442], [0.3599, 1.2966], [0.2666, 1.1877], [0.1911, 1.108], [0.1278, 1.0525], [0.0722, 1.0177], [0.0208, 1.0015], [-0.0293, 1.003], [-0.0811, 1.0222], [-0.1378, 1.0603], [-0.2028, 1.1196], [-0.2808, 1.2038], [-0.3779, 1.3182], [-0.5025, 1.4708], [-0.6663, 1.6722], [-0.8863, 1.9367], [-1.1857, 2.282], [-1.5945, 2.7263], [-2.1434, 3.2772], [-2.8428, 3.9055], [-3.6327, 4.4995], [-4.3291, 4.8452], [-4.6763, 4.7346], [-4.5551, 4.1726], [-4.0927, 3.3888], [-3.5095, 2.6216], [-2.9556, 1.9858], [-2.4895, 1.4977], [-2.1176, 1.1338], [-1.8273, 0.8638], [-1.6024, 0.6617], [-1.4288, 0.508], [-1.2953, 0.3888], [-1.1934, 0.2941], [-1.1172, 0.2167], [-1.0622, 0.1514], [-1.0255, 0.0942], [-1.0052, 0.0418], [-1.0002, -0.0084], [-1.0103, -0.0591], [-1.036, -0.1128], [-1.0785, -0.1723], [-1.1403, -0.2411], [-1.2246, -0.3237], [-1.3363, -0.4257], [-1.4822, -0.5552], [-1.6717, -0.7234], [-1.9168, -0.9459], [-2.2328, -1.2443], [-2.6355, -1.6465], [-3.1335, -2.1827], [-3.7077, -2.8681], [-4.2722, -3.6603], [-4.6445, -4.4003], [-4.6112, -4.8285], [-4.1215, -4.772], [-3.3655, -4.3151], [-2.5923, -3.6902], [-1.9416, -3.0806], [-1.4427, -2.5649], [-1.0744, -2.1556], [-0.8048, -1.8396], [-0.6059, -1.5982], [-0.4569, -1.4146], [-0.3427, -1.2759], [-0.2528, -1.1724], [-0.1797, -1.0971], [-0.118, -1.0453], [-0.0633, -1.0137], [-0.0124, -1.0005], [0.0378, -1.005], [0.0902, -1.0273], [0.148, -1.0688], [0.2149, -1.1319], [0.2956, -1.2207], [0.3967, -1.341], [0.5269, -1.5009], [0.6989, -1.7118], [0.9304, -1.9886], [1.246, -2.3494], [1.6763, -2.8116], [2.2509, -3.3793], [2.9726, -4.0125], [3.7633, -4.5819], [4.4182, -4.862], [4.688, -4.6673], [4.4952, -4.0486], [3.9977, -3.2539], [3.4117, -2.5042], [2.8705, -1.8937], [2.4206, -1.4286], [2.0635, -1.0826], [1.7853, -0.8257], [1.57, -0.6329], [1.4038, -0.4858], [1.2761, -0.3713], [1.1789, -0.28], [1.1065, -0.205], [1.0548, -0.1413], [1.021, -0.0851], [1.0033, -0.0333]], - shape_superformula(phi_step, 4, 4, 1, 7, 8) - ); } test_shape_superformula(); diff --git a/test/test_sphere_spiral_extrude.scad b/test/test_sphere_spiral_extrude.scad index ad973790..62d3810a 100644 --- a/test/test_sphere_spiral_extrude.scad +++ b/test/test_sphere_spiral_extrude.scad @@ -10,643 +10,11 @@ module test_sphere_spiral_extrude_star() { include ; module test_sphere_spiral_extrude(sections) { - expected = [ - [[0, -8.233, -39.195], [0, -6.798, -38.967], [0, -6.57, -37.532], [0, -5.911, -38.827], [0, -4.475, -38.6], [0, -5.503, -39.627], [0, -4.843, -40.922], [0, -6.138, -40.262], [0, -7.165, -41.29], [0, -6.938, -39.854]] - , [[0.293, -8.377, -39.164], [0.242, -6.933, -38.94], [0.234, -6.699, -37.496], [0.211, -6.04, -38.802], [0.16, -4.596, -38.578], [0.197, -5.633, -39.608], [0.174, -4.974, -40.914], [0.219, -6.274, -40.245], [0.255, -7.311, -41.276], [0.247, -7.077, -39.832]] - , [[0.595, -8.51, -39.132], [0.494, -7.059, -38.912], [0.477, -6.819, -37.46], [0.431, -6.162, -38.776], [0.329, -4.711, -38.556], [0.402, -5.756, -39.589], [0.357, -5.098, -40.905], [0.448, -6.402, -40.228], [0.521, -7.447, -41.261], [0.504, -7.207, -39.809]] - , [[0.907, -8.633, -39.1], [0.754, -7.176, -38.884], [0.728, -6.93, -37.424], [0.66, -6.276, -38.75], [0.506, -4.819, -38.534], [0.617, -5.871, -39.57], [0.548, -5.216, -40.896], [0.685, -6.521, -40.21], [0.796, -7.573, -41.246], [0.77, -7.328, -39.786]] - , [[1.229, -8.743, -39.067], [1.024, -7.283, -38.855], [0.988, -7.032, -37.386], [0.897, -6.38, -38.723], [0.691, -4.92, -38.511], [0.84, -5.978, -39.55], [0.749, -5.326, -40.887], [0.932, -6.631, -40.192], [1.081, -7.689, -41.23], [1.045, -7.438, -39.762]] - , [[1.559, -8.842, -39.034], [1.301, -7.38, -38.825], [1.256, -7.123, -37.349], [1.142, -6.476, -38.696], [0.884, -5.014, -38.488], [1.071, -6.076, -39.529], [0.957, -5.429, -40.877], [1.187, -6.732, -40.173], [1.374, -7.794, -41.214], [1.329, -7.538, -39.738]] - , [[1.898, -8.927, -39], [1.587, -7.465, -38.795], [1.531, -7.204, -37.311], [1.395, -6.562, -38.669], [1.084, -5.1, -38.464], [1.31, -6.165, -39.508], [1.174, -5.523, -40.866], [1.45, -6.823, -40.154], [1.677, -7.888, -41.198], [1.621, -7.627, -39.713]] - , [[2.244, -9, -38.966], [1.88, -7.54, -38.765], [1.814, -7.274, -37.272], [1.655, -6.638, -38.641], [1.291, -5.178, -38.44], [1.557, -6.245, -39.487], [1.398, -5.609, -40.856], [1.721, -6.904, -40.134], [1.987, -7.97, -41.18], [1.921, -7.704, -39.688]] - , [[2.598, -9.059, -38.931], [2.18, -7.603, -38.734], [2.103, -7.333, -37.233], [1.922, -6.704, -38.613], [1.505, -5.248, -38.416], [1.811, -6.315, -39.465], [1.63, -5.685, -40.844], [2, -6.974, -40.113], [2.305, -8.04, -41.163], [2.228, -7.77, -39.662]] - , [[2.958, -9.104, -38.895], [2.487, -7.654, -38.703], [2.398, -7.38, -37.194], [2.196, -6.758, -38.584], [1.725, -5.309, -38.391], [2.071, -6.374, -39.443], [1.869, -5.752, -40.833], [2.285, -7.032, -40.093], [2.631, -8.097, -41.144], [2.542, -7.823, -39.635]] - , [[3.325, -9.134, -38.859], [2.8, -7.693, -38.671], [2.699, -7.416, -37.154], [2.476, -6.802, -38.555], [1.951, -5.361, -38.366], [2.338, -6.423, -39.42], [2.114, -5.809, -40.821], [2.577, -7.079, -40.071], [2.963, -8.141, -41.125], [2.862, -7.864, -39.608]] - , [[3.697, -9.15, -38.823], [3.118, -7.719, -38.639], [3.005, -7.439, -37.114], [2.761, -6.834, -38.525], [2.183, -5.403, -38.341], [2.61, -6.46, -39.397], [2.366, -5.856, -40.808], [2.874, -7.114, -40.05], [3.301, -8.171, -41.106], [3.188, -7.892, -39.581]] - , [[4.074, -9.15, -38.785], [3.442, -7.731, -38.606], [3.316, -7.449, -37.073], [3.052, -6.854, -38.495], [2.42, -5.435, -38.315], [2.888, -6.487, -39.373], [2.623, -5.892, -40.795], [3.177, -7.136, -40.028], [3.646, -8.188, -41.086], [3.52, -7.906, -39.553]] - , [[4.456, -9.135, -38.748], [3.77, -7.73, -38.572], [3.632, -7.446, -37.031], [3.347, -6.862, -38.464], [2.662, -5.457, -38.289], [3.171, -6.501, -39.349], [2.886, -5.917, -40.782], [3.485, -7.146, -40.005], [3.995, -8.19, -41.066], [3.856, -7.906, -39.525]] - , [[4.841, -9.105, -38.709], [4.103, -7.716, -38.538], [3.951, -7.43, -36.99], [3.646, -6.857, -38.433], [2.908, -5.468, -38.262], [3.458, -6.503, -39.325], [3.153, -5.931, -40.768], [3.798, -7.143, -39.982], [4.348, -8.178, -41.044], [4.196, -7.892, -39.496]] - , [[5.23, -9.058, -38.67], [4.438, -7.687, -38.504], [4.273, -7.401, -36.947], [3.949, -6.84, -38.401], [3.158, -5.469, -38.235], [3.749, -6.494, -39.3], [3.425, -5.933, -40.754], [4.115, -7.127, -39.958], [4.706, -8.151, -41.023], [4.54, -7.864, -39.466]] - , [[5.621, -8.995, -38.631], [4.777, -7.644, -38.469], [4.597, -7.357, -36.905], [4.255, -6.81, -38.369], [3.411, -5.459, -38.208], [4.044, -6.471, -39.274], [3.701, -5.923, -40.739], [4.434, -7.096, -39.934], [5.067, -8.108, -41.001], [4.887, -7.822, -39.436]] - , [[6.013, -8.915, -38.591], [5.117, -7.587, -38.434], [4.924, -7.3, -36.862], [4.564, -6.766, -38.337], [3.668, -5.438, -38.18], [4.341, -6.436, -39.249], [3.98, -5.901, -40.724], [4.757, -7.052, -39.909], [5.43, -8.051, -40.978], [5.237, -7.764, -39.406]] - , [[6.407, -8.819, -38.551], [5.46, -7.515, -38.398], [5.252, -7.229, -36.818], [4.874, -6.709, -38.304], [3.927, -5.405, -38.152], [4.641, -6.387, -39.222], [4.263, -5.867, -40.708], [5.082, -6.994, -39.884], [5.796, -7.977, -40.955], [5.588, -7.691, -39.375]] - , [[6.802, -8.706, -38.509], [5.803, -7.428, -38.362], [5.581, -7.143, -36.774], [5.186, -6.638, -38.271], [4.188, -5.36, -38.123], [4.942, -6.325, -39.196], [4.547, -5.82, -40.692], 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[7.325, 29.378, 17.761], [7.639, 30.64, 24.843], [9.366, 37.565, 25.796], [7.834, 31.419, 29.221], [8.148, 32.68, 36.303], [6.887, 27.621, 31.337]] - , [[4.574, 21.521, 34.848], [5.227, 24.59, 28.357], [4.145, 19.5, 23.367], [5.63, 26.487, 24.345], [6.283, 29.557, 17.854], [6.548, 30.806, 24.95], [8.033, 37.793, 25.928], [6.712, 31.578, 29.335], [6.977, 32.827, 36.432], [5.896, 27.736, 31.441]] - , [[3.798, 21.539, 34.934], [4.347, 24.655, 28.445], [3.446, 19.541, 23.43], [4.687, 26.582, 24.435], [5.237, 29.698, 17.947], [5.454, 30.933, 25.056], [6.696, 37.973, 26.061], [5.589, 31.696, 29.45], [5.807, 32.93, 36.56], [4.905, 27.816, 31.545]] - , [[3.026, 21.529, 35.019], [3.47, 24.689, 28.533], [2.749, 19.557, 23.494], [3.744, 26.642, 24.525], [4.188, 29.803, 18.039], [4.36, 31.021, 25.162], [5.355, 38.106, 26.193], [4.466, 31.774, 29.564], [4.637, 32.992, 36.687], [3.916, 27.861, 31.648]] - , [[2.259, 21.491, 35.104], [2.595, 24.691, 28.621], [2.055, 19.548, 23.557], [2.803, 26.669, 24.614], [3.139, 29.87, 18.131], [3.266, 31.07, 25.268], [4.014, 38.191, 26.325], [3.344, 31.812, 29.678], [3.47, 33.012, 36.815], [2.929, 27.87, 31.751]] - , [[1.498, 21.425, 35.188], [1.725, 24.662, 28.708], [1.365, 19.515, 23.62], [1.864, 26.663, 24.704], [2.091, 29.9, 18.224], [2.173, 31.08, 25.373], [2.673, 38.228, 26.457], [2.224, 31.81, 29.792], [2.307, 32.991, 36.942], [1.947, 27.843, 31.853]] - , [[0.745, 21.332, 35.272], [0.859, 24.602, 28.795], [0.679, 19.456, 23.682], [0.93, 26.623, 24.792], [1.044, 29.893, 18.316], [1.084, 31.052, 25.478], [1.335, 38.218, 26.589], [1.109, 31.769, 29.905], [1.15, 32.928, 37.068], [0.97, 27.782, 31.955]] - , [[0, 21.213, 35.355], [0, 24.512, 28.882], [0, 19.374, 23.744], [0, 26.55, 24.881], [0, 29.849, 18.407], [0, 30.985, 25.583], [0, 38.161, 26.72], [0, 31.688, 30.018], [0, 32.824, 37.194], [0, 27.687, 32.057]] - ]; + expected = [[[0, -8.23276, -39.1947], [0, -6.79756, -38.9674], [0, -6.57025, -37.5322], [0, -5.91056, -38.8269], [0, 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[8.73939, 24.0113, 27.9995], [6.94511, 19.0815, 23.1074], [9.3802, 25.7719, 23.9816], [10.417, 28.6206, 17.4805], [10.8852, 29.9067, 24.5219], [13.3202, 36.597, 25.3961], [11.1745, 30.7016, 28.8737], [11.6426, 31.9878, 35.9151], [9.84832, 27.058, 31.023]], [[6.91936, 21.2956, 34.5883], [7.86437, 24.204, 28.0894], [6.24643, 19.2245, 23.1727], [8.44841, 26.0015, 24.0729], [9.39342, 28.91, 17.5741], [9.80931, 30.19, 24.6293], [12.0113, 36.967, 25.5295], [10.0663, 30.981, 28.9896], [10.4822, 32.261, 36.0448], [8.8643, 27.2815, 31.1281]], [[6.13621, 21.3995, 34.6754], [6.98648, 24.3648, 28.179], [5.54621, 19.3419, 23.2377], [7.51198, 26.1974, 24.164], [8.36225, 29.1626, 17.6675], [8.72689, 30.4343, 24.7364], [10.6927, 37.2897, 25.6627], [8.95225, 31.2202, 29.1052], [9.3169, 32.4919, 36.1741], [7.87662, 27.469, 31.2329]], [[5.35421, 21.4746, 34.7621], [6.10692, 24.4935, 28.2682], [4.84538, 19.4338, 23.3023], [6.57212, 26.3593, 24.2547], [7.32483, 29.3783, 17.7607], [7.63931, 30.6396, 24.8433], [9.36604, 37.5652, 25.7956], [7.83366, 31.4191, 29.2205], [8.14813, 32.6804, 36.3031], [6.88659, 27.6206, 31.3372]], [[4.57441, 21.5209, 34.8483], [5.22685, 24.5904, 28.357], [4.14489, 19.5002, 23.3666], [5.63008, 26.4874, 24.3451], [6.28251, 29.5569, 17.8537], [6.54797, 30.8058, 24.9499], [8.03316, 37.7931, 25.9284], [6.71204, 31.5777, 29.3355], [6.9775, 32.8266, 36.4316], [5.89554, 27.7363, 31.4412]], [[3.79788, 21.5388, 34.9341], [4.34743, 24.6555, 28.4454], [3.44565, 19.5413, 23.4305], [4.68707, 26.5817, 24.4352], [5.23662, 29.6983, 17.9465], [5.45431, 30.9329, 25.0561], [6.69572, 37.9733, 26.0609], [5.58885, 31.6959, 29.4501], [5.80654, 32.9305, 36.5598], [4.90476, 27.8163, 31.5448]], [[3.02565, 21.5286, 35.0193], [3.46981, 24.689, 28.5334], [2.74859, 19.5572, 23.494], [3.74432, 26.6422, 24.525], [4.18848, 29.8026, 18.0391], [4.35971, 31.021, 25.1622], [5.35544, 38.106, 26.1932], [4.46554, 31.774, 29.5644], [4.63678, 32.9924, 36.6875], [3.91555, 27.8606, 31.648]], [[2.25875, 21.4906, 35.104], [2.59514, 24.6911, 28.6211], [2.0546, 19.5482, 23.5571], [2.80304, 26.6691, 24.6144], [3.13943, 29.8696, 18.1315], [3.26559, 31.0701, 25.2679], [4.01403, 38.1909, 26.3252], [3.34357, 31.812, 29.6784], [3.46974, 33.0124, 36.8148], [2.92921, 27.8695, 31.7508]], [[1.49818, 21.425, 35.1883], [1.72454, 24.662, 28.7084], [1.36459, 19.5146, 23.6199], [1.86443, 26.6626, 24.7036], [2.09078, 29.8996, 18.2237], [2.17335, 31.0803, 25.3733], [2.67319, 38.2284, 26.457], [2.22438, 31.8101, 29.7921], [2.30694, 32.9908, 36.9417], [1.947, 27.8433, 31.8532]], [[0.744945, 21.3324, 35.2721], [0.859124, 24.6021, 28.7953], [0.679434, 19.4564, 23.6823], [0.929691, 26.6229, 24.7924], [1.04387, 29.8925, 18.3156], [1.08436, 31.0519, 25.4785], [1.33461, 38.2184, 26.5886], [1.10938, 31.7685, 29.9054], [1.14987, 32.9279, 37.0682], [0.970179, 27.7823, 31.9553]], [[0, 21.2132, 35.3553], [0, 24.5116, 28.8818], [0, 19.3742, 23.7444], [0, 26.5502, 24.8809], [0, 29.8486, 18.4074], [0, 30.9852, 25.5834], [0, 38.1612, 26.7199], [0, 31.6876, 30.0184], [0, 32.8242, 37.1943], [0, 27.6867, 32.0569]]]; + for(i = [0:len(sections) - 1]) { - assertEqualPoints(expected[i], sections[i], float_digits = 3); - //round_echo_pts(sections[i], float_digits = 3); + assertEqualPoints(expected[i], sections[i]); } } diff --git a/test/test_split_str.scad b/test/test_split_str.scad deleted file mode 100644 index eea83793..00000000 --- a/test/test_split_str.scad +++ /dev/null @@ -1,11 +0,0 @@ -module test_split_str() { - echo("==== test_split_str ===="); - - include ; - include ; - include ; - - assertEqual(["hello", "world"], split_str("hello,world", ",")); -} - -test_split_str(); \ No newline at end of file diff --git a/test/test_sub_str.scad b/test/test_sub_str.scad deleted file mode 100644 index 61a5e8cb..00000000 --- a/test/test_sub_str.scad +++ /dev/null @@ -1,11 +0,0 @@ -module test_sub_str() { - echo("==== test_sub_str ===="); - - include ; - include ; - - assertEqual("hello", sub_str("helloworld", 0, 5)); - assertEqual("world", sub_str("helloworld", 5)); -} - -test_sub_str(); \ No newline at end of file diff --git a/test/test_torus_knot.scad b/test/test_torus_knot.scad new file mode 100644 index 00000000..77857f4e --- /dev/null +++ b/test/test_torus_knot.scad @@ -0,0 +1,18 @@ +include ; +include ; + +module test_torus_knot() { + echo("==== test_torus_knot ===="); + + p = 2; + q = 3; + phi_step = 0.05; + star_radius = 0.5; + + expected = [[3, 0, 0], [2.97384, 0.298379, -0.149438], [2.89643, 0.587135, -0.29552], [2.7709, 0.857141, -0.434966], [2.60231, 1.10024, -0.564642], [2.39728, 1.30964, -0.681639], [2.16371, 1.48027, -0.783327], [1.91025, 1.60898, -0.867423], [1.64587, 1.69465, -0.932039], [1.37936, 1.73821, -0.975723], [1.11882, 1.74247, -0.997495], [0.871303, 1.7119, -0.996865], [0.642387, 1.65232, -0.973848], [0.435975, 1.57043, -0.92896], [0.254127, 1.4734, -0.863209], [0.0970392, 1.36839, -0.778073], [-0.0368675, 1.26207, -0.675463], [-0.150741, 1.16019, -0.557684], [-0.248997, 1.06727, -0.42738], [-0.336937, 0.986246, -0.287478], [-0.420311, 0.918397, -0.14112], [-0.504864, 0.86324, 0.00840725], [-0.595869, 0.818619, 0.157746], [-0.697712, 0.780889, 0.303542], [-0.813523, 0.745199, 0.44252], [-0.944901, 0.705862, 0.571561], [-1.09173, 0.656784, 0.687766], [-1.25214, 0.59192, 0.788525], [-1.42251, 0.505745, 0.871576], [-1.5977, 0.393683, 0.935053], [-1.7713, 0.252493, 0.97753], [-1.93598, 0.0805688, 0.998054], [-2.08394, -0.121856, 0.996165], [-2.20739, -0.352622, 0.971903], [-2.29902, -0.607671, 0.925815], [-2.35246, -0.881197, 0.858934], [-2.36268, -1.16591, 0.772764], [-2.32638, -1.45337, 0.66924], [-2.24217, -1.73444, 0.550686], [-2.11074, -1.99977, 0.419764], [-1.9349, -2.24026, 0.279415], [-1.71938, -2.44758, 0.132792], [-1.47071, -2.6146, -0.0168139], [-1.19683, -2.73578, -0.166042], [-0.906703, -2.80745, -0.311541], [-0.609834, -2.828, -0.450044], [-0.315791, -2.79796, -0.57844], [-0.0336987, -2.71992, -0.693845], [0.228228, -2.59835, -0.793668], [0.463095, -2.43935, -0.875667], [0.665652, -2.25025, -0.938], [0.832522, -2.03917, -0.979268], [0.962312, -1.81458, -0.998543], [1.0556, -1.58474, -0.995394], [1.11481, -1.35733, -0.96989], [1.14397, -1.13892, -0.922604], [1.14839, -0.934724, -0.854599], [1.13424, -0.74829, -0.767401], [1.1081, -0.581381, -0.662969], [1.07651, -0.433954, -0.543648], [1.0455, -0.304247, -0.412118], [1.02016, -0.188996, -0.271333], [1.00429, -0.0837354, -0.124454], [1.00018, 0.0168192, 0.0252194], [1.00839, 0.118334, 0.174327], [1.02778, 0.226397, 0.319519], [1.05553, 0.346063, 0.457536], [1.08735, 0.481434, 0.585277], [1.11781, 0.635299, 0.699875], [1.14066, 0.808857, 0.798754], [1.1493, 1.00155, 0.879696], [1.13721, 1.21101, 0.940881], [1.09848, 1.4331, 0.980936], [1.02819, 1.66213, 0.998962], [0.922807, 1.89109, 0.994553], [0.780515, 2.11208, 0.967808], [0.601388, 2.31671, 0.919329], [0.387492, 2.49656, 0.850203], [0.142852, 2.64374, 0.761984], [-0.126699, 2.75128, 0.656652], [-0.413781, 2.81359, 0.536573], [-0.709825, 2.8268, 0.404444], [-1.0055, 2.78901, 0.263232], [-1.29121, 2.70041, 0.116108], [-1.55757, 2.56331, -0.033623], [-1.79591, 2.38204, -0.182599], [-1.99874, 2.1627, -0.327474], [-2.16008, 1.91287, -0.464995], [-2.27583, 1.64121, -0.592074], [-2.34391, 1.35694, -0.705855], [-2.36431, 1.06941, -0.803784], [-2.33909, 0.787574, -0.883663], [-2.27218, 0.519515, -0.943696], [-2.16908, 0.272067, -0.982535], [-2.03653, 0.0504715, -0.999309], [-1.88207, -0.141841, -0.993641], [-1.71354, -0.30336, -0.965658], [-1.53862, -0.434489, -0.915988], [-1.36439, -0.537411, -0.845747], [-1.19687, -0.615853, -0.756512], [-1.04071, -0.674756, -0.650288], [-0.898953, -0.719872, -0.529459], [-0.772885, -0.757313, -0.396741], [-0.66203, -0.793087, -0.255112], [-0.564251, -0.832646, -0.107754], [-0.475957, -0.880473, 0.0420244], [-0.392422, -0.939738, 0.190859], [-0.308163, -1.01205, 0.335407], [-0.217383, -1.0973, 0.472422], [-0.114431, -1.19365, 0.598828], [0.0057428, -1.29759, 0.711785], [0.147166, -1.40417, 0.808758], [0.31249, -1.50727, 0.887567], [0.502712, -1.60001, 0.946444], [0.717015, -1.67519, 0.984065], [0.952712, -1.72573, 0.999586], [1.20531, -1.74517, 0.992659], [1.4687, -1.72812, 0.963439], [1.73544, -1.67063, 0.912582], [1.99715, -1.57049, 0.841231], [2.24492, -1.42745, 0.750987], [2.46983, -1.24333, 0.643878], [2.66343, -1.02194, 0.522309], [2.81821, -0.768962, 0.389009], [2.92803, -0.491682, 0.246974], [2.98845, -0.198637, 0.0993915]]; + actual = torus_knot(p, q, phi_step); + + assertEqualPoints(expected, actual); +} + +test_torus_knot(); \ No newline at end of file diff --git a/test/test_triangulate.scad b/test/test_triangulate.scad new file mode 100644 index 00000000..39261d27 --- /dev/null +++ b/test/test_triangulate.scad @@ -0,0 +1,26 @@ +include ; +include ; + +module test_triangulate() { + echo("==== test_triangulate ===="); + + + shape = [ + [0, 0], + [10, 0], + [12, 5], + [5, 10], + [10, 15], + [0, 20], + [-5, 18], + [-18, 3], + [-4, 10] + ]; + + expected = [[8, 0, 1], [1, 2, 3], [3, 4, 5], [5, 6, 7], [8, 1, 3], [5, 7, 8], [8, 3, 5]]; + actual = triangulate(shape); + + assertEqualPoints(expected, actual); +} + +test_triangulate(); \ No newline at end of file diff --git a/test/test_trim_shape.scad b/test/test_trim_shape.scad new file mode 100644 index 00000000..5c5411b1 --- /dev/null +++ b/test/test_trim_shape.scad @@ -0,0 +1,18 @@ +include ; +include ; +include ; +include ; + +module test_trim_shape() { + echo("==== test_trim_shape ===="); + + taiwan = shape_taiwan(50); + offseted = bijection_offset(taiwan, -2); + + expected = [[10.6338, 19.2796], [10.0046, 20.2443], [9.90826, 20.5883], [8.70107, 20.8781], [7.92074, 21.1601], [7.86725, 21.2196], [7.27987, 21.0324], [7.09336, 21.4286], [6.37935, 19.021], [4.68179, 20.5971], [4.5527, 20.5497], [2.93485, 20.2511], [2.81634, 20.2087], [2.73817, 20.1409], [2.18145, 19.775], [1.37773, 19.5192], [1.2485, 19.3686], [0.910901, 18.828], [0.76564, 17.6214], [0.347453, 17.4878], [0.384341, 17.2143], [-0.098055, 16.5572], [-0.218527, 16.3137], [-0.405555, 15.5988], [-0.698227, 15.3605], [-0.7087, 15.33], [-0.320271, 13.0644], [-2.60331, 13.5214], [-2.98653, 13.1043], [-3.10016, 12.8995], [-3.142, 12.5466], [-3.51015, 11.7766], [-4.57544, 10.6037], [-4.70456, 10.1567], [-5.14938, 9.39273], [-5.2474, 8.94799], [-5.59061, 7.97586], [-5.62525, 7.94754], [-5.62269, 7.96175], [-6.33, 7.144], [-6.34104, 6.89284], [-6.7609, 5.93534], [-6.87067, 5.84916], [-6.91022, 5.65005], [-7.61745, 5.02019], [-7.82187, 4.44883], [-8.03107, 4.06493], [-8.21974, 3.51881], [-8.61249, 3.00185], [-8.69757, 2.91941], [-8.73113, 2.77248], [-9.10025, 2.07081], [-9.3238, 1.86887], [-9.30876, 1.91017], [-9.59926, 1.52971], [-9.69857, 1.16721], [-10.0582, 0.403593], [-10.3384, -0.0369127], [-10.3854, -0.132622], [-10.3951, -0.194325], [-10.2707, -0.739663], [-10.249, -0.964726], [-10.2079, -1.03632], [-9.93828, -2.07816], [-10.1738, -2.69596], [-9.679, -2.94903], [-10.1969, -5.13922], [-10.45, -5.40183], [-10.7508, -6.14493], [-10.6782, -6.47661], [-10.715, -6.55157], [-10.0504, -6.65196], [-9.57877, -8.84089], [-10.2006, -8.19261], [-9.81559, -8.91674], [-9.65581, -9.94319], [-9.12163, -10.7459], [-9.22681, -11.5141], [-9.01465, -11.8442], [-8.73247, -12.4252], [-8.48376, -13.4262], [-8.48489, -13.4305], [-8.0699, -13.8936], [-7.7349, -14.5209], [-7.41546, -14.6692], [-7.0645, -14.8905], [-6.80517, -15.1143], [-6.79263, -15.1225], [-6.16377, -15.4209], [-5.49479, -15.9866], [-5.4225, -16.0949], [-5.53602, -16.0266], [-4.80354, -16.6014], [-4.40453, -17.1464], [-4.19976, -17.6117], [-4.00409, -17.8586], [-3.97777, -17.9015], [-3.83889, -17.3565], [-3.33584, -16.4856], [-3.19723, -15.9876], [-3.05908, -15.1064], [-2.63023, -14.3537], [-2.24981, -13.8734], [-1.91247, -13.0155], [-1.33334, -12.2667], [-1.12254, -12.1685], [-0.675112, -11.6726], [0.101845, -11.1595], [0.270335, -10.2843], [0.880024, -9.55879], [1.38186, -9.13658], [1.33812, -9.23203], [1.80844, -8.5697], [1.98972, -7.7937], [2.26128, -7.29646], [2.33773, -7.04836], [2.59675, -6.51487], [3.01217, -6.07782], [3.00479, -5.62291], [3.13547, -4.69461], [3.35489, -4.05881], [3.63333, -3.5265], [3.8947, -3.17889], [4.68681, 1.37928], [4.94669, 1.90737], [5.34344, 3.84582], [5.66428, 4.72607], [5.77584, 5.26262], [5.79433, 5.62233], [5.88933, 6.02115], [5.79416, 6.3079], [5.7619, 7.19402], [6.03794, 8.02087], [6.36442, 8.50081], [6.47507, 8.97173], [6.74051, 9.5319], [6.76126, 9.47511], [7.6015, 10.6679], [7.85706, 10.8721], [7.92577, 10.9651], [7.92595, 10.9508], [7.96742, 11.5364], [8.08626, 11.9958], [8.08561, 12.006], [8.1501, 12.7625], [10.5031, 12.7536], [9.26392, 13.5338], [8.58567, 14.7305], [8.55847, 16.0185], [8.5956, 16.121], [8.48033, 16.6489], [8.46518, 17.3066], [8.50618, 17.927], [8.63904, 18.5685], [8.86699, 19.2643], [9.22929, 19.8277]]; + actual = trim_shape(offseted, 3, len(offseted) - 6); + + assertEqualPoints(expected, actual); +} + +test_trim_shape(); \ No newline at end of file diff --git a/test/util/test_parse_number.scad b/test/util/test_parse_number.scad new file mode 100644 index 00000000..1e5d30ce --- /dev/null +++ b/test/util/test_parse_number.scad @@ -0,0 +1,13 @@ +module test_parse_number() { + echo("==== test_parse_number ===="); + + include ; + include ; + include ; + include ; + + assertEqualNum(11, parse_number("10") + 1); + assertEqualNum(-0.1, parse_number("-1.1") + 1); +} + +test_parse_number(); diff --git a/test/util/test_slice.scad b/test/util/test_slice.scad new file mode 100644 index 00000000..a8cb0dd5 --- /dev/null +++ b/test/util/test_slice.scad @@ -0,0 +1,15 @@ +module test_slice() { + echo("==== test_slice ===="); + + include ; + include ; + + lt = [for(c = "helloworld") c]; + expected1 = [for(c = "hello") c]; + expected2 = [for(c = "world") c]; + + assert(expected1 == slice(lt, 0, 5)); + assert(expected2 == slice(lt, 5)); +} + +test_slice(); \ No newline at end of file diff --git a/test/util/test_sort.scad b/test/util/test_sort.scad new file mode 100644 index 00000000..354568ce --- /dev/null +++ b/test/util/test_sort.scad @@ -0,0 +1,23 @@ +module test_sort() { + echo("==== test_sort ===="); + + include ; + include ; + + assertEqualPoints( + [[2, 0, 0], [5, 0, 0], [7, 0, 0], [9, 0, 0], [10, 0, 0]], + sort([[10, 0, 0], [5, 0, 0], [7, 0, 0], [2, 0, 0], [9, 0, 0]], by = "x") + ); + + assertEqualPoints( + [[2, 0, 0], [5, 0, 0], [7, 0, 0], [9, 0, 0], [10, 0, 0]], + sort([[10, 0, 0], [5, 0, 0], [7, 0, 0], [2, 0, 0], [9, 0, 0]], by = "idx", idx = 0) + ); + + assertEqualPoints( + [[0, 2, 0], [0, 5, 0], [0, 7, 0], [0, 9, 0], [0, 10, 0]], + sort([[0, 10, 0], [0, 5, 0], [0, 7, 0], [0, 2, 0], [0, 9, 0]], by = "y") + ); +} + +test_sort(); diff --git a/test/util/test_split_str.scad b/test/util/test_split_str.scad new file mode 100644 index 00000000..1e02a232 --- /dev/null +++ b/test/util/test_split_str.scad @@ -0,0 +1,11 @@ +module test_split_str() { + echo("==== test_split_str ===="); + + include ; + include ; + include ; + + assert(["hello", "world","abc", "xyz"] == split_str("hello,world,abc,xyz", ",")); +} + +test_split_str(); \ No newline at end of file diff --git a/test/util/test_sub_str.scad b/test/util/test_sub_str.scad new file mode 100644 index 00000000..88a7c3ce --- /dev/null +++ b/test/util/test_sub_str.scad @@ -0,0 +1,11 @@ +module test_sub_str() { + echo("==== test_sub_str ===="); + + include ; + include ; + + assert("hello" == sub_str("helloworld", 0, 5)); + assert("world" == sub_str("helloworld", 5)); +} + +test_sub_str(); \ No newline at end of file