From b10b23cc7e10c39e7cffb56dbd7f626400d28503 Mon Sep 17 00:00:00 2001 From: Justin Lin Date: Sat, 10 Apr 2021 18:51:13 +0800 Subject: [PATCH] update README --- README.md | 490 +++++++++++++++++++++++++++++++----------------------- 1 file changed, 284 insertions(+), 206 deletions(-) diff --git a/README.md b/README.md index 501e864b..fee96cef 100644 --- a/README.md +++ b/README.md @@ -41,232 +41,310 @@ These examples incubate dotSCAD and dotSCAD refactors these examples. See [examp [![examples](examples/images/gallery.JPG)](examples#dogfooding-examples) -## Documentation +# API Documentation -### 2D Module -- [`arc(radius, angle, width = 1, width_mode = "LINE_CROSS")`](https://openhome.cc/eGossip/OpenSCAD/lib3x-arc.html) -- [`hexagons(radius, spacing, levels)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-hexagons.html) -- [`hull_polyline2d(points, width = 1)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-hull_polyline2d.html) -- [`line2d(p1, p2, width = 1, p1Style = "CAP_SQUARE", p2Style = "CAP_SQUARE")`](https://openhome.cc/eGossip/OpenSCAD/lib3x-line2d.html) -- [`multi_line_text(lines, line_spacing = 15, size = 10, font = "Arial", ...)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-multi_line_text.html) -- [`pie(radius, angle)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-pie.html) -- [`polyline2d(points, width = 1, startingStyle = "CAP_SQUARE", endingStyle = "CAP_SQUARE", ...)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-polyline2d.html) -- [`polygon_hull(points)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-polygon_hull.html) -- [`rounded_square(size, corner_r, center = false)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-rounded_square.html) +--- -### 3D Module -- [`crystal_ball(radius, theta = 360, phi = 180, thickness = undef)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-crystal_ball.html) -- [`function_grapher(points, thickness = 1, style = "FACES")`](https://openhome.cc/eGossip/OpenSCAD/lib3x-function_grapher.html) -- [`hull_polyline3d(points, diameter = 1)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-hull_polyline3d.html) -- [`line3d(p1, p2, diameter = 1, p1Style = "CAP_CIRCLE", p2Style = "CAP_CIRCLE")`](https://openhome.cc/eGossip/OpenSCAD/lib3x-line3d.html) -- [`loft(sections, slices = 1)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-loft.html) -- [`polyhedron_hull(points)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-polyhedron_hull.html) -- [`polyline3d(points, diameter, startingStyle = "CAP_CIRCLE", endingStyle = "CAP_CIRCLE")`](https://openhome.cc/eGossip/OpenSCAD/lib3x-polyline3d.html) -- [`rounded_cube(size, corner_r, center = false)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-rounded_cube.html) -- [`rounded_cylinder(radius, h, round_r, convexity = 2, center = false)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-rounded_cylinder.html) -- [`starburst(r1, r2, n, height)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-starburst.html) -- [`sweep(sections, triangles = "SOLID")`](https://openhome.cc/eGossip/OpenSCAD/lib3x-sweep.html) +## 2D Module -### Transformation -- [`along_with(points, angles, twist = 0, scale = 1.0, method = "AXIS_ANGLE")`](https://openhome.cc/eGossip/OpenSCAD/lib3x-along_with.html) -- [`bend(size, angle, frags = 24)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-bend.html) -- [`hollow_out(shell_thickness)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-hollow_out.html) -- [`shear(sx = [0, 0], sy = [0, 0], sz = [0, 0])`](https://openhome.cc/eGossip/OpenSCAD/lib3x-shear.html) + Signature | Description +--|-- +[arc(radius, angle, width = 1, width_mode = "LINE_CROSS")](https://openhome.cc/eGossip/OpenSCAD/lib3x-arc.html) | create an arc. +[hexagons(radius, spacing, levels)](https://openhome.cc/eGossip/OpenSCAD/lib3x-hexagons.html) | create hexagons in a hexagon. +[hull_polyline2d(points, width = 1)](https://openhome.cc/eGossip/OpenSCAD/lib3x-hull_polyline2d.html) | create a 2D polyline from a list of `[x, y]`. +[line2d(p1, p2, width = 1, p1Style = "CAP_SQUARE", p2Style = "CAP_SQUARE")](https://openhome.cc/eGossip/OpenSCAD/lib3x-line2d.html) | create a line from two points. +[multi_line_text(lines, line_spacing = 15, size = 10, font = "Arial", ...)](https://openhome.cc/eGossip/OpenSCAD/lib3x-multi_line_text.html) | create multi-line text from a list of strings. +[pie(radius, angle)](https://openhome.cc/eGossip/OpenSCAD/lib3x-pie.html) | create a pie (circular sector). +[polyline2d(points, width = 1, startingStyle = "CAP_SQUARE", endingStyle = "CAP_SQUARE", ...)](https://openhome.cc/eGossip/OpenSCAD/lib3x-polyline2d.html) | create a polyline from a list of `[x, y]` coordinates. +[polygon_hull(points)](https://openhome.cc/eGossip/OpenSCAD/lib3x-polygon_hull.html) | create a convex polygon by hulling a list of points. It avoids using hull and small 2D primitives to create the polygon. +[rounded_square(size, corner_r, center = false)](https://openhome.cc/eGossip/OpenSCAD/lib3x-rounded_square.html) | create a rounded square in the first quadrant. -### 2D Function -- [`bijection_offset(pts, d, epsilon = 0.0001)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-bijection_offset.html) -- [`contours(points, threshold)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-contours.html) -- [`in_shape(shapt_pts, pt, include_edge = false, epsilon = 0.0001)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-in_shape.html) -- [`trim_shape(shape_pts, from, to, epsilon = 0.0001)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-trim_shape.html) +## 3D Module -### 2D/3D Function -- [`angle_between(vt1, vt2)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-angle_between.html) -- [`bezier_surface(t_step, ctrl_pts)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-bezier_surface.html) -- [`bezier_smooth(path_pts, round_d, t_step = 0.1, closed = false, angle_threshold = 0)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-bezier_smooth.html) -- [`cross_sections(shape_pts, path_pts, angles, twist = 0, scale = 1.0)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-cross_sections.html) -- [`in_polyline(line_pts, pt, epsilon = 0.0001)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-in_polyline.html) -- [`lines_intersection(line1, line2, ext = false, epsilon = 0.0001)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-lines_intersection.html) -- [`paths2sections(paths)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-paths2sections.html) -- [`path_scaling_sections(shape_pts, edge_path)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-path_scaling_sections.html) -- [`midpt_smooth(points, n, closed = false)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-midpt_smooth.html) + Signature | Description +--|-- +[crystal_ball(radius, theta = 360, phi = 180, thickness = undef)](https://openhome.cc/eGossip/OpenSCAD/lib3x-crystal_ball.html) | create a crystal ball based on [spherical coordinates (r, θ, φ) used in mathematics](https://en.wikipedia.org/wiki/Spherical_coordinate_system). +[function_grapher(points, thickness = 1, style = "FACES")](https://openhome.cc/eGossip/OpenSCAD/lib3x-function_grapher.html) | create the graph of `f(x, y)` from a list of `[x, y, f(x, y)]`. +[hull_polyline3d(points, diameter = 1)](https://openhome.cc/eGossip/OpenSCAD/lib3x-hull_polyline3d.html) | create a 3D polyline from a list of `[x, y, z]`. +[line3d(p1, p2, diameter = 1, p1Style = "CAP_CIRCLE", p2Style = "CAP_CIRCLE")](https://openhome.cc/eGossip/OpenSCAD/lib3x-line3d.html) | create a 3D line from two points. +[loft(sections, slices = 1)](https://openhome.cc/eGossip/OpenSCAD/lib3x-loft.html) | develop a smooth skin between crosssections with different geometries. +[polyhedron_hull(points)](https://openhome.cc/eGossip/OpenSCAD/lib3x-polyhedron_hull.html) | create a convex polyhedron by hulling a list of points. It avoids using `hull` and small 3D primitives to create the polyhedron. +[polyline3d(points, diameter, startingStyle = "CAP_CIRCLE", endingStyle = "CAP_CIRCLE")](https://openhome.cc/eGossip/OpenSCAD/lib3x-polyline3d.html) | create a polyline from a list of `[x, y, z]`. +[rounded_cube(size, corner_r, center = false)](https://openhome.cc/eGossip/OpenSCAD/lib3x-rounded_cube.html) | create a cube in the first octant. +[rounded_cylinder(radius, h, round_r, convexity = 2, center = false)](https://openhome.cc/eGossip/OpenSCAD/lib3x-rounded_cylinder.html) | create a rounded cylinder. +[starburst(r1, r2, n, height)](https://openhome.cc/eGossip/OpenSCAD/lib3x-starburst.html) | a 3D version of [`shape_starburst`](https://openhome.cc/eGossip/OpenSCAD/lib3x-starburst.html). +[sweep(sections, triangles = "SOLID")](https://openhome.cc/eGossip/OpenSCAD/lib3x-sweep.html) | develop a smooth skin from crosssections with the same umber of sides. -### Path -- [`arc_path(radius, angle)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-arc_path.html) -- [`archimedean_spiral(arm_distance, init_angle, point_distance, num_of_points, rt_dir = "CT_CLK")`](https://openhome.cc/eGossip/OpenSCAD/lib3x-archimedean_spiral.html) -- [`bauer_spiral(n, radius = 1, rt_dir = "CT_CLK")`](https://openhome.cc/eGossip/OpenSCAD/lib3x-bauer_spiral.html) -- [`bezier_curve(t_step, points)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-bezier_curve.html) -- [`bspline_curve(t_step, degree, points, knots, weights)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-bspline_curve.html) -- [`curve(t_step, points, tightness = 0)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-curve.html) -- [`fibonacci_lattice(n, radius = 1, dir = "CT_CLK")`](https://openhome.cc/eGossip/OpenSCAD/lib3x-fibonacci_lattice.html) -- [`golden_spiral(from, to, point_distance, rt_dir = "CT_CLK")`](https://openhome.cc/eGossip/OpenSCAD/lib3x-golden_spiral.html) -- [`helix(radius, levels, level_dist, vt_dir = "SPI_DOWN", rt_dir = "CT_CLK")`](https://openhome.cc/eGossip/OpenSCAD/lib3x-helix.html) -- [`sphere_spiral(radius, za_step, z_circles = 1, begin_angle = 0, end_angle = 0, ...)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-sphere_spiral.html) -- [`torus_knot(p, q, phi_step)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-torus_knot.html) +## Transformation -### Extrusion -- [`bend_extrude(size, thickness, angle, frags = 24)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-bend_extrude.html) -- [`box_extrude(height, shell_thickness, bottom_thickness, offset_mode = "delta", chamfer = false, ...)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-box_extrude.html) -- [`ellipse_extrude(semi_minor_axis, height, center = false, convexity = 10, twist = 0, slices = 20)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-ellipse_extrude.html) -- [`rounded_extrude(size, round_r, angle = 90, twist = 0, convexity = 10)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-rounded_extrude.html) -- [`stereographic_extrude(shadow_side_leng)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-stereographic_extrude.html) + Signature | Description +--|-- +[along_with(points, angles, twist = 0, scale = 1.0, method = "AXIS_ANGLE")](https://openhome.cc/eGossip/OpenSCAD/lib3x-along_with.html) | put children along the given path. If there's only one child, put the child for each point. +[bend(size, angle, frags = 24)](https://openhome.cc/eGossip/OpenSCAD/lib3x-bend.html) | bend a 3D object. +[hollow_out(shell_thickness) ](https://openhome.cc/eGossip/OpenSCAD/lib3x-hollow_out.html)| hollow out a 2D object. +[shear(sx = [0, 0], sy = [0, 0], sz = [0, 0])](https://openhome.cc/eGossip/OpenSCAD/lib3x-shear.html) | shear all child elements along the X-axis, Y-axis, or Z-axis. -### 2D Shape -- [`shape_arc(radius, angle, width, width_mode = "LINE_CROSS")`](https://openhome.cc/eGossip/OpenSCAD/lib3x-shape_arc.html) -- [`shape_circle(radius, n)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-shape_circle.html) -- [`shape_cyclicpolygon(sides, circle_r, corner_r)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-shape_cyclicpolygon.html) -- [`shape_ellipse(axes)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-shape_ellipse.html) -- [`shape_liquid_splitting(radius, centre_dist, tangent_angle = 30, t_step = 0.1)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-shape_liquid_splitting.html) -- [`shape_path_extend(stroke_pts, path_pts, scale = 1.0, closed = false)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-shape_path_extend.html) -- [`shape_pentagram(r)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-shape_pentagram.html) -- [`shape_pie(radius, angle)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-shape_pie.html) -- [`shape_square(size, corner_r = 0)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-shape_square.html) -- [`shape_starburst(r1, r2, n)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-shape_starburst.html) -- [`shape_superformula(phi_step, m1, m2, n1, n2 = 1, n3 = 1, a = 1, b = 1)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-shape_superformula.html) -- [`shape_taiwan(h, distance = 0)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-shape_taiwan.html) -- [`shape_trapezium(length, h, corner_r = 0)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-shape_trapezium.html) +## 2D Function -### 2D Shape Extrusion -- [`archimedean_spiral_extrude(shape_pts, arm_distance, init_angle, point_distance, num_of_points, ...)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-archimedean_spiral_extrude.html) -- [`golden_spiral_extrude(shape_pts, from, to, point_distance, ...)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-golden_spiral_extrude.html) -- [`helix_extrude(shape_pts, radius, levels, level_dist, ...)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-helix_extrude.html) -- [`path_extrude(shape_pts, path_pts, ...)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-path_extrude.html) -- [`ring_extrude(shape_pts, radius, angle = 360, ...)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-ring_extrude.html) -- [`sphere_spiral_extrude(shape_pts, radius, za_step, ...)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-sphere_spiral_extrude.html) + Signature | Description +--|-- +[bijection_offset(pts, d, epsilon = 0.0001)](https://openhome.cc/eGossip/OpenSCAD/lib3x-bijection_offset.html) | move 2D outlines outward or inward by a given amount. Each point of the offsetted shape is paired with exactly one point of the original shape. +[contours(points, threshold)](https://openhome.cc/eGossip/OpenSCAD/lib3x-contours.html) | compute contour polygons by applying [marching squares](https://en.wikipedia.org/wiki/Marching_squares) to a rectangular list of numeric values. +[in_shape(shapt_pts, pt, include_edge = false, epsilon = 0.0001)](https://openhome.cc/eGossip/OpenSCAD/lib3x-in_shape.html) | check whether a point is inside a shape. +[trim_shape(shape_pts, from, to, epsilon = 0.0001)](https://openhome.cc/eGossip/OpenSCAD/lib3x-trim_shape.html) | trim a tangled-edge shape to a non-tangled shape. -### Util -- list - - [`util/bsearch(sorted, target)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-bsearch.html) - - [`util/has(lt, elem, sorted = false)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-has.html) - - [`util/find_index(lt, test)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-find_index.html) - - [`util/dedup(lt, ...)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-dedup.html) - - [`util/flat(lt, depth = 1)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-flat.html) - - [`util/reverse(lt)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-reverse.html) - - [`util/slice(lt, begin, end)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-slice.html) - - [`util/sort(lt, by = "idx", idx = 0)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-sort.html) - - [`util/sum(lt)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-sum.html) - - [`util/swap(lt, i, j)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-swap.html) - - [`util/zip(lts, combine)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-zip.html) - - [`util/every(lt, test)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-every.html) - - [`util/some(lt, test)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-some.html) -- random - - [`util/choose(choices, seed)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-choose.html) - - [`util/rand(min_value = 0, max_value = 1, seed_value = undef)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-rand.html) - - [`util/shuffle(lt, seed = undef)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-shuffle.html) -- string - - [`util/parse_number(t)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-parse_number.html) - - [`util/split_str(t, delimiter)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-split_str.html) - - [`util/sub_str(t, begin, end)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-sub_str.html) -- math - - [`util/degrees(radians)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-degrees.html) - - [`util/radians(degrees)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-radians.html) - - [`util/polar_coordinate(point)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-polar_coordinate.html) - - [`util/spherical_coordinate(point)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-spherical_coordinate.html) - - [`util/lerp(v1, v2, amt)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-lerp.html) - - [`util/fibseq(from, to)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-fibseq.html) -- set - - [`util/set/hashset(lt, ...)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-hashset.html) - - [`util/set/hashset_add(set, elem, ...)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-hashset_add.html) - - [`util/set/hashset_has(set, elem, ...)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-hashset_has.html) - - [`util/set/hashset_del(set, elem, ...)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-hashset_del.html) - - [`util/set/hashset_len(set)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-hashset_len.html) - - [`util/set/hashset_elems(set)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-hashset_elems.html) -- map - - [`util/map/hashmap(kv_lt, ...)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-hashmap.html) - - [`util/map/hashmap_put(map, key, value, ...)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-hashmap_put.html) - - [`util/map/hashmap_get(map, key, ...)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-hashmap_get.html) - - [`util/map/hashmap_del(map, key, ...)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-hashmap_del.html) - - [`util/map/hashmap_len(map)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-hashmap_len.html) - - [`util/map/hashmap_keys(map)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-hashmap_keys.html) - - [`util/map/hashmap_values(map)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-hashmap_values.html) - - [`util/map/hashmap_entries(map)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-hashmap_entries.html) +## 2D/3D Function -### Matrix -- [`matrix/m_determinant(m)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-m_determinant.html) -- [`matrix/m_mirror(v)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-m_mirror.html) -- [`matrix/m_rotation(a, v)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-m_rotation.html) -- [`matrix/m_scaling(s)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-m_scaling.html) -- [`matrix/m_shearing(sx = [0, 0], sy = [0, 0], sz = [0, 0])`](https://openhome.cc/eGossip/OpenSCAD/lib3x-m_shearing.html) -- [`matrix/m_translation(v)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-m_translation.html) + Signature | Description +--|-- +[angle_between(vt1, vt2)](https://openhome.cc/eGossip/OpenSCAD/lib3x-angle_between.html) | return the angle between two vectors. +[bezier_surface(t_step, ctrl_pts)](https://openhome.cc/eGossip/OpenSCAD/lib3x-bezier_surface.html) | given a set of control points, this function returns points of the Bézier surface. +[bezier_smooth(path_pts, round_d, t_step = 0.1, closed = false, angle_threshold = 0)](https://openhome.cc/eGossip/OpenSCAD/lib3x-bezier_smooth.html) | use bazier curves to smooth a path. +[cross_sections(shape_pts, path_pts, angles, twist = 0, scale = 1.0)](https://openhome.cc/eGossip/OpenSCAD/lib3x-cross_sections.html) | given a 2D shape, points and angles along the path, this function returns all cross-sections. +[in_polyline(line_pts, pt, epsilon = 0.0001)](https://openhome.cc/eGossip/OpenSCAD/lib3x-in_polyline.html) | check whether a point is on a line. +[lines_intersection(line1, line2, ext = false, epsilon = 0.0001)](https://openhome.cc/eGossip/OpenSCAD/lib3x-lines_intersection.html) | find the intersection of two line segments. Return `[]` if lines don't intersect. +[paths2sections(paths)](https://openhome.cc/eGossip/OpenSCAD/lib3x-paths2sections.html) | given a list of paths, this function returns all cross-sections described by those paths. +[path_scaling_sections(shape_pts, edge_path)](https://openhome.cc/eGossip/OpenSCAD/lib3x-path_scaling_sections.html) | given an edge path with the first point at the outline of a shape, this function uses the path to calculate scaling factors and returns all scaled sections in the reversed order of the edge path. +[midpt_smooth(points, n, closed = false)](https://openhome.cc/eGossip/OpenSCAD/lib3x-midpt_smooth.html) | given a 2D path, this function constructs a mid-point smoothed version by joining the mid-points of the lines of the path. -### Point Transformation -- [`ptf/ptf_bend(size, point, radius, angle)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-ptf_bend.html) -- [`ptf/ptf_circle(size, point)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-ptf_circle.html) -- [`ptf/ptf_ring(size, point, radius, angle = 360, twist = 0)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-ptf_ring.html) -- [`ptf/ptf_rotate(point, a, v)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-ptf_rotate.html) -- [`ptf/ptf_sphere(size, point, radius, angle = [180, 360])`](https://openhome.cc/eGossip/OpenSCAD/lib3x-ptf_sphere.html) -- [`ptf/ptf_torus(size, point, radius, angle = [360, 360], twist = 0)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-ptf_torus.html) -- [`ptf/ptf_x_twist(size, point, angle)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-ptf_x_twist.html) -- [`ptf/ptf_y_twist(size, point, angle)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-ptf_y_twist.html) +## Path + + Signature | Description +--|-- +[arc_path(radius, angle)](https://openhome.cc/eGossip/OpenSCAD/lib3x-arc_path.html) | create an arc path. +[archimedean_spiral(arm_distance, init_angle, point_distance, num_of_points, rt_dir = "CT_CLK")](https://openhome.cc/eGossip/OpenSCAD/lib3x-archimedean_spiral.html) | get all points and angles on the path of an archimedean spiral. +[bauer_spiral(n, radius = 1, rt_dir = "CT_CLK")](https://openhome.cc/eGossip/OpenSCAD/lib3x-bauer_spiral.html) | create visually even spacing of n points on the surface of the sphere. Successive points will all be approximately the same distance apart. +[bezier_curve(t_step, points)](https://openhome.cc/eGossip/OpenSCAD/lib3x-bezier_curve.html) | given a set of control points, this function returns points of the Bézier path. +[bspline_curve(t_step, degree, points, knots, weights)](https://openhome.cc/eGossip/OpenSCAD/lib3x-bspline_curve.html) | B-spline interpolation using [de Boor's algorithm](https://en.wikipedia.org/wiki/De_Boor%27s_algorithm). +[curve(t_step, points, tightness = 0)](https://openhome.cc/eGossip/OpenSCAD/lib3x-curve.html) | create a curved path. An implementation of [Centripetal Catmull-Rom spline](https://en.wikipedia.org/wiki/Centripetal_Catmull%E2%80%93Rom_spline). +[fibonacci_lattice(n, radius = 1, dir = "CT_CLK")](https://openhome.cc/eGossip/OpenSCAD/lib3x-fibonacci_lattice.html) | create visually even spacing of n points on the surface of the sphere. Nearest-neighbor points will all be approximately the same distance apart. +[golden_spiral(from, to, point_distance, rt_dir = "CT_CLK")](https://openhome.cc/eGossip/OpenSCAD/lib3x-golden_spiral.html) | get all points and angles on the path of a golden spiral based on Fibonacci numbers. The distance between two points is almost constant. +[helix(radius, levels, level_dist, vt_dir = "SPI_DOWN", rt_dir = "CT_CLK")](https://openhome.cc/eGossip/OpenSCAD/lib3x-helix.html) | get all points on the path of a spiral around a cylinder. +[sphere_spiral(radius, za_step, z_circles = 1, begin_angle = 0, end_angle = 0, ...) ](https://openhome.cc/eGossip/OpenSCAD/lib3x-sphere_spiral.html)| create all points and angles on the path of a spiral around a sphere. It returns a vector of `[[x, y, z], [ax, ay, az]]`. +[torus_knot(p, q, phi_step)](https://openhome.cc/eGossip/OpenSCAD/lib3x-torus_knot.html) | generate a path of [The (p,q)-torus knot](https://en.wikipedia.org/wiki/Torus_knot). + +## Extrusion + + Signature | Description +--|-- +[bend_extrude(size, thickness, angle, frags = 24)](https://openhome.cc/eGossip/OpenSCAD/lib3x-bend_extrude.html) | extrude and bend a 2D shape. +[box_extrude(height, shell_thickness, bottom_thickness, offset_mode = "delta", chamfer = false, ...)](https://openhome.cc/eGossip/OpenSCAD/lib3x-box_extrude.html) | create a box (container) from a 2D object. +[ellipse_extrude(semi_minor_axis, height, center = false, convexity = 10, twist = 0, slices = 20)](https://openhome.cc/eGossip/OpenSCAD/lib3x-ellipse_extrude.html) | extrude a 2D object along the path of an ellipse from 0 to 180 degrees. +[rounded_extrude(size, round_r, angle = 90, twist = 0, convexity = 10)](https://openhome.cc/eGossip/OpenSCAD/lib3x-rounded_extrude.html) | extrude a 2D object roundly from 0 to 180 degrees. +[stereographic_extrude(shadow_side_leng)](https://openhome.cc/eGossip/OpenSCAD/lib3x-stereographic_extrude.html) | take a 2D polygon as input and extend it onto a sphere. + +## 2D Shape + + Signature | Description +--|-- +[shape_arc(radius, angle, width, width_mode = "LINE_CROSS")](https://openhome.cc/eGossip/OpenSCAD/lib3x-shape_arc.html) | return points on the path of an arc shape. +[shape_circle(radius, n)](https://openhome.cc/eGossip/OpenSCAD/lib3x-shape_circle.html) | return points on the path of a circle. +[shape_cyclicpolygon(sides, circle_r, corner_r)](https://openhome.cc/eGossip/OpenSCAD/lib3x-shape_cyclicpolygon.html) | return points on the path of a regular cyclic polygon. +[shape_ellipse(axes)](https://openhome.cc/eGossip/OpenSCAD/lib3x-shape_ellipse.html) | return points on the path of an ellipse. +[shape_liquid_splitting(radius, centre_dist, tangent_angle = 30, t_step = 0.1)](https://openhome.cc/eGossip/OpenSCAD/lib3x-shape_liquid_splitting.html) | return shape points of two splitting liquid shapes, kind of how cells divide. +[shape_path_extend(stroke_pts, path_pts, scale = 1.0, closed = false)](https://openhome.cc/eGossip/OpenSCAD/lib3x-shape_path_extend.html) | extend a 2D stroke along a path to create a 2D shape. +[shape_pentagram(r)](https://openhome.cc/eGossip/OpenSCAD/lib3x-shape_pentagram.html) | return shape points of a pentagram. +[shape_pie(radius, angle)](https://openhome.cc/eGossip/OpenSCAD/lib3x-shape_pie.html) | return shape points of a pie (circular sector) shape. +[shape_square(size, corner_r = 0)](https://openhome.cc/eGossip/OpenSCAD/lib3x-shape_square.html) | return shape points of a rounded square or rectangle. +[shape_starburst(r1, r2, n)](https://openhome.cc/eGossip/OpenSCAD/lib3x-shape_starburst.html) | returns shape points of a star. +[shape_superformula(phi_step, m1, m2, n1, n2 = 1, n3 = 1, a = 1, b = 1)](https://openhome.cc/eGossip/OpenSCAD/lib3x-shape_superformula.html) | return shape points of [Superformula](https://en.wikipedia.org/wiki/Superformula). +[shape_taiwan(h, distance = 0)](https://openhome.cc/eGossip/OpenSCAD/lib3x-shape_taiwan.html) | return shape points of [Taiwan](https://www.google.com.tw/maps?q=taiwan&um=1&ie=UTF-8&sa=X&ved=0ahUKEwjai9XrqurTAhVIopQKHbEHClwQ_AUICygC). +[shape_trapezium(length, h, corner_r = 0)](https://openhome.cc/eGossip/OpenSCAD/lib3x-shape_trapezium.html) | return shape points of an isosceles trapezoid. + +## 2D Shape Extrusion + + Signature | Description +--|-- +[archimedean_spiral_extrude(shape_pts, arm_distance, init_angle, point_distance, num_of_points, ...)](https://openhome.cc/eGossip/OpenSCAD/lib3x-archimedean_spiral_extrude.html) | extrude a 2D shape along the path of an archimedean spiral. +[golden_spiral_extrude(shape_pts, from, to, point_distance, ...)](https://openhome.cc/eGossip/OpenSCAD/lib3x-golden_spiral_extrude.html) | extrude a 2D shape along the path of a golden spiral. +[helix_extrude(shape_pts, radius, levels, level_dist, ...)](https://openhome.cc/eGossip/OpenSCAD/lib3x-helix_extrude.html) | extrude a 2D shape along a helix path. +[path_extrude(shape_pts, path_pts, ...)](https://openhome.cc/eGossip/OpenSCAD/lib3x-path_extrude.html) | extrude a 2D shape along a path. +[ring_extrude(shape_pts, radius, angle = 360, ...)](https://openhome.cc/eGossip/OpenSCAD/lib3x-ring_extrude.html) | rotational extrusion spins a 2D shape around the Z-axis. +[sphere_spiral_extrude(shape_pts, radius, za_step, ...)](https://openhome.cc/eGossip/OpenSCAD/lib3x-sphere_spiral_extrude.html) | extrude a 2D shape along the path of a sphere spiral. + +## Util + +### util/list + + Signature | Description +--|-- +[util/bsearch(sorted, target)](https://openhome.cc/eGossip/OpenSCAD/lib3x-bsearch.html) | search a value in a list whose elements must be sorted by zyx. +[util/has(lt, elem, sorted = false)](https://openhome.cc/eGossip/OpenSCAD/lib3x-has.html) | return `true` If `lt` contains elem. +[util/find_index(lt, test)](https://openhome.cc/eGossip/OpenSCAD/lib3x-find_index.html) | return the index of the first element that satisfies the testing function. +[util/dedup(lt, ...)](https://openhome.cc/eGossip/OpenSCAD/lib3x-dedup.html) | eliminate duplicate vectors. +[util/flat(lt, depth = 1)](https://openhome.cc/eGossip/OpenSCAD/lib3x-flat.html) | return a new list with all sub-list elements concatenated into it recursively up to the specified depth. +[util/reverse(lt)](https://openhome.cc/eGossip/OpenSCAD/lib3x-reverse.html) | reverse a list. +[util/slice(lt, begin, end)](https://openhome.cc/eGossip/OpenSCAD/lib3x-slice.html) | return a list selected from `begin` to `end`, or to the `end` of the list (`end` not included). +[util/sort(lt, by = "idx", idx = 0)](https://openhome.cc/eGossip/OpenSCAD/lib3x-sort.html) | sort a list. +[util/sum(lt)](https://openhome.cc/eGossip/OpenSCAD/lib3x-sum.html) | use `+` to sum up all elements in a list. +[util/swap(lt, i, j)](https://openhome.cc/eGossip/OpenSCAD/lib3x-swap.html) | swap two elements in a list. +[util/zip(lts, combine)](https://openhome.cc/eGossip/OpenSCAD/lib3x-zip.html) | make a list that aggregates elements from each of the lists. +[util/every(lt, test)](https://openhome.cc/eGossip/OpenSCAD/lib3x-every.html) | test whether all elements in the list pass the test implemented by the provided function. +[util/some(lt, test)](https://openhome.cc/eGossip/OpenSCAD/lib3x-some.html) | test whether at least one element in the list passes the test implemented by the provided function. + +### util/random + + Signature | Description +--|-- +[util/choose(choices, seed)](https://openhome.cc/eGossip/OpenSCAD/lib3x-choose.html) | choose an element from the given list. +[util/rand(min_value = 0, max_value = 1, seed_value = undef)](https://openhome.cc/eGossip/OpenSCAD/lib3x-rand.html) | generate a pseudo random number. +[util/shuffle(lt, seed = undef)](https://openhome.cc/eGossip/OpenSCAD/lib3x-shuffle.html) | randomizes the order of the elements. + +### util/string + + Signature | Description +--|-- +[util/parse_number(t)](https://openhome.cc/eGossip/OpenSCAD/lib3x-parse_number.html) | parse the string argument as an number. +[util/split_str(t, delimiter)](https://openhome.cc/eGossip/OpenSCAD/lib3x-split_str.html) | split the given string around matches of the given delimiting character. +[util/sub_str(t, begin, end)](https://openhome.cc/eGossip/OpenSCAD/lib3x-sub_str.html) | return the part of the string from `begin` to `end`, or to the `end` of the string (`end` not included). + +### util/math + + Signature | Description +--|-- +[util/degrees(radians)](https://openhome.cc/eGossip/OpenSCAD/lib3x-degrees.html) | convert a radian measurement to the corresponding value in degrees. +[util/radians(degrees)](https://openhome.cc/eGossip/OpenSCAD/lib3x-radians.html) | convert a degree measurement to the corresponding value in radians. +[util/polar_coordinate(point)](https://openhome.cc/eGossip/OpenSCAD/lib3x-polar_coordinate.html) | convert from Cartesian to Polar coordinates. +[util/spherical_coordinate(point)](https://openhome.cc/eGossip/OpenSCAD/lib3x-spherical_coordinate.html) | convert from Cartesian to Spherical coordinates (used in mathematics). +[util/lerp(v1, v2, amt)](https://openhome.cc/eGossip/OpenSCAD/lib3x-lerp.html) | linear interpolate the vector v1 to v2. +[util/fibseq(from, to)](https://openhome.cc/eGossip/OpenSCAD/lib3x-fibseq.html) | generate a Fibonacci sequence. + +### util/set + + Signature | Description +--|-- +[util/set/hashset(lt, ...)](https://openhome.cc/eGossip/OpenSCAD/lib3x-hashset.html) | model the mathematical set, backed by a hash table. +[util/set/hashset_add(set, elem, ...)](https://openhome.cc/eGossip/OpenSCAD/lib3x-hashset_add.html) | add an element to a `hashset`. +[util/set/hashset_has(set, elem, ...)](https://openhome.cc/eGossip/OpenSCAD/lib3x-hashset_has.html) | return `true` if a `hashset` contains the specified element. +[util/set/hashset_del(set, elem, ...)](https://openhome.cc/eGossip/OpenSCAD/lib3x-hashset_del.html) | del an element from a `hashset`. +[util/set/hashset_len(set)](https://openhome.cc/eGossip/OpenSCAD/lib3x-hashset_len.html) | return the length of the elements in a `hashset`. +[util/set/hashset_elems(set)](https://openhome.cc/eGossip/OpenSCAD/lib3x-hashset_elems.html) | returns a list containing all elements in a `hashset`. No guarantees to the order. + +### util/map + + Signature | Description +--|-- +[util/map/hashmap(kv_lt, ...)](https://openhome.cc/eGossip/OpenSCAD/lib3x-hashmap.html) | map keys to values. +[util/map/hashmap_put(map, key, value, ...)](https://openhome.cc/eGossip/OpenSCAD/lib3x-hashmap_put.html) | put a key/value pair to a `hashmap`. +[util/map/hashmap_get(map, key, ...)](https://openhome.cc/eGossip/OpenSCAD/lib3x-hashmap_get.html) | get the value of the specified key from a `hashmap`. +[util/map/hashmap_del(map, key, ...)](https://openhome.cc/eGossip/OpenSCAD/lib3x-hashmap_del.html) | delete the mapping for the specified key from a `hashmap` if present. +[util/map/hashmap_len(map)](https://openhome.cc/eGossip/OpenSCAD/lib3x-hashmap_len.html) | return the length of a `hashmap`. +[util/map/hashmap_keys(map)](https://openhome.cc/eGossip/OpenSCAD/lib3x-hashmap_keys.html) | return a list containing all keys in a `hashmap`. +[util/map/hashmap_values(map)](https://openhome.cc/eGossip/OpenSCAD/lib3x-hashmap_values.html) | return a list containing all values in a `hashmap`. +[util/map/hashmap_entries(map)](https://openhome.cc/eGossip/OpenSCAD/lib3x-hashmap_entries.html) | return a list containing all `[key, value]`s in a `hashmap`. + +## Matrix + + Signature | Description +--|-- +[matrix/m_determinant(m)](https://openhome.cc/eGossip/OpenSCAD/lib3x-m_determinant.html) | calculate a determinant of a square matrix. +[matrix/m_mirror(v)](https://openhome.cc/eGossip/OpenSCAD/lib3x-m_mirror.html) | generate a transformation matrix which can pass into `multmatrix` to mirror the child element on a plane through the origin. +[matrix/m_rotation(a, v)](https://openhome.cc/eGossip/OpenSCAD/lib3x-m_rotation.html) | Generate a transformation matrix which can pass into `multmatrix` to rotate the child element about the axis of the coordinate system or around an arbitrary axis. +[matrix/m_scaling(s)](https://openhome.cc/eGossip/OpenSCAD/lib3x-m_scaling.html) | generate a transformation matrix which can pass into `multmatrix` to scale its child elements using the specified vector. +[matrix/m_shearing(sx = [0, 0], sy = [0, 0], sz = [0, 0])](https://openhome.cc/eGossip/OpenSCAD/lib3x-m_shearing.html) | generate a transformation matrix which can pass into `multmatrix` to shear all child elements along the X-axis, Y-axis, or Z-axis in 3D. +[matrix/m_translation(v)](https://openhome.cc/eGossip/OpenSCAD/lib3x-m_translation.html) | generate a transformation matrix which can pass into multmatrix to translates (moves) its child elements along the specified vector. + +## Point Transformation + + Signature | Description +--|-- +[ptf/ptf_bend(size, point, radius, angle)](https://openhome.cc/eGossip/OpenSCAD/lib3x-ptf_bend.html) | transform a point inside a rectangle to a point of an arc. +[ptf/ptf_circle(size, point)](https://openhome.cc/eGossip/OpenSCAD/lib3x-ptf_circle.html) | transform a point inside a rectangle to a point inside a circle. +[ptf/ptf_ring(size, point, radius, angle = 360, twist = 0)](https://openhome.cc/eGossip/OpenSCAD/lib3x-ptf_ring.html) | transform a point inside a rectangle to a point of a ring. +[ptf/ptf_rotate(point, a, v)](https://openhome.cc/eGossip/OpenSCAD/lib3x-ptf_rotate.html) | rotate a point a degrees around the axis of the coordinate system or an arbitrary axis. +[ptf/ptf_sphere(size, point, radius, angle = [180, 360])](https://openhome.cc/eGossip/OpenSCAD/lib3x-ptf_sphere.html) | transform a point inside a rectangle to a point of a sphere. +[ptf/ptf_torus(size, point, radius, angle = [360, 360], twist = 0)](https://openhome.cc/eGossip/OpenSCAD/lib3x-ptf_torus.html) | transform a point inside a rectangle to a point of a torus. +[ptf/ptf_x_twist(size, point, angle)](https://openhome.cc/eGossip/OpenSCAD/lib3x-ptf_x_twist.html) | twist a point along the x-axis. +[ptf/ptf_y_twist(size, point, angle)](https://openhome.cc/eGossip/OpenSCAD/lib3x-ptf_y_twist.html) | twist a point along the y-axis. ---- -### Turtle -- [`turtle/footprints2(cmds, start = [0, 0])`](https://openhome.cc/eGossip/OpenSCAD/lib3x-footprints2.html) -- [`turtle/footprints3(cmds, start = [0, 0, 0])`](https://openhome.cc/eGossip/OpenSCAD/lib3x-footprints3.html) -- [`turtle/lsystem2(axiom, rules, n, angle, leng = 1, heading = 0, ...)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-lsystem2.html) -- [`turtle/lsystem3(axiom, rules, n, angle, leng = 1, heading = 0, ...)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-lsystem3.html) -- [`turtle/t2d(t, cmd, point, angle, leng)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-t2d.html) -- [`turtle/t3d(t, cmd, point, unit_vectors, leng, angle)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-t3d.html) +## Turtle -### Voxel -- [`voxel/vx_ascii(char, center = false, invert = false)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-vx_ascii.html) -- [`voxel/vx_bezier(p1, p2, p3, p4)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-vx_bezier.html) -- [`voxel/vx_circle(radius, filled = false)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-vx_circle.html) -- [`voxel/vx_contour(points, sorted = false)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-vx_contour.html) -- [`voxel/vx_curve(points, tightness = 0)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-vx_curve.html) -- [`voxel/vx_cylinder(r, h, filled = false, thickness = 1)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-vx_cylinder.html) -- [`voxel/vx_difference(points1, points2)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-vx_difference.html) -- [`voxel/vx_from(binaries, center = false, invert = false)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-vx_from.html) -- [`voxel/vx_gray(levels, center = false, invert = false, normalize = false)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-vx_gray.html) -- [`voxel/vx_intersection(points1, points2)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-vx_intersection.html) -- [`voxel/vx_line(p1, p2)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-vx_line.html) -- [`voxel/vx_polygon(points, filled = false)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-vx_polygon.html) -- [`voxel/vx_polyline(points)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-vx_polyline.html) -- [`voxel/vx_sphere(radius, filled = false, thickness = 1)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-vx_sphere.html) -- [`voxel/vx_union(points1, points2)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-vx_union.html) + Signature | Description +--|-- +[turtle/footprints2(cmds, start = [0, 0])](https://openhome.cc/eGossip/OpenSCAD/lib3x-footprints2.html) | drive a turtle with `["forward", length]` or `["turn", angle]`. This function is intended to use a turtle to imitate freehand drawing. +[turtle/footprints3(cmds, start = [0, 0, 0])](https://openhome.cc/eGossip/OpenSCAD/lib3x-footprints3.html) | a 3D verion of `footprint2`. +[turtle/lsystem2(axiom, rules, n, angle, leng = 1, heading = 0, ...)](https://openhome.cc/eGossip/OpenSCAD/lib3x-lsystem2.html) | 2D implementation of [L-system](https://en.wikipedia.org/wiki/L-system). +[turtle/lsystem3(axiom, rules, n, angle, leng = 1, heading = 0, ...)](https://openhome.cc/eGossip/OpenSCAD/lib3x-lsystem3.html) | 3D implementation of [L-system](https://en.wikipedia.org/wiki/L-system). +[turtle/t2d(t, cmd, point, angle, leng)](https://openhome.cc/eGossip/OpenSCAD/lib3x-t2d.html) | an implementation of Turtle Graphics. +[turtle/t3d(t, cmd, point, unit_vectors, leng, angle)](https://openhome.cc/eGossip/OpenSCAD/lib3x-t3d.html) | a 3D version of `t2d`. -### Part -- [`part/cone(radius, length = 0, spacing = 0.5, angle = 50, void = false, ends = false)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-cone.html) -- [`part/connector_peg(radius, height, spacing = 0.5, void = false, ends = false)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-connector_peg.html) -- [`part/joint_T(shaft_r, shaft_h, t_leng, thickness, spacing = 0.5, center = false)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-joint_T.html) +## Voxel -### Surface -- [`surface/sf_bend(levels, radius, thickness, depth, angle = 180, invert = false)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-sf_bend.html) -- [`surface/sf_ring(levels, radius, thickness, depth, angle = 360, twist = 0, invert = false)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-sf_ring.html) -- [`surface/sf_solidify(surface1, surface2, slicing = "SLASH")`](https://openhome.cc/eGossip/OpenSCAD/lib3x-sf_solidify.html) -- [`surface/sf_sphere(levels, radius, thickness, depth, angle = [180, 360], invert = false)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-sf_sphere.html) -- [`surface/sf_square(levels, thickness, depth, x_twist = 0, y_twist = 0, invert = false)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-sf_square.html) -- [`surface/sf_torus(levels, radius, thickness, depth, angle = [360, 360], twist = 0, invert = false)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-sf_torus.html) + Signature | Description +--|-- +[voxel/vx_ascii(char, center = false, invert = false)](https://openhome.cc/eGossip/OpenSCAD/lib3x-vx_ascii.html) | generate 8x8 voxel points of printable ASCII characters (codes 32dec to 126dec). +[voxel/vx_bezier(p1, p2, p3, p4)](https://openhome.cc/eGossip/OpenSCAD/lib3x-vx_bezier.html) | return voxel-by-voxel points of Bézier Curve. +[voxel/vx_circle(radius, filled = false)](https://openhome.cc/eGossip/OpenSCAD/lib3x-vx_circle.html) | return points that can be used to draw a voxel-style circle. +[voxel/vx_contour(points, sorted = false)](https://openhome.cc/eGossip/OpenSCAD/lib3x-vx_contour.html) | return the contour which encircles the area. +[voxel/vx_curve(points, tightness = 0)](https://openhome.cc/eGossip/OpenSCAD/lib3x-vx_curve.html) | the curve is drawn only from the 2nd control point to the second-last control point. +[voxel/vx_cylinder(r, h, filled = false, thickness = 1)](https://openhome.cc/eGossip/OpenSCAD/lib3x-vx_cylinder.html) | return points that can be used to draw a voxel-style cylinder. +[voxel/vx_difference(points1, points2)](https://openhome.cc/eGossip/OpenSCAD/lib3x-vx_difference.html) | create a difference of two lists of points. +[voxel/vx_from(binaries, center = false, invert = false)](https://openhome.cc/eGossip/OpenSCAD/lib3x-vx_from.html) | given a list of 0s and 1s that represent a black-and-white image. This function translates them into voxel points. +[voxel/vx_gray(levels, center = false, invert = false, normalize = false)](https://openhome.cc/eGossip/OpenSCAD/lib3x-vx_gray.html) | given a list of numbers (0 ~ 255) that represent a gray image. This function translates them into a list of `[x, y, level]`s. +[voxel/vx_intersection(points1, points2)](https://openhome.cc/eGossip/OpenSCAD/lib3x-vx_intersection.html) | create an intersection of two lists of points. +[voxel/vx_line(p1, p2)](https://openhome.cc/eGossip/OpenSCAD/lib3x-vx_line.html) | given two points. it returns points that can be used to draw a voxel-style line. +[voxel/vx_polygon(points, filled = false)](https://openhome.cc/eGossip/OpenSCAD/lib3x-vx_polygon.html) | return points that can be used to draw a voxel-style polygon. +[voxel/vx_polyline(points)](https://openhome.cc/eGossip/OpenSCAD/lib3x-vx_polyline.html) | return points that can be used to draw a voxel-style polyline. +[voxel/vx_sphere(radius, filled = false, thickness = 1)](https://openhome.cc/eGossip/OpenSCAD/lib3x-vx_sphere.html) | return points that can be used to draw a voxel-style sphere. +[voxel/vx_union(points1, points2)](https://openhome.cc/eGossip/OpenSCAD/lib3x-vx_union.html) | create a union of two lists of points. -### Noise -- [`noise/nz_cell(points, p, dist = "euclidean")`](https://openhome.cc/eGossip/OpenSCAD/lib3x-nz_cell.html) -- [`noise/nz_perlin1(x, seed = undef)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-nz_perlin1.html) -- [`noise/nz_perlin1s(xs, seed = undef)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-nz_perlin1s.html) -- [`noise/nz_perlin2(x, y, seed = undef)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-nz_perlin2.html) -- [`noise/nz_perlin2s(points, seed = undef)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-nz_perlin2s.html) -- [`noise/nz_perlin3(x, y, z, seed = undef)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-nz_perlin3.html) -- [`noise/nz_perlin3s(points, seed = undef)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-nz_perlin3s.html) -- [`noise/nz_worley2(x, y, seed = undef, grid_w = 10, dist = "euclidean")`](https://openhome.cc/eGossip/OpenSCAD/lib3x-nz_worley2.html) -- [`noise/nz_worley2s(points, seed = undef, grid_w = 10, dist = "euclidean")`](https://openhome.cc/eGossip/OpenSCAD/lib3x-nz_worley2s.html) -- [`noise/nz_worley3(x, y, z, seed = undef, tile_w = 10, dist = "euclidean")`](https://openhome.cc/eGossip/OpenSCAD/lib3x-nz_worley3.html) -- [`noise/nz_worley3s(points, seed = undef, tile_w = 10, dist = "euclidean")`](https://openhome.cc/eGossip/OpenSCAD/lib3x-nz_worley3s.html) +## Part -### Voronoi + Signature | Description +--|-- +[part/cone(radius, length = 0, spacing = 0.5, angle = 50, void = false, ends = false)](https://openhome.cc/eGossip/OpenSCAD/lib3x-cone.html) | create a cone for rotatable models. +[part/connector_peg(radius, height, spacing = 0.5, void = false, ends = false)](https://openhome.cc/eGossip/OpenSCAD/lib3x-connector_peg.html) | create a connector peg. +[part/joint_T(shaft_r, shaft_h, t_leng, thickness, spacing = 0.5, center = false)](https://openhome.cc/eGossip/OpenSCAD/lib3x-joint_T.html) | create a joint_T for rotatable models. -- [`voronoi/vrn2_cells_from(points)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-vrn2_cells_from.html) -- [`voronoi/vrn2_cells_space(size, grid_w, seed = undef)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-vrn2_cells_space.html) -- [`voronoi/vrn2_from(points, spacing = 1, r = 0, delta = 0, chamfer = false, region_type = "square")`](https://openhome.cc/eGossip/OpenSCAD/lib3x-vrn2_from.html) -- [`voronoi/vrn2_space(size, grid_w, seed = undef, spacing = 1, r = 0, delta = 0, chamfer = false, region_type = "square")`](https://openhome.cc/eGossip/OpenSCAD/lib3x-vrn2_space.html) -- [`voronoi/vrn3_from(points, spacing = 1)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-vrn3_from.html) -- [`voronoi/vrn3_space(size, grid_w, seed = undef, spacing = 1)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-vrn3_space.html) +## Surface -### Maze + Signature | Description +--|-- +[surface/sf_bend(levels, radius, thickness, depth, angle = 180, invert = false)](https://openhome.cc/eGossip/OpenSCAD/lib3x-sf_bend.html) | bend a photo. +[surface/sf_ring(levels, radius, thickness, depth, angle = 360, twist = 0, invert = false)](https://openhome.cc/eGossip/OpenSCAD/lib3x-sf_ring.html) | turn a photo into a ring. +[surface/sf_solidify(surface1, surface2, slicing = "SLASH")](https://openhome.cc/eGossip/OpenSCAD/lib3x-sf_solidify.html) | solidify two square surfaces. +[surface/sf_sphere(levels, radius, thickness, depth, angle = [180, 360], invert = false)](https://openhome.cc/eGossip/OpenSCAD/lib3x-sf_sphere.html) | map a photo onto a sphere. +[surface/sf_square(levels, thickness, depth, x_twist = 0, y_twist = 0, invert = false)](https://openhome.cc/eGossip/OpenSCAD/lib3x-sf_square.html) | turn a photo into a twistable square. +[surface/sf_torus(levels, radius, thickness, depth, angle = [360, 360], twist = 0, invert = false)](https://openhome.cc/eGossip/OpenSCAD/lib3x-sf_torus.html) | turn a photo to a torus. -- [`maze/mz_square_cells(rows, columns, start = [0, 0], ...)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-mz_square_cells.html) -- [`maze/mz_square_get(cell, query)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-mz_square_get.html) -- [`maze/mz_square_walls(cells, rows, columns, cell_width, left_border = true, bottom_border = true)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-mz_square_walls.html) -- [`maze/mz_hex_walls(cells, rows, columns, cell_radius, left_border = true, bottom_border = true)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-mz_hex_walls.html) -- [`maze/mz_square_initialize(rows, columns, mask)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-mz_square_initialize.html) -- [`maze/mz_hamiltonian(rows, columns, start = [0, 0], seed = undef)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-mz_hamiltonian.html) -- [`maze/mz_theta_cells(rows, beginning_number, start = [0, 0], seed = undef)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-mz_theta_cells.html) -- [`maze/mz_theta_get(cell, query)`](https://openhome.cc/eGossip/OpenSCAD/lib3x-mz_theta_get.html) \ No newline at end of file +## Noise + + Signature | Description +--|-- +[noise/nz_cell(points, p, dist = "euclidean")](https://openhome.cc/eGossip/OpenSCAD/lib3x-nz_cell.html) | an implementation of [Worley noise](https://en.wikipedia.org/wiki/Worley_noise). +[noise/nz_perlin1(x, seed = undef)](https://openhome.cc/eGossip/OpenSCAD/lib3x-nz_perlin1.html) | return the 1D [Perlin noise](https://en.wikipedia.org/wiki/Perlin_noise) value at the x coordinate. +[noise/nz_perlin1s(xs, seed = undef)](https://openhome.cc/eGossip/OpenSCAD/lib3x-nz_perlin1s.html) | return 1D [Perlin noise](https://en.wikipedia.org/wiki/Perlin_noise) values at x coordinates. +[noise/nz_perlin2(x, y, seed = undef)](https://openhome.cc/eGossip/OpenSCAD/lib3x-nz_perlin2.html) | return the 2D [Perlin noise](https://en.wikipedia.org/wiki/Perlin_noise) value at the (x, y) coordinate. +[noise/nz_perlin2s(points, seed = undef)](https://openhome.cc/eGossip/OpenSCAD/lib3x-nz_perlin2s.html) | return 2D [Perlin noise](https://en.wikipedia.org/wiki/Perlin_noise) values at (x, y) coordinates. +[noise/nz_perlin3(x, y, z, seed = undef)](https://openhome.cc/eGossip/OpenSCAD/lib3x-nz_perlin3.html) | return the 3D [Perlin noise](https://en.wikipedia.org/wiki/Perlin_noise) value at the (x, y, z) coordinate. +[noise/nz_perlin3s(points, seed = undef)](https://openhome.cc/eGossip/OpenSCAD/lib3x-nz_perlin3s.html) | return 3D [Perlin noise](https://en.wikipedia.org/wiki/Perlin_noise) values at (x, y, z) coordinates. +[noise/nz_worley2(x, y, seed = undef, grid_w = 10, dist = "euclidean")](https://openhome.cc/eGossip/OpenSCAD/lib3x-nz_worley2.html) | return the 2D [Worley noise](https://en.wikipedia.org/wiki/Worley_noise) value at the (x, y) coordinate. +[noise/nz_worley2s(points, seed = undef, grid_w = 10, dist = "euclidean")](https://openhome.cc/eGossip/OpenSCAD/lib3x-nz_worley2s.html) | return 2D [Worley noise](https://en.wikipedia.org/wiki/Worley_noise) values at (x, y) coordinates. +[noise/nz_worley3(x, y, z, seed = undef, tile_w = 10, dist = "euclidean")](https://openhome.cc/eGossip/OpenSCAD/lib3x-nz_worley3.html) | return the 3D [Worley noise](https://en.wikipedia.org/wiki/Worley_noise) value at the (x, y, z) coordinate. +[noise/nz_worley3s(points, seed = undef, tile_w = 10, dist = "euclidean")](https://openhome.cc/eGossip/OpenSCAD/lib3x-nz_worley3s.html) | return 3D [Worley noise](https://en.wikipedia.org/wiki/Worley_noise) values at (x, y, z) coordinates. + +## Voronoi + + Signature | Description +--|-- +[voronoi/vrn2_cells_from(points)](https://openhome.cc/eGossip/OpenSCAD/lib3x-vrn2_cells_from.html) | create cell shapes of [Voronoi](https://en.wikipedia.org/wiki/Voronoi_diagram) from a list of points. +[voronoi/vrn2_cells_space(size, grid_w, seed = undef)](https://openhome.cc/eGossip/OpenSCAD/lib3x-vrn2_cells_space.html) | create cell shapes of [Voronoi](https://en.wikipedia.org/wiki/Voronoi_diagram) in the first quadrant. +[voronoi/vrn2_from(points, spacing = 1, ...)](https://openhome.cc/eGossip/OpenSCAD/lib3x-vrn2_from.html) | create a [Voronoi](https://en.wikipedia.org/wiki/Voronoi_diagram) from a list of points. +[voronoi/vrn2_space(size, grid_w, seed = undef, spacing = 1, ...)](https://openhome.cc/eGossip/OpenSCAD/lib3x-vrn2_space.html) | create a [Voronoi](https://en.wikipedia.org/wiki/Voronoi_diagram) in the first quadrant. +[voronoi/vrn3_from(points, spacing = 1)](https://openhome.cc/eGossip/OpenSCAD/lib3x-vrn3_from.html) | create a 3D version of [Voronoi](https://en.wikipedia.org/wiki/Voronoi_diagram). +[voronoi/vrn3_space(size, grid_w, seed = undef, spacing = 1)](https://openhome.cc/eGossip/OpenSCAD/lib3x-vrn3_space.html) | create a [Voronoi](https://en.wikipedia.org/wiki/Voronoi_diagram) in the first octant. + +## Maze + + Signature | Description +--|-- +[maze/mz_square_cells(rows, columns, start = [0, 0], ...)](https://openhome.cc/eGossip/OpenSCAD/lib3x-mz_square_cells.html) | return cell data of a square maze. +[maze/mz_square_get(cell, query)](https://openhome.cc/eGossip/OpenSCAD/lib3x-mz_square_get.html) | a helper for getting data from a square-maze cell. +[maze/mz_square_walls(cells, rows, columns, cell_width, ...)](https://openhome.cc/eGossip/OpenSCAD/lib3x-mz_square_walls.html) | a helper for creating square wall data from maze cells. +[maze/mz_hex_walls(cells, rows, columns, cell_radius, ...)](https://openhome.cc/eGossip/OpenSCAD/lib3x-mz_hex_walls.html) | a helper for creating hex wall data from maze cells. +[maze/mz_square_initialize(rows, columns, mask)](https://openhome.cc/eGossip/OpenSCAD/lib3x-mz_square_initialize.html) | a helper for initializing cell data of a maze. +[maze/mz_hamiltonian(rows, columns, start = [0, 0], seed = undef)](https://openhome.cc/eGossip/OpenSCAD/lib3x-mz_hamiltonian.html) | create a hamiltonian path from a maze. +[maze/mz_theta_cells(rows, beginning_number, start = [0, 0], seed = undef)](https://openhome.cc/eGossip/OpenSCAD/lib3x-mz_theta_cells.html) | return cell data of a theta maze. +[maze/mz_theta_get(cell, query)](https://openhome.cc/eGossip/OpenSCAD/lib3x-mz_theta_get.html) | a helper for getting data from a theta-maze cell. \ No newline at end of file