ship 3.2

LICENSE

@@ -1,7 +1,7 @@
                    GNU LESSER GENERAL PUBLIC LICENSE
                        Version 3, 29 June 2007
 
- Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
+ Copyright (C) 2007 Free Software Foundation, Inc. <https://fsf.org/>
  Everyone is permitted to copy and distribute verbatim copies
  of this license document, but changing it is not allowed.
 

LICENSE.svg

@@ -1 +0,0 @@
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README.md

@@ -1,10 +1,8 @@
-# dotSCAD 3.1
+# dotSCAD 3.2
 
 > **Reduce the burden of mathematics/algorithm when playing OpenSCAD.**
 
-![dotSCAD](featured_img/TorusKnotMaze.JPG)
+![dotSCAD](featured_img/TorusKnotDragon_and_Pearl.JPG)
-
-[![license/LGPL](LICENSE.svg)](https://github.com/JustinSDK/lib-openscad/blob/master/LICENSE)
 
 ## Introduction
 
@@ -12,7 +10,7 @@ Some of my [3D models](https://github.com/JustinSDK/dotSCAD#examples) require co
 
 The idea of the name dotSCAD comes from the filename extension ".scad" of OpenSCAD. 
 
-## Get Started
+## Getting started
 
 OpenSCAD uses three library locations, the installation library, built-in library, and user defined libraries. Check [Setting OPENSCADPATH](https://en.wikibooks.org/wiki/OpenSCAD_User_Manual/Libraries#Setting_OPENSCADPATH) in [OpenSCAD User Manual/Libraries](https://en.wikibooks.org/wiki/OpenSCAD_User_Manual/Libraries) for details.
 
@@ -39,111 +37,110 @@ These examples incubate dotSCAD and dotSCAD refactors these examples. See [examp
 
 [![examples](examples/images/gallery.JPG)](examples#dogfooding-examples)
 
-# API Documentation
+# API Reference
 
 ## 2D Module
 
  Signature | Description
 --|--
-[**arc**(radius, angle, width = 1, width_mode = "LINE_CROSS")](https://openhome.cc/eGossip/OpenSCAD/lib3x-arc.html) | create an arc.
+[**arc**(radius, angle[, width, width_mode"])](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, p1Style, p2Style])](https://openhome.cc/eGossip/OpenSCAD/lib3x-line2d.html) | create a line from two points. 
-[**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, size, font, ...])](https://openhome.cc/eGossip/OpenSCAD/lib3x-multi_line_text.html) | create multi-line text from a list of strings.
-[**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 polyline2de 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.
+[**polyline2d**(points[, width, startingStyle, endingStyle, ...])](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.
+[**rounded_square**(size, corner_r[, center])](https://openhome.cc/eGossip/OpenSCAD/lib3x-rounded_square.html) | create a rounded square in the first quadrant.
 
 ## 3D Module
 
  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).
+[**crystal_ball**(radius[, theta, phi, thickness])](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).
-[**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, p1Style, p2Style])](https://openhome.cc/eGossip/OpenSCAD/lib3x-line3d.html) | create a 3D line from two points.
-[**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])](https://openhome.cc/eGossip/OpenSCAD/lib3x-loft.html) | develop a smooth skin between crosssections with different geometries.
-[**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]`.
+[**polyline3d**(points, diameter[, startingStyle, endingStyle])](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_cube**(size, corner_r[, center])](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.
+[**rounded_cylinder**(radius, h, round_r[, convexity, center])](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])](https://openhome.cc/eGossip/OpenSCAD/lib3x-sweep.html) | develop a smooth skin from crosssections with the same umber of sides.
-[**sweep**(sections, triangles = "SOLID")](https://openhome.cc/eGossip/OpenSCAD/lib3x-sweep.html) | develop a smooth skin from crosssections with the same umber of sides.
 
 ## Transformation
 
  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.
+[**along_with**(points, angles[, twist, scale, method])](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.
+[**bend**(size, angle[, frags])](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.
+[**shear**([sx, sy, sz])](https://openhome.cc/eGossip/OpenSCAD/lib3x-shear.html) | shear all child elements along the X-axis, Y-axis, or Z-axis.
+[**select**(i)](https://openhome.cc/eGossip/OpenSCAD/lib3x-select.html) | select module objects.
+[**polyline_join**(points)](https://openhome.cc/eGossip/OpenSCAD/lib3x-polyline_join.html) | place a join on each point. Hull each pair of joins and union all convex hulls.
 
 ## 2D Function
 
  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.
+[**bijection_offset**(pts, d[, epsilon])](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.
+[**in_shape**(shapt_pts, pt[, include_edge, epsilon])](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.
+[**trim_shape**(shape_pts, from, to[, epsilon])](https://openhome.cc/eGossip/OpenSCAD/lib3x-trim_shape.html) | trim a tangled-edge shape to a non-tangled shape.
 
 ## 2D/3D Function
 
  Signature | Description
 --|--
 [**angle_between**(vt1, vt2)](https://openhome.cc/eGossip/OpenSCAD/lib3x-angle_between.html) | return the angle between two vectors.
-[**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.
+[**bezier_smooth**(path_pts, round_d[, t_step, closed, angle_threshold])](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.
+[**cross_sections**(shape_pts, path_pts, angles[, twist, scale])](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.
+[**in_polyline**(line_pts, pt[, epsilon])](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.
+[**lines_intersection**(line1, line2[, ext, epsilon])](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.
+[**rails2sections**(rails)](https://openhome.cc/eGossip/OpenSCAD/lib3x-rails2sections.html) | create sections along rails.
 [**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.
+[**midpt_smooth**(points, n[, closed])](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.
 
 ## 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. 
+[**archimedean_spiral**(arm_distance, init_angle, point_distance, num_of_points[, rt_dir])](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.
+[**bauer_spiral**(n, radius = 1[, rt_dir])](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). 
+[**curve**(t_step, points[, tightness])](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. 
+[**fibonacci_lattice**(n, radius = 1[, dir])](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.
+[**golden_spiral**(from, to, point_distance[, rt_dir)]](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. 
+[**helix**(radius, levels, level_dist[, vt_dir, rt_dir])](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]]`. 
+[**sphere_spiral**(radius, za_step[, z_circles, begin_angle, end_angle, ...]) ](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.
+[**bend_extrude**(size, thickness, angle[, frags])](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.
+[**box_extrude**(height, shell_thickness, bottom_thickness[, offset_mode, chamfer, ...])](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.
+[**ellipse_extrude**(semi_minor_axis, height[, center, convexity, twist, slices])](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.
+[**rounded_extrude**(size, round_r[, angle, twist, convexity])](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_arc**(radius, angle, width[, width_mode])](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_liquid_splitting**(radius, centre_dist[, tangent_angle, t_step])](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_path_extend**(stroke_pts, path_pts[, scale, closed])](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_square**(size[, corner_r])](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_star**([outer_radius, inner_radius, n])](https://openhome.cc/eGossip/OpenSCAD/lib3x-shape_star.html) | create a 2D 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_superformula**(phi_step, m1, m2, n1, [n2, n3, a, b])](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_taiwan**(h[, distance])](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. 
+[**shape_trapezium**(length, h[, corner_r])](https://openhome.cc/eGossip/OpenSCAD/lib3x-shape_trapezium.html) | return shape points of an isosceles trapezoid. 
 
 ## 2D Shape Extrusion
 
@@ -153,7 +150,7 @@ These examples incubate dotSCAD and dotSCAD refactors these examples. See [examp
 [**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.
+[**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
@@ -163,13 +160,13 @@ These examples incubate dotSCAD and dotSCAD refactors these examples. See [examp
  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/has**(lt, elem[, sorted])](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/flat**(lt[, depth])](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/sort**(lt[, by, idx])](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.
@@ -181,8 +178,8 @@ These examples incubate dotSCAD and dotSCAD refactors these examples. See [examp
  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/rand**([min_value, max_value, seed_value])](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/shuffle**(lt[, seed])](https://openhome.cc/eGossip/OpenSCAD/lib3x-shuffle.html) | randomizes the order of the elements.
 
 ### util/string
 
@@ -235,7 +232,7 @@ These examples incubate dotSCAD and dotSCAD refactors these examples. See [examp
 [**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_shearing**([sx, sy, sz])](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.
 [**maxtrix/m_transpose**(m)](https://openhome.cc/eGossip/OpenSCAD/lib3x-m_transpose.html) | transpose a matrix.
 
@@ -245,10 +242,10 @@ These examples incubate dotSCAD and dotSCAD refactors these examples. See [examp
 --|--
 [**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_ring**(size, point, radius[, angle, twist])](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_sphere**(size, point, radius[, angle])](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_torus**(size, point, radius[, angle, twist])](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.
 
@@ -258,8 +255,8 @@ These examples incubate dotSCAD and dotSCAD refactors these examples. See [examp
 --|--
 [**triangle/tri_circumcenter**(shape_pts)](https://openhome.cc/eGossip/OpenSCAD/lib3x-tri_circumcenter.html) | return the circumcenter of a triangle.
 [**triangle/tri_incenter**(shape_pts)](https://openhome.cc/eGossip/OpenSCAD/lib3x-tri_incenter.html) | return the incenter of a triangle.
-[**triangle/tri_ear_clipping**(shape_pts,  ret = "TRI_INDICES", ...)](https://openhome.cc/eGossip/OpenSCAD/lib3x-tri_ear_clipping.html) | triangulation by [ear clipping](https://en.wikipedia.org/wiki/Polygon_triangulation#Ear_clipping_method).
+[**triangle/tri_ear_clipping**(shape_pts[, ret, ...])](https://openhome.cc/eGossip/OpenSCAD/lib3x-tri_ear_clipping.html) | triangulation by [ear clipping](https://en.wikipedia.org/wiki/Polygon_triangulation#Ear_clipping_method).
-[**triangle/tri_delaunay**(points, ret = "TRI_INDICES")](https://openhome.cc/eGossip/OpenSCAD/lib3x-tri_delaunay.html) | Join a set of points to make a [Delaunay triangulation](https://en.wikipedia.org/wiki/Delaunay_triangulation).
+[**triangle/tri_delaunay**(points[, ret])](https://openhome.cc/eGossip/OpenSCAD/lib3x-tri_delaunay.html) | Join a set of points to make a [Delaunay triangulation](https://en.wikipedia.org/wiki/Delaunay_triangulation).
 [**triangle/tri_delaunay_indices**(d)](https://openhome.cc/eGossip/OpenSCAD/lib3x-tri_delaunay_indices.html) | return triangle indices from a delaunay object.
 [**triangle/tri_delaunay_shapes**(d)](https://openhome.cc/eGossip/OpenSCAD/lib3x-tri_delaunay_shapes.html) | return triangle shapes from a delaunay object.
 [**triangle/tri_delaunay_voronoi**(d)](https://openhome.cc/eGossip/OpenSCAD/lib3x-tri_delaunay_voronoi.html) | return [Voronoi](https://en.wikipedia.org/wiki/Voronoi_diagram) cells from a delaunay object.
@@ -270,10 +267,10 @@ These examples incubate dotSCAD and dotSCAD refactors these examples. See [examp
 
  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/footprints2**(cmds[, start])](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/footprints3**(cmds[, start])](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/lsystem2**(axiom, rules, n, angle[, leng, heading, ...])](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/lsystem3**(axiom, rules, n, angle[, leng, heading, ...])](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`.
 
@@ -281,40 +278,40 @@ These examples incubate dotSCAD and dotSCAD refactors these examples. See [examp
 
  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_ascii**(char[, center, invert])](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_circle**(radius[, filled])](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_contour**(points[, sorted])](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_curve**(points[, tightness])](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_cylinder**(r, h[, filled, thickness])](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_from**(binaries[, center, invert])](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_gray**(levels[, center, invert, normalize])](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_polygon**(points[, filled])](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_sphere**(radius[, filled, thickness])](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.
 
 ## Part
 
  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/cone**(radius[, length, spacing, angle, void, ends])](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/connector_peg**(radius, height[, spacing, void, ends])](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.
+[**part/joint_T**(shaft_r, shaft_h, t_leng, thickness,[ spacing, center])](https://openhome.cc/eGossip/OpenSCAD/lib3x-joint_T.html) | create a joint_T for rotatable models.
 
 ## Surface
 
  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_bend**(levels, radius, thickness, depth[, angle, invert])](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_ring**(levels, radius, thickness, depth[, angle, twist, invert])](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_solidify**(surface1, surface2[, slicing])](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_sphere**(levels, radius, thickness, depth[, angle, invert)]](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_square**(levels, thickness, depth[, x_twist, y_twist, invert])](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.
+[**surface/sf_torus**(levels, radius, thickness, depth[, angle, twist, invert])](https://openhome.cc/eGossip/OpenSCAD/lib3x-sf_torus.html) | turn a photo to a torus.
 [**surface/sf_curve**(levels, curve_path, ...)](https://openhome.cc/eGossip/OpenSCAD/lib3x-sf_curve.html) | curve a photo.
 [**surface/sf_splines**(ctrl_pts, row_spline, column_spline)](https://openhome.cc/eGossip/OpenSCAD/lib3x-sf_splines.html) | generalized-spline surface.
 [**surface/sf_thicken**(points, thickness, ...)](https://openhome.cc/eGossip/OpenSCAD/lib3x-sf_thicken.html) | thicken a surface.
@@ -325,38 +322,54 @@ These examples incubate dotSCAD and dotSCAD refactors these examples. See [examp
 
  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_cell**(points, p[, dist])](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_perlin1**(x[, seed])](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_perlin1s**(xs[, seed])](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_perlin2**(x, y[, seed])](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_perlin2s**(points[, seed])](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_perlin3**(x, y, z[, seed])](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_perlin3s**(points[, seed])](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_worley2**(x, y[, seed, grid_w, dist])](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_worley2s**(points[, seed, grid_w, dist])](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_worley3**(x, y, z[, seed, grid_w, dist])](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.
+[**noise/nz_worley3s**(points[, seed, grid_w, dist])](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_cells_space**(size, grid_w[, seed])](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_from**(points[, spacing, ...])](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/vrn2_space**(size, grid_w[, seed, spacing, ...])](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_from**(points[, spacing])](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. 
+[**voronoi/vrn3_space**(size, grid_w[, seed, spacing])](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_cells**(rows, columns[, start, ...])](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_hamiltonian**(rows, columns[, start, seed])](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_cells**(rows, beginning_number[, start, seed])](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.
+
+## Polyhedra
+
+ Signature | Description
+--|--
+[**polyhedra/star**([outerRadius, innerRadius, height, n])](https://openhome.cc/eGossip/OpenSCAD/lib3x-polyhedra_star.html) | create a 3D star.
+[**polyhedra/polar_zonohedra**(n[, theta])](https://openhome.cc/eGossip/OpenSCAD/lib3x-polyhedra_polar_zonohedra.html) | create a [polar zonohedra](https://mathworld.wolfram.com/PolarZonohedron.html).
+[**polyhedra/tetrahedron**(radius[, detail])](https://openhome.cc/eGossip/OpenSCAD/lib3x-polyhedra_tetrahedron.html) | create a tetrahedron.
+[**polyhedra/hexahedron**(radius[, detail])](https://openhome.cc/eGossip/OpenSCAD/lib3x-polyhedra_hexahedron.html) | create a hexahedron.
+[**polyhedra/octahedron**(radius[, detail])](https://openhome.cc/eGossip/OpenSCAD/lib3x-polyhedra_octahedron.html) | create a octahedron.
+[**polyhedra/dodecahedron**(radius[, detail])](https://openhome.cc/eGossip/OpenSCAD/lib3x-polyhedra_dodecahedron.html) | create a dodecahedron.
+[**polyhedra/icosahedron**(radius[, detail])](https://openhome.cc/eGossip/OpenSCAD/lib3x-polyhedra_icosahedron.html) | create a icosahedron.
+[**polyhedra/superellipsoid**(radius[, detail])](https://openhome.cc/eGossip/OpenSCAD/lib3x-polyhedra_superellipsoid.html) | create a superellipsoid.
+
+----
+

RELEASE.md

@@ -1,5 +1,56 @@
 > Version numbers are based on [Semantic Versioning](https://semver.org/).
 
+# v3.2
+
+## Deprecated:
+
+ Name | Description
+--|--
+**paths2sections** | use **rails2sections** instead.
+**hull_polyline2d**, **hull_polyline3d** | use **polyline_join** instead.
+**shape_starburst**, **shape_pentagram** | use **shape_star** instead.
+**starburst** | use **polyhedra/star** instead.
+
+## New parameters:
+
+- `angle_between` adds `ccw`.
+
+## New modules/functions:
+
+### Matrix
+
+## 2D/3D Function
+
+ Signature | Description
+--|--
+[**rails2sections**(rails)](https://openhome.cc/eGossip/OpenSCAD/lib3x-rails2sections.html) | create sections along rails.
+
+## Transformation
+
+ Signature | Description
+--|--
+[**select**(i)](https://openhome.cc/eGossip/OpenSCAD/lib3x-select.html) | select module objects.
+[**polyline_join**(points)](https://openhome.cc/eGossip/OpenSCAD/lib3x-polyline_join.html) | place a join on each point. Hull each pair of joins and union all convex hulls.
+
+## 2D Shape
+
+ Signature | Description
+--|--
+[**shape_star**([outer_radius, inner_radius, n])](https://openhome.cc/eGossip/OpenSCAD/lib3x-shape_star.html) | create a 2D star.
+
+## Polyhedra
+
+ Signature | Description
+--|--
+[**polyhedra/star**([outerRadius, innerRadius, height, n])](https://openhome.cc/eGossip/OpenSCAD/lib3x-polyhedra_star.html) | create a 3D star.
+[**polyhedra/polar_zonohedra**(n[, theta])](https://openhome.cc/eGossip/OpenSCAD/lib3x-polyhedra_polar_zonohedra.html) | create a [polar zonohedra](https://mathworld.wolfram.com/PolarZonohedron.html).
+[**polyhedra/tetrahedron**(radius[, detail])](https://openhome.cc/eGossip/OpenSCAD/lib3x-polyhedra_tetrahedron.html) | create a tetrahedron.
+[**polyhedra/hexahedron**(radius[, detail])](https://openhome.cc/eGossip/OpenSCAD/lib3x-polyhedra_hexahedron.html) | create a hexahedron.
+[**polyhedra/octahedron**(radius[, detail])](https://openhome.cc/eGossip/OpenSCAD/lib3x-polyhedra_octahedron.html) | create a octahedron.
+[**polyhedra/dodecahedron**(radius[, detail])](https://openhome.cc/eGossip/OpenSCAD/lib3x-polyhedra_dodecahedron.html) | create a dodecahedron.
+[**polyhedra/icosahedron**(radius[, detail])](https://openhome.cc/eGossip/OpenSCAD/lib3x-polyhedra_icosahedron.html) | create a icosahedron.
+[**polyhedra/superellipsoid**(radius[, detail])](https://openhome.cc/eGossip/OpenSCAD/lib3x-polyhedra_superellipsoid.html) | create a superellipsoid.
+
 # v3.1
 
 ## Deprecated:

docs/lib3x-along_with.md

@@ -73,7 +73,8 @@ Puts children along the given path. If there's only one child, it will put the c
 					scale([2, 1]) 
 						circle(1.25, $fn = 24);    
 		}
-
+        
+		rotate([90, 0, 0])
 		for(a = [0:30:330]) {
 			rotate(a) 
 				translate([5, 0, 0]) 

docs/lib3x-arc_path.md

@@ -11,21 +11,21 @@ Creates an arc path. You can pass a 2 element vector to define the central angle
 
 ## Examples
   
-    use <arc_path.scad>;
+	use <arc_path.scad>;
-    use <hull_polyline2d.scad>;
+	use <polyline_join.scad>;
-    
+
-    $fn = 24;
+	$fn = 24;
-    points = arc_path(radius = 20, angle = [45, 290]);
+	points = arc_path(radius = 20, angle = [45, 290]);
-    hull_polyline2d(points, width = 2);
+	polyline_join(points) circle(1);
 
 ![arc_path](images/lib3x-arc_path-1.JPG)
 
     use <arc_path.scad>;
-    use <hull_polyline2d.scad>;
+    use <polyline_join.scad>;
     
     $fn = 24;
     points = arc_path(radius = 20, angle = 135);
-    hull_polyline2d(points, width = 2);
+    polyline_join(points) circle(1);
 
 ![arc_path](images/lib3x-arc_path-2.JPG)
 

docs/lib3x-archimedean_spiral.md

@@ -48,7 +48,7 @@ An `init_angle` less than 180 degrees is not recommended because the function us
 
 ![archimedean_spiral](images/lib3x-archimedean_spiral-2.JPG)
 
-    include <archimedean_spiral.scad>;
+    use <archimedean_spiral.scad>;
     
     t = "3.141592653589793238462643383279502884197169399375105820974944592307816406286";
 
@@ -60,8 +60,8 @@ An `init_angle` less than 180 degrees is not recommended because the function us
 	); 
 	
 	for(i = [0: len(points) - 1]) {
-	    translate(points[i][0])          
+	    translate(points[i].x)          
-	        rotate(points[i][1] + 90)  
+	        rotate(points[i].y + 90)  
 	            text(t[i], valign = "center", halign = "center");
 	}
 

docs/lib3x-bauer_spiral.md

@@ -15,7 +15,7 @@ Creates visually even spacing of n points on the surface of the sphere. Successi
 ## Examples
 
     use <bauer_spiral.scad>;
-    use <hull_polyline3d.scad>;
+    use <polyline_join.scad>;
 
     n = 200;
     radius = 20;
@@ -26,7 +26,7 @@ Creates visually even spacing of n points on the surface of the sphere. Successi
             sphere(1, $fn = 24);
     }
 
-    hull_polyline3d(pts, 1);
+    polyline_join(pts) sphere(.5);
 
 ![bauer_spiral](images/lib3x-bauer_spiral-1.JPG)
 

docs/lib3x-bezier_curve.md

@@ -1,6 +1,6 @@
 # bezier_curve
 
-Given a set of control points, the `bezier_curve` function returns points of the Bézier path. Combined with the `polyline`, `polyline3d` or `hull_polyline3d` module defined in my library, you can create a Bézier curve.
+Given a set of control points, the `bezier_curve` function returns points of the Bézier path. 
 
 ## Parameters
 
@@ -9,13 +9,13 @@ Given a set of control points, the `bezier_curve` function returns points of the
 
 ## Examples
 
-If you have four control points and combine with the `hull_polyline3d` module:
+If you have four control points:
 
-    use <hull_polyline3d.scad>;
+    use <polyline_join.scad>;
 	use <bezier_curve.scad>;
 
 	t_step = 0.05;
-	width = 2;
+	radius = 2;
 	
 	p0 = [0, 0, 0];
 	p1 = [40, 60, 35];
@@ -26,6 +26,7 @@ If you have four control points and combine with the `hull_polyline3d` module:
 	    [p0, p1, p2, p3]
 	);
 	
-	hull_polyline3d(points, width);      
+	polyline_join(points)
+	    sphere(radius);      
 
 ![bezier_curve](images/lib3x-bezier_curve-1.JPG)

docs/lib3x-bezier_smooth.md

@@ -12,7 +12,7 @@ Given a path, the `bezier_smooth` function uses bazier curves to smooth all corn
 
 ## Examples
 
-	use <hull_polyline3d.scad>;
+	use <polyline_join.scad>;
 	use <bezier_smooth.scad>;
 
 	width = 2;
@@ -25,15 +25,15 @@ Given a path, the `bezier_smooth` function uses bazier curves to smooth all corn
 		[-10, -10, 50]
 	];
 
-	hull_polyline3d(
+	polyline_join(path_pts)
-		path_pts, width
+	    sphere(width / 2);
-	);
 
 	smoothed_path_pts = bezier_smooth(path_pts, round_d);
 
-	color("red") translate([30, 0, 0]) hull_polyline3d(
+	color("red") 
-		smoothed_path_pts, width
+	translate([30, 0, 0]) 
-	);
+	polyline_join(smoothed_path_pts) 
+	    sphere(width / 2);
 
 ![bezier_smooth](images/lib3x-bezier_smooth-1.JPG)
 

docs/lib3x-bspline_curve.md

@@ -1,6 +1,6 @@
 # bspline_curve
 
-[B-spline](https://en.wikipedia.org/wiki/B-spline) interpolation using [de Boor's algorithm](https://en.wikipedia.org/wiki/De_Boor%27s_algorithm). This function returns points of the B-spline path. Combined with the `polyline`, `polyline3d` or `hull_polyline3d` module, you can create a B-spline curve.
+[B-spline](https://en.wikipedia.org/wiki/B-spline) interpolation using [de Boor's algorithm](https://en.wikipedia.org/wiki/De_Boor%27s_algorithm). This function returns points of the B-spline path. 
 
 **Since:** 2.1
 

docs/lib3x-contours.md

@@ -11,7 +11,7 @@ Computes contour polygons by applying [marching squares](https://en.wikipedia.or
 
 ## Examples
 
-    use <hull_polyline2d.scad>;
+    use <polyline_join.scad>;
 	use <surface/sf_thicken.scad>;
     use <contours.scad>;
 
@@ -36,7 +36,8 @@ Computes contour polygons by applying [marching squares](https://en.wikipedia.or
         translate([0, 0, z])
         linear_extrude(1)
         for(isoline = contours(points, z)) {
-            hull_polyline2d(isoline, width = 1);
+            polyline_join(isoline)
+			    circle(.5);
         }    
     }
 

docs/lib3x-curve.md

@@ -17,7 +17,7 @@ Draws a curved line from control points. The curve is drawn only from the 2nd co
 ## Examples
 
 	use <curve.scad>;
-	use <hull_polyline3d.scad>;
+	use <polyline_join.scad>;
 
 	pts = [
 		[28, 2, 1],
@@ -32,12 +32,14 @@ Draws a curved line from control points. The curve is drawn only from the 2nd co
 	tightness = 0;
 	points = curve(t_step, pts, tightness);
 
-	hull_polyline3d(points, 1);   
+	polyline_join(points)
+	    sphere(.5);   
 
 	#for(pt = pts) {
 		translate(pt)
 			sphere(1);
 	}
-	#hull_polyline3d(pts, .1);  
+	#polyline_join(pts)
+	    sphere(.05);  
 
 ![curve](images/lib3x-curve-3.JPG)

docs/lib3x-fibonacci_lattice.md

@@ -31,7 +31,7 @@ Creates visually even spacing of n points on the surface of the sphere. Nearest-
 ![fibonacci_lattice](images/lib3x-fibonacci_lattice-1.JPG)
 
     use <fibonacci_lattice.scad>;
-    use <hull_polyline3d.scad>;
+    use <polyline_join.scad>;
 
     n = 200;
     radius = 20;
@@ -49,7 +49,8 @@ Creates visually even spacing of n points on the surface of the sphere. Nearest-
     ];
 
     for(spiral = spirals) {
-        hull_polyline3d(spiral, 1);	
+        polyline_join(spiral)
+		    sphere(.5);	
     }
         
 ![fibonacci_lattice](images/lib3x-fibonacci_lattice-2.JPG)

docs/lib3x-footprints2.md

@@ -11,7 +11,7 @@ Drive a turtle with `["forward", length]` or `["turn", angle]`. This function is
 
 ## Examples
 	    
-	use <polyline2d.scad>;
+	use <polyline_join.scad>;
 	use <turtle/footprints2.scad>;
 	
 	function arc_cmds(radius, angle, steps) = 
@@ -48,7 +48,8 @@ Drive a turtle with `["forward", length]` or `["turn", angle]`. This function is
 		)
 	);
 
-	polyline2d(poly, width = 1);
+	polyline_join(poly)
+	    circle(.5);
 
 ![footprints2](images/lib3x-footprints2-1.JPG)
 

docs/lib3x-footprints3.md

@@ -11,7 +11,7 @@ A 3D verion of [footprint2](https://openhome.cc/eGossip/OpenSCAD/lib3x-footprint
 
 ## Examples
 	    
-	use <hull_polyline3d.scad>;
+	use <polyline_join.scad>;
 	use <turtle/footprints3.scad>;
 	
 	function xy_arc_cmds(radius, angle, steps) = 
@@ -49,7 +49,8 @@ A 3D verion of [footprint2](https://openhome.cc/eGossip/OpenSCAD/lib3x-footprint
 		)
 	);
 
-	hull_polyline3d(poly, thickness = 1);
+	polyline_join(poly)
+	    sphere(.5);
 
 ![footprints3](images/lib3x-footprints3-1.JPG)
 

docs/lib3x-hashmap_del.md

@@ -7,7 +7,7 @@ This function deletes the mapping for the specified key from a [util/map/hashmap
 ## Parameters
 
 - `map` : The original map.
-- `key` : Adds the specified element to the specified set
+- `key` : The specified key.
 - `eq` : A equality function. If it's ignored, use `==` to compare elements.
 - `hash` : A hash function. If it's ignored, convert each element to a string and hash it. 
 

docs/lib3x-hashmap_get.md

@@ -7,7 +7,7 @@ This function gets the value of the specified key from a [util/map/hashmap](http
 ## Parameters
 
 - `map` : The original map.
-- `key` : Adds the specified element to the specified set
+- `key` : The specified key.
 - `eq` : A equality function. If it's ignored, use `==` to compare elements.
 - `hash` : A hash function. If it's ignored, convert each element to a string and hash it. 
 

docs/lib3x-hashmap_put.md

@@ -7,6 +7,10 @@ Puts a key/value pair to a [util/map/hashmap](https://openhome.cc/eGossip/OpenSC
 ## Parameters
 
 - `map` : The original map.
+- `key` : The specified key.
+- `value` : The specified value.
+- `eq` : A equality function. If it's ignored, use `==` to compare elements.
+- `hash` : A hash function. If it's ignored, convert each element to a string and hash it. 
 
 ## Examples
 

docs/lib3x-helix.md

@@ -14,7 +14,7 @@ Gets all points on the path of a spiral around a cylinder. Its `$fa`, `$fs` and
 ## Examples
     
 	use <helix.scad>;
-	use <hull_polyline3d.scad>;
+	use <polyline_join.scad>;
 	
 	$fn = 12;
 	
@@ -30,12 +30,13 @@ Gets all points on the path of a spiral around a cylinder. Its `$fa`, `$fs` and
 	    translate(p) sphere(5);
 	}
 	
-	hull_polyline3d(points, 2);
+	polyline_join(points)
+	    sphere(1);
 
 ![helix](images/lib3x-helix-1.JPG)
 
 	use <helix.scad>;
-	use <hull_polyline3d.scad>;
+	use <polyline_join.scad>;
 
 	$fn = 12;
 
@@ -47,7 +48,8 @@ Gets all points on the path of a spiral around a cylinder. Its `$fa`, `$fs` and
 		rt_dir = "CLK"
 	);
 
-	hull_polyline3d(points, 2);
+	polyline_join(points)
+	    sphere(1);
 
 	%cylinder(h = 100, r1 = 40, r2 = 20);
 

docs/lib3x-hull_polyline2d.md

@@ -1,22 +0,0 @@
-# hull_polyline2d
-
-Creates a 2D polyline from a list of `[x, y]` coordinates. As the name says, it uses the built-in hull operation for each pair of points (created by the `circle` module). It's slow. However, it can be used to create metallic effects for a small `$fn`, large `$fa` or `$fs`.
-
-## Parameters
-
-- `points` : The list of `[x, y]` points of the polyline. The points are indexed from 0 to n-1.
-- `width` : The line width. Default to 1.
-- `$fa`, `$fs`, `$fn` : Check [the circle module](https://en.wikibooks.org/wiki/OpenSCAD_User_Manual/Using_the_2D_Subsystem#circle) for more details.
-
-## Examples
-
-	use <hull_polyline2d.scad>;
-	
-	$fn = 4;
-	
-	hull_polyline2d(
-	    points = [[1, 2], [-5, -4], [-5, 3], [5, 5]], 
-	    width = 1
-	);
-
-![hull_polyline3d](images/lib3x-hull_polyline2d-1.JPG)

docs/lib3x-hull_polyline3d.md

@@ -1,45 +0,0 @@
-# hull_polyline3d
-
-Creates a 3D polyline from a list of `[x, y, z]` coordinates. As the name says, it uses the built-in hull operation for each pair of points (created by the `sphere` module). It's slow. However, it can be used to create metallic effects for a small `$fn`, large `$fa` or `$fs`.
-
-## Parameters
-
-- `points` : The list of `[x, y, z]` points of the polyline. The points are indexed from 0 to n-1.
-- `diameter` : The line diameter. Default to 1.
-- `$fa`, `$fs`, `$fn` : Check [the sphere module](https://en.wikibooks.org/wiki/OpenSCAD_User_Manual/Primitive_Solids#sphere) for more details.
-
-## Examples
-
-    use <hull_polyline3d.scad>;
-
-	hull_polyline3d(
-	    points = [
-	        [1, 2, 3], 
-	        [4, -5, -6], 
-	        [-1, -3, -5], 
-	        [0, 0, 0]
-	    ], 
-	    diameter = 1, 
-	    $fn = 3
-	);
-
-![polyline3d](images/lib3x-hull_polyline3d-1.JPG)
-
-    use <hull_polyline3d.scad>;
-    
-	r = 50;
-	points = [
-	    for(a = [0:180]) 
-	        [
-	           r * cos(-90 + a) * cos(a), 
-	           r * cos(-90 + a) * sin(a), 
-	           r * sin(-90 + a)
-	        ]
-	];
-	
-	for(i = [0:7]) {
-	    rotate(45 * i) 
-	        hull_polyline3d(points, 2, $fn = 3);
-	}
-
-![polyline3d](images/lib3x-hull_polyline3d-2.JPG)

docs/lib3x-loft.md

@@ -11,7 +11,7 @@ When having uniform cross sections, you can use [sweep](https://openhome.cc/eGos
 
 ## Examples
 
-	use <shape_starburst.scad>;
+	use <shape_star.scad>;
 	use <shape_circle.scad>;
 	use <ptf/ptf_rotate.scad>;
 	use <loft.scad>;
@@ -19,7 +19,7 @@ When having uniform cross sections, you can use [sweep](https://openhome.cc/eGos
 	sects = [
 		for(i = 10; i >= 4; i = i - 1)
 		[
-			for(p = shape_starburst(15, 12, i % 2 == 1 ? i : i - 1)) ptf_rotate([p[0], p[1], 5 * (i - 4)], i * 10)
+			for(p = shape_star(15, 12, i % 2 == 1 ? i : i - 1)) ptf_rotate([p.x, p.y, 5 * (i - 4)], i * 10)
 		]
 	];
 	loft(sects, slices = 3);
@@ -28,16 +28,16 @@ When having uniform cross sections, you can use [sweep](https://openhome.cc/eGos
 	difference() {
 		loft(
 			[
-				[for(p = shape_circle(10, $fn = 3)) [p[0], p[1], 15]],
+				[for(p = shape_circle(10, $fn = 3)) [p.x, p.y, 15]],
-				[for(p = shape_circle(15, $fn = 24)) [p[0], p[1], 0]]        
+				[for(p = shape_circle(15, $fn = 24)) [p.x, p.y, 0]]        
 			],
 			slices = 4
 		);
 
 		loft(
 			[
-				[for(p = shape_circle(8, $fn = 3)) [p[0], p[1], 15.1]],
+				[for(p = shape_circle(8, $fn = 3)) [p.x, p.y, 15.1]],
-				[for(p = shape_circle(13, $fn = 24)) [p[0], p[1], -0.1]]        
+				[for(p = shape_circle(13, $fn = 24)) [p.x, p.y, -0.1]]        
 			],
 			slices = 4
 		);    

docs/lib3x-lsystem3.md

@@ -33,14 +33,11 @@
 [lsystem3-collections.scad](https://github.com/JustinSDK/dotSCAD/blob/master/examples/turtle/lsystem3_collection.scad) collects several L-system grammars. Here's one of them.
 
 	use <turtle/lsystem3.scad>;
-	use <hull_polyline3d.scad>;
+	use <polyline_join.scad>;
 
 	for(line = hilbert_curve()) {
-		hull_polyline3d(
+		polyline_join([line[0], line[1]])
-			[line[0], line[1]], 
+		    sphere(.25, $fn = 4);
-			thickness = 0.5, 
-			$fn = 4
-		);
 	}  
 
 	function hilbert_curve(n = 3, angle = 90, leng = 1, heading = 0, start = [0, 0, 0]) = 
@@ -60,14 +57,11 @@
     // a stochastic L-system
 
 	use <turtle/lsystem3.scad>;
-	use <hull_polyline3d.scad>;
+	use <polyline_join.scad>;
 
 	for(line = vine()) {
-		hull_polyline3d(
+		polyline_join([line[0], line[1]])
-			[line[0], line[1]], 
+		    sphere(.25, $fn = 4);
-			thickness = 0.5, 
-			$fn = 4
-		);
 	}  
 
 	function vine(n = 3, angle = 18, leng = 1, heading = 0, start = [0, 0, 0]) = 

docs/lib3x-midpt_smooth.md

@@ -12,14 +12,14 @@ Given a 2D path, this function constructs a mid-point smoothed version by joinin
 
 ## Examples
 
-    use <hull_polyline2d.scad>;
+    use <polyline_join.scad>;
     use <shape_taiwan.scad>;
     use <midpt_smooth.scad>;
 
     taiwan = shape_taiwan(50);  
     smoothed = midpt_smooth(taiwan, 20, true);
 
-    translate([0, 0, 0]) hull_polyline2d(taiwan, .25); 
+    translate([0, 0, 0]) polyline_join(taiwan) circle(.125); 
-    #translate([10, 0, 0]) hull_polyline2d(smoothed, .25);
+    #translate([10, 0, 0]) polyline_join(smoothed) circle(.125);
 
 ![midpt_smooth](images/lib3x-midpt_smooth-1.JPG)

docs/lib3x-mz_hamiltonian.md

@@ -14,13 +14,14 @@ Creates a hamiltonian path from a maze. The path is the result of maze traversal
 ## Examples
     
     use <maze/mz_hamiltonian.scad>;
-    use <hull_polyline2d.scad>;
+    use <polyline_join.scad>;
 
     rows = 5;
     columns = 10;
 
     path = mz_hamiltonian(rows, columns, [0, 0]);
-    hull_polyline2d(path, .5);
+    polyline_join(path)
+	    circle(.25);
 
 ![mz_hamiltonian](images/lib3x-mz_hamiltonian-1.JPG)
 

docs/lib3x-mz_hex_walls.md

@@ -17,7 +17,7 @@ It's a helper for creating wall data from maze cells. You can transform wall poi
     
 	use <maze/mz_square_cells.scad>;
 	use <maze/mz_hex_walls.scad>;
-	use <hull_polyline2d.scad>;
+	use <polyline_join.scad>;
 
 	rows = 10;
 	columns = 12;
@@ -28,7 +28,8 @@ It's a helper for creating wall data from maze cells. You can transform wall poi
 	walls = mz_hex_walls(cells, rows, columns, cell_width);
 
 	for(wall = walls) {
-		hull_polyline2d(wall, wall_thickness, $fn = 24);
+		polyline_join(wall) 
+		    circle(wall_thickness, $fn = 24);
 	}
 	
 ![mz_hex_walls](images/lib3x-mz_hex_walls-1.JPG)

docs/lib3x-mz_theta_cells.md

@@ -25,7 +25,7 @@ The value of `type` is the wall type of the cell. It can be `0`, `1`, `2` or `3`
 ## Examples
     
 	use <maze/mz_theta_cells.scad>;
-	use <hull_polyline2d.scad>;
+	use <polyline_join.scad>;
 
 	rows = 8;
 	beginning_number = 8;
@@ -58,11 +58,13 @@ The value of `type` is the wall type of the cell. It can be `0`, `1`, `2` or `3`
 			outerVt2 = vt_from_angle(theta2, outerR);
 			
 			if(type == INWARD_WALL || type == INWARD_CCW_WALL) {
-				hull_polyline2d([innerVt1, innerVt2], width = wall_thickness);
+				polyline_join([innerVt1, innerVt2])
+				    circle(wall_thickness / 2);
 			}
 
 			if(type == CCW_WALL || type == INWARD_CCW_WALL) {
-				hull_polyline2d([innerVt2, outerVt2], width = wall_thickness);
+				polyline_join([innerVt1, innerVt2])
+				    circle(wall_thickness / 2);
 			}
 		} 
 	}
@@ -73,7 +75,8 @@ The value of `type` is the wall type of the cell. It can be `0`, `1`, `2` or `3`
 	for(theta = [0:thetaStep:360 - thetaStep]) {
 		vt1 = vt_from_angle(theta, r);
 		vt2 = vt_from_angle(theta + thetaStep, r);
-		hull_polyline2d([vt1, vt2], width = wall_thickness);
+		polyline_join([vt1, vt2])
+			circle(wall_thickness / 2);
 	} 
 
 ![mz_theta_cells](images/lib3x-mz_theta_cells-3.JPG)

docs/lib3x-mz_theta_get.md

@@ -13,7 +13,7 @@ It's a helper for getting data from a theta-maze cell.
     
 	use <maze/mz_theta_cells.scad>;
 	use <maze/mz_theta_get.scad>;
-	use <hull_polyline2d.scad>;
+	use <polyline_join.scad>;
 
 	rows = 8;
 	beginning_number = 8;
@@ -39,11 +39,13 @@ It's a helper for getting data from a theta-maze cell.
 			outerVt2 = vt_from_angle(theta2, outerR);
 			
 			if(type == "INWARD_WALL" || type == "INWARD_CCW_WALL") {
-				hull_polyline2d([innerVt1, innerVt2], width = wall_thickness);
+				polyline_join([innerVt1, innerVt2])
+				    circle(wall_thickness / 2);
 			}
 
 			if(type == "CCW_WALL" || type == "INWARD_CCW_WALL") {
-				hull_polyline2d([innerVt2, outerVt2], width = wall_thickness);
+				polyline_join([innerVt1, innerVt2])
+				    circle(wall_thickness / 2);
 			}
 		} 
 	}
@@ -53,7 +55,8 @@ It's a helper for getting data from a theta-maze cell.
 	for(theta = [0:thetaStep:360 - thetaStep]) {
 		vt1 = vt_from_angle(theta, r);
 		vt2 = vt_from_angle(theta + thetaStep, r);
-		hull_polyline2d([vt1, vt2], width = wall_thickness);
+		polyline_join([vt1, vt2])
+			circle(wall_thickness / 2);
 	} 
 
 ![mz_theta_get](images/lib3x-mz_theta_get-1.JPG)

docs/lib3x-nz_cell.md

@@ -26,8 +26,8 @@ It's an implementation of [Worley noise](https://en.wikipedia.org/wiki/Worley_no
 
     feature_points = [for(pt_angle = pts_angles) pt_angle[0] + half_size];
     noised = [
-        for(y = [0:size[1] - 1]) 
+        for(y = [0:size.y - 1]) 
-            for(x = [0:size[0] - 1]) 
+            for(x = [0:size.x - 1]) 
                 [x, y, nz_cell(feature_points, [x, y])]
     ];
 

docs/lib3x-nz_perlin1.md

@@ -11,13 +11,12 @@ Returns the 1D [Perlin noise](https://en.wikipedia.org/wiki/Perlin_noise) value
 
 ## Examples
 
-    use <hull_polyline2d.scad>;
+    use <polyline_join.scad>;
     use <util/rand.scad>;
     use <noise/nz_perlin1.scad>;
 
     seed = rand();
-    hull_polyline2d(
+    polyline_join([for(x = [0:.1:10]) [x, nz_perlin1(x, seed)]])
-        [for(x = [0:.1:10]) [x, nz_perlin1(x, seed)]], width = .1
+	    circle(.05);
-    );
 
 ![nz_perlin1](images/lib3x-nz_perlin1-1.JPG)

docs/lib3x-nz_perlin1s.md

@@ -11,13 +11,14 @@ Returns 1D [Perlin noise](https://en.wikipedia.org/wiki/Perlin_noise) values at
 
 ## Examples
 
-    use <hull_polyline2d.scad>;
+    use <polyline_join.scad>;
     use <noise/nz_perlin1s.scad>;
 
     xs = [for(x = [0:.1:10]) x];
     ys = nz_perlin1s(xs);
     points = [for(i = [0:len(xs) - 1]) [xs[i], ys[i]]];
 
-    hull_polyline2d(points, width = .1);
+    polyline_join(points)
+	    circle(.05);
 
 ![nz_perlin1s](images/lib3x-nz_perlin1s-1.JPG)

docs/lib3x-nz_perlin2.md

@@ -13,7 +13,7 @@ Returns the 2D [Perlin noise](https://en.wikipedia.org/wiki/Perlin_noise) value
 ## Examples
 
     use <util/rand.scad>;
-    use <hull_polyline2d.scad>;
+    use <polyline_join.scad>;
     use <surface/sf_thicken.scad>;
     use <noise/nz_perlin2.scad>;
     use <contours.scad>;
@@ -31,7 +31,8 @@ Returns the 2D [Perlin noise](https://en.wikipedia.org/wiki/Perlin_noise) value
 
     translate([11, 0])
     for(isoline = contours(points, 0)) {
-        hull_polyline2d(isoline, width = .1);
+        polyline_join(isoline)
+		    circle(.05);
     }   
 
 ![nz_perlin2](images/lib3x-nz_perlin2-1.JPG)

docs/lib3x-nz_worley2.md

@@ -27,12 +27,12 @@ It divides the space into grids. The nucleus of each cell is randomly placed in
     seed = 51;
 
     points = [
-        for(y = [0:size[1] - 1]) 
+        for(y = [0:size.y - 1]) 
-            for(x = [0:size[0] - 1]) 
+            for(x = [0:size.x - 1]) 
                 [x, y]
     ];
 
-    cells = [for(p = points) nz_worley2(p[0], p[1], seed, grid_w, dist)];
+    cells = [for(p = points) nz_worley2(p.x, p.y, seed, grid_w, dist)];
 
     max_dist = max([for(c = cells) c[2]]);
     for(i = [0:len(cells) - 1]) {

docs/lib3x-nz_worley2s.md

@@ -25,8 +25,8 @@ It divides the space into grids. The nucleus of each cell is randomly placed in
     seed = 51;
 
     points = [
-        for(y = [0:size[1] - 1]) 
+        for(y = [0:size.y - 1]) 
-            for(x = [0:size[0] - 1]) 
+            for(x = [0:size.x - 1]) 
                 [x, y]
     ];
 

docs/lib3x-nz_worley3.md

@@ -26,7 +26,7 @@ It divides the space into grids. The nucleus of each cell is randomly placed in
 
     points = vx_sphere(20);
 
-    cells = [for(p = points) nz_worley3(p[0], p[1], p[2], seed, grid_w, dist)];
+    cells = [for(p = points) nz_worley3(p.x, p.y, p.z, seed, grid_w, dist)];
 
     max_dist = max([for(c = cells) c[3]]);
     for(i = [0:len(cells) - 1]) {

docs/lib3x-nz_worley3s.md

@@ -18,12 +18,12 @@ It divides the space into grids. The nucleus of each cell is randomly placed in
     use <voxel/vx_sphere.scad>;
     use <noise/nz_worley3s.scad>;
 
-    tile_w = 10;
+    grid_w = 10;
     dist = "euclidean"; // [euclidean, manhattan, chebyshev, border] 
     seed = 51;
 
     points = vx_sphere(20);
-    cells = nz_worley3s(points, seed, tile_w, dist);
+    cells = nz_worley3s(points, seed, grid_w, dist);
 
     for(i = [0:len(cells) - 1]) {
         c = (norm([cells[i][0], cells[i][1], cells[i][2]]) % 20) / 20;

docs/lib3x-path_scaling_sections.md

@@ -15,7 +15,7 @@ You can use any point as the first point of the edge path. Just remember that yo
 
 ## Examples
 
-	use <hull_polyline3d.scad>;
+	use <polyline_join.scad>;
 	use <shape_taiwan.scad>;
 	use <path_scaling_sections.scad>;
 	use <sweep.scad>;
@@ -33,12 +33,13 @@ You can use any point as the first point of the edge path. Just remember that yo
 		fst_pt + [0, 0, 60]
 	];
 
-	#hull_polyline3d(edge_path);
+	#polyline_join(edge_path) 
+	    sphere(.5);
 	sweep(path_scaling_sections(taiwan, edge_path));
 
 ![path_scaling_sections](images/lib3x-path_scaling_sections-1.JPG)
 
-	use <hull_polyline3d.scad>;
+	use <polyline_join.scad>;
 	use <shape_taiwan.scad>;
 	use <path_scaling_sections.scad>;
 	use <sweep.scad>;
@@ -58,7 +59,8 @@ You can use any point as the first point of the edge path. Just remember that yo
 		fst_pt + [0, 0, 60]
 	]);
 
-	#hull_polyline3d(edge_path);
+	#polyline_join(edge_path) 
+	    sphere(.5);
 	sweep(path_scaling_sections(taiwan, edge_path));
 
 ![path_scaling_sections](images/lib3x-path_scaling_sections-2.JPG)
@@ -67,7 +69,7 @@ You can use any point as the first point of the edge path. Just remember that yo
 	use <path_scaling_sections.scad>;
 	use <sweep.scad>;
 	use <bezier_curve.scad>;
-	use <rotate_p.scad>;
+	use <ptf/ptf_rotate.scad>;
 
 	taiwan = shape_taiwan(100);
 	fst_pt = [13, 0, 0];
@@ -91,7 +93,7 @@ You can use any point as the first point of the edge path. Just remember that yo
 		for(i = [0:leng - 1]) 
 		[
 			for(p = sections[i]) 
-				rotate_p(p, twist_step * i)        
+				ptf_rotate(p, twist_step * i)        
 		]
 	];
 
@@ -99,11 +101,11 @@ You can use any point as the first point of the edge path. Just remember that yo
 
 ![path_scaling_sections](images/lib3x-path_scaling_sections-3.JPG)	
 
-	use <hull_polyline3d.scad>;
+	use <polyline_join.scad>;
 	use <shape_taiwan.scad>;
 	use <path_scaling_sections.scad>;
 	use <sweep.scad>;
-    use <rotate_p.scad>;
+    use <ptf/ptf_rotate.scad>;
 
 	taiwan = shape_taiwan(100);
 
@@ -115,15 +117,16 @@ You can use any point as the first point of the edge path. Just remember that yo
     a = atan2(fst_pt[1], fst_pt[0]);
 	edge_path = [
 		fst_pt,
-		fst_pt + rotate_p([0, 0, 10], a),
+		fst_pt + ptf_rotate([0, 0, 10], a),
-		fst_pt + rotate_p([10, 0, 20], a),
+		fst_pt + ptf_rotate([10, 0, 20], a),
-		fst_pt + rotate_p([8, 0, 30], a),
+		fst_pt + ptf_rotate([8, 0, 30], a),
-		fst_pt + rotate_p([10, 0, 40], a),
+		fst_pt + ptf_rotate([10, 0, 40], a),
-		fst_pt + rotate_p([0, 0, 50], a),
+		fst_pt + ptf_rotate([0, 0, 50], a),
-		fst_pt + rotate_p([0, 0, 60], a)
+		fst_pt + ptf_rotate([0, 0, 60], a)
 	];
 
-	#hull_polyline3d(edge_path);
+	#polyline_join(edge_path) 
+	    sphere(.5);
 	sweep(path_scaling_sections(taiwan, edge_path));
 
 ![path_scaling_sections](images/lib3x-path_scaling_sections-4.JPG)

docs/lib3x-paths2sections.md

@@ -11,7 +11,7 @@ You paths should be indexed count-clockwisely.
 ## Examples
 
 	use <paths2sections.scad>;
-	use <hull_polyline3d.scad>;
+	use <polyline_join.scad>;
 	use <sweep.scad>;
 	
 	paths = [
@@ -26,14 +26,15 @@ You paths should be indexed count-clockwisely.
 	sweep(sections);
 	
 	#for(path = paths) {
-	    hull_polyline3d(path, 0.5);
+	    polyline_join(path)
+		    sphere(.25);
 	}
 
 ![paths2sections](images/lib3x-paths2sections-1.JPG)
 
 	use <bezier_curve.scad>;
 	use <paths2sections.scad>;
-	use <hull_polyline3d.scad>;
+	use <polyline_join.scad>;
 	use <sweep.scad>;
 	
 	t_step = 0.05;
@@ -59,7 +60,8 @@ You paths should be indexed count-clockwisely.
 	sweep(sections);
 	
 	#for(path = paths) {
-	    hull_polyline3d(path, 0.5);
+	    polyline_join(path)
+		    sphere(.25);
 	}
 
 ![paths2sections](images/lib3x-paths2sections-2.JPG)

docs/lib3x-polyhedra_dodecahedron.md

@@ -0,0 +1,22 @@
+# dodecahedron
+
+Creates a dodecahedron.
+
+**Since:** 3.2
+
+## Parameters
+
+- `radius` : Radius of the dodecahedron.
+- `detail` : Default to 0. Setting this to a value greater than 0 adds vertices making it no longer a dodecahedron.
+
+## Examples
+
+	use <polyhedra/dodecahedron.scad>;
+
+	for(i = [0:5]) {
+		translate([i * 2, 0])
+			dodecahedron(radius = 1, detail = i);
+	}
+
+![dodecahedron](images/lib3x-polyhedra_dodecahedron-1.JPG)
+

docs/lib3x-polyhedra_hexahedron.md

@@ -0,0 +1,22 @@
+# hexahedron
+
+Creates a hexahedron.
+
+**Since:** 3.2
+
+## Parameters
+
+- `radius` : Radius of the hexahedron.
+- `detail` : Default to 0. Setting this to a value greater than 0 adds vertices making it no longer a hexahedron.
+
+## Examples
+
+	use <polyhedra/hexahedron.scad>;
+
+	for(i = [0:5]) {
+		translate([i * 2, 0])
+			hexahedron(radius = 1, detail = i);
+	}
+
+![hexahedron](images/lib3x-polyhedra_hexahedron-1.JPG)
+

docs/lib3x-polyhedra_icosahedron.md

@@ -0,0 +1,22 @@
+# icosahedron
+
+Creates a icosahedron.
+
+**Since:** 3.2
+
+## Parameters
+
+- `radius` : Radius of the icosahedron.
+- `detail` : Default to 0. Setting this to a value greater than 0 adds vertices making it no longer a icosahedron.
+
+## Examples
+
+	use <polyhedra/icosahedron.scad>;
+
+	for(i = [0:5]) {
+		translate([i * 2, 0])
+			icosahedron(radius = 1, detail = i);
+	}
+
+![icosahedron](images/lib3x-polyhedra_icosahedron-1.JPG)
+

docs/lib3x-polyhedra_octahedron.md

@@ -0,0 +1,22 @@
+# octahedron
+
+Creates a octahedron.
+
+**Since:** 3.2
+
+## Parameters
+
+- `radius` : Radius of the octahedron.
+- `detail` : Default to 0. Setting this to a value greater than 0 adds vertices making it no longer a octahedron.
+
+## Examples
+
+	use <polyhedra/octahedron.scad>;
+
+	for(i = [0:5]) {
+		translate([i * 2, 0])
+			octahedron(radius = 1, detail = i);
+	}
+
+![octahedron](images/lib3x-polyhedra_octahedron-1.JPG)
+

docs/lib3x-polyhedra_polar_zonohedra.md

@@ -0,0 +1,22 @@
+# polar_zonohedra
+
+Creates a [polar zonohedra](https://mathworld.wolfram.com/PolarZonohedron.html).
+
+**Since:** 3.2
+
+## Parameters
+
+- `n` : n equal rhombs surrounding one vertex. (rotational symmetry)
+- `theta` : the pitch angle of the edges. Default to 35.5.
+
+## Examples
+
+	use <polyhedra/polar_zonohedra.scad>;
+
+	for(n = [3:8]) {
+		translate([0.5 * n * (n - 3), 0, 0])
+			polar_zonohedra(n);
+	}
+
+![polar_zonohedra](images/lib3x-polyhedra_polar_zonohedra-1.JPG)
+

docs/lib3x-polyhedra_star.md

@@ -0,0 +1,24 @@
+# star
+
+Create a star. Default to a pentagram.
+
+**Since:** 3.2
+
+## Parameters
+
+- `outer_radius`: The outer radius of the star. Default to 1.
+- `inner_radius`: The inner radius of the star. Default to 0.381966.
+- `height`: The star height. Default to 0.5.
+- `n`: The burst number. Default to 5.
+
+## Examples
+
+	use <polyhedra/star.scad>;
+
+	for(i = [3:6]) {
+		translate([(i - 3) * 2, 0])
+			star(n = i);
+	}
+
+![star](images/lib3x-polyhedra_star-1.JPG)
+

docs/lib3x-polyhedra_superellipsoid.md

@@ -0,0 +1,27 @@
+# superellipsoid
+
+Creates a [superellipsoid](https://en.wikipedia.org/wiki/Superellipsoid).
+
+**Since:** 3.2
+
+## Parameters
+
+- `e` :  The east-west parameter.
+- `n` : The north-south parameter.
+
+## Examples
+
+	use <polyhedra/superellipsoid.scad>;
+
+	$fn = 24;
+
+	step = 0.5;
+
+	for(e = [0:step:4]) {
+		for(n = [0:step:4])
+			translate([e / step, n / step] * 3)
+			superellipsoid(e, n);
+	}
+
+![superellipsoid](images/lib3x-polyhedra_superellipsoid-1.JPG)
+

docs/lib3x-polyhedra_tetrahedron.md

@@ -0,0 +1,22 @@
+# tetrahedron
+
+Creates a tetrahedron.
+
+**Since:** 3.2
+
+## Parameters
+
+- `radius` : Radius of the tetrahedron.
+- `detail` : Default to 0. Setting this to a value greater than 0 adds vertices making it no longer a tetrahedron.
+
+## Examples
+
+	use <polyhedra/tetrahedron.scad>;
+
+	for(i = [0:5]) {
+		translate([i * 2, 0])
+			tetrahedron(radius = 1, detail = i);
+	}
+
+![tetrahedron](images/lib3x-polyhedra_tetrahedron-1.JPG)
+

docs/lib3x-polyline_join.md

@@ -0,0 +1,42 @@
+# polyline_join
+
+Place a join on each point. Hull each pair of joins and union all convex hulls.
+
+**Since:** 3.2
+
+## Parameters
+
+- `points` : a list of points.
+
+## Examples
+  
+    use <polyline_join.scad>;
+    
+    polyline_join([[0, 0], [10, 0], [10, 10], [0, 10]]) 
+        square(1);
+        
+    polyline_join([[15, 0], [25, 0], [25, 10], [15, 10]]) {
+        square(1);
+        circle(1);
+        square(1);
+        circle(2);
+    }
+
+![polyline_join](images/lib3x-polyline_join-1.JPG)
+
+    use <polyline_join.scad>;
+        
+    polyline_join([[0, 0, 0], [10, 0, 0], [10, 0, 10], [10, 10, 10]]) 
+        cube(1);
+        
+    polyline_join([[15, 0, 0], [25, 0, 0], [25, 0, 10], [25, 10, 10]]) {
+        cube(1);
+        sphere(1);
+        cube(1);
+        sphere(2);
+    }
+
+![polyline_join](images/lib3x-polyline_join-2.JPG)
+
+
+

docs/lib3x-polysections.md

@@ -1,141 +0,0 @@
-# polysections
-
-Crosscutting a tube-like shape at different points gets several cross-sections. This module can operate reversely. It uses cross-sections to construct a tube-like shape. For example, imagine that you have the following cross-sections:
-
-![polysections](images/lib3x-polysections-1.JPG)
-
-This module can use them to construct the following model:
-
-![polysections](images/lib3x-polysections-2.JPG)
-
-Looks like extruding along the path? Yes, it can perform the task; however, it's more flexible. 
-
-You can also view it as a better polyline3d module if you want. If you have only the points of a path, using `polyline3d` or `hull_polyline3d` is a simple solution. If you know the cross sections along a path, you can use `polysections` to do more. 
-
-When using this module, you should use points to represent each cross section. The points of your cross section should have count-clockwise indexes. For example:
-
-![polysections](images/lib3x-polysections-10.JPG)
-
-If your cross section is hollow, set the `triangles` parameter to `"HOLLOW"` and index the points as the following:
-
-![polysections](images/lib3x-polysections-5.JPG)
-
-You can cut triangles by yourself. For example, the above shape can be cut into triangles such as:
-
-![polysections](images/lib3x-polysections-6.JPG)
-
-The indexes of the above triangles is:
-
-    [
-		[0, 3, 1],
-		[1, 3, 4],
-		[1, 4, 2],
-		[2, 4, 5],
-		[2, 5, 0],
-		[0, 5, 3]
-	]
-
-When defining triangles, you can use clockwise or counter-clockwise indexes. 
-
-## Parameters
-
-- `sections` : A list of cross-sections. Each cross-section is represented by a list of points. See the example below.
-- `triangles` : `"SOLID"` (default), `"HOLLOW"`,  or user-defined indexes. See example below.
-
-## Examples
-
-	use <rotate_p.scad>;
-	use <polysections.scad>;
-
-	section1 = [
-		[20, 0, 0],
-		[18, 9, 0],
-		[15, 10, 0],
-		[10, 0, 0]
-	];
-
-	// spin section1
-	sections = [
-		for(i = [0:55]) 
-			[
-				for(p = section1)
-					let(pt = rotate_p(p, [90, 0, 10 * i]))
-					[pt[0], pt[1] , pt[2] + i]
-			]
-	];
-
-	polysections(sections);
-
-![polysections](images/lib3x-polysections-7.JPG)
-
-	use <rotate_p.scad>;
-	use <polysections.scad>;
-	
-	section1 = [
-	    // outer
-		[20, 0, 0],
-		[18, 9, 0],
-		[15, 10, 0],
-		[10, 0, 0],
-	    // inner
-        [18, 2, 0],
-        [17, 7, 0],
-        [15, 7, 0],
-	    [12, 2, 0]
-	];
-	
-	// spin section1
-	sections = [
-	    for(i = [0:55]) 
-	        [
-	            for(p = section1)
-	                let(pt = rotate_p(p, [90, 0, 10 * i]))
-	                [pt[0], pt[1] , pt[2] + i]
-	        ]
-	];
-	    
-	polysections(sections, "HOLLOW");
-
-![polysections](images/lib3x-polysections-8.JPG)
-
-	use <rotate_p.scad>;
-	use <polysections.scad>;
-	
-	section1 = [
-	    // outer
-        [30, 0, 0],
-	    [15, 10, 0],
-	    [10, 0, 0],
-	    // inner
-	    [26, 1, 0],
-	    [15, 8, 0],
-	    [12, 1, 0],        
-	];
-	
-	// spin section1
-	sections = [
-	    for(i = [0:55]) 
-	        [
-	            for(p = section1)
-	                let(pt = rotate_p(p, [90, 0, 10 * i]))
-	                [pt[0], pt[1] , pt[2] + i]
-	        ]
-	];
-	    
-	polysections(
-	   sections = sections, 
-	   triangles = [
-            [0, 3, 1],
-            [1, 3, 4],
-            [1, 4, 2],
-            [2, 4, 5],
-            [2, 5, 0],
-            [0, 5, 3]
-        ]
-	);
-
-![polysections](images/lib3x-polysections-9.JPG)
-
-
-
-

docs/lib3x-ptf_circle.md

@@ -13,29 +13,31 @@ Transform a point inside a rectangle to a point inside a circle. You can use it
 
 ## Examples
 
-    use <hull_polyline3d.scad>;
+    use <polyline_join.scad>;
     use <ptf/ptf_circle.scad>;
 
     size = [10, 10];
 
     rows = [
-        for(y = [0:size[1]])
+        for(y = [0:size.y])
-            [for(x = [0:size[0]]) [x, y]]
+            [for(x = [0:size.x]) [x, y]]
     ];
 
     columns = [
-        for(x = [0:size[0]])
+        for(x = [0:size.x])
-            [for(y = [0:size[1]]) [x, y]]
+            [for(y = [0:size.y]) [x, y]]
     ];
 
     for(line = rows) {
         transformed = [for(p = line) ptf_circle(size, p)];
-        hull_polyline3d(transformed, thickness = .1);
+        polyline_join(transformed)
+		    sphere(.05);
     }
 
     for(line = columns) {
         transformed = [for(p = line) ptf_circle(size, p)];
-        hull_polyline3d(transformed, thickness = .1);
+        polyline_join(transformed)
+		    sphere(.05);
     }
 
 ![ptf_circle](images/lib3x-ptf_circle-2.JPG)

docs/lib3x-ptf_ring.md

@@ -16,30 +16,32 @@ Transforms a point inside a rectangle to a point of a ring. It can create things
 
 ## Examples
 
-    use <hull_polyline3d.scad>;
+    use <polyline_join.scad>;
     use <ptf/ptf_ring.scad>;
 
     size = [20, 10];
     radius = 5;
 
     rows = [
-        for(y = [0:size[1]])
+        for(y = [0:size.y])
-            [for(x = [0:size[0]]) [x, y]]
+            [for(x = [0:size.x]) [x, y]]
     ];
 
     columns = [
-        for(x = [0:size[0]])
+        for(x = [0:size.x])
-            [for(y = [0:size[1]]) [x, y]]
+            [for(y = [0:size.y]) [x, y]]
     ];
 
     for(line = rows) {
         transformed = [for(p = line) ptf_ring(size, p, radius, 360, 180)];
-        hull_polyline3d(transformed, thickness = .5);
+		polyline_join(transformed)
+		    sphere(.25);
     }
 
     for(line = columns) {
         transformed = [for(p = line) ptf_ring(size, p, radius, 360, 180)];
-        hull_polyline3d(transformed, thickness = .5);
+		polyline_join(transformed)
+		    sphere(.25);
     }
 
 ![ptf_ring](images/lib3x-ptf_ring-2.JPG)

docs/lib3x-ptf_rotate.md

@@ -26,7 +26,7 @@ Rotates a point `a` degrees around the axis of the coordinate system or an arbit
 	           sphere(1);   
 	}  
 
-![ptf_rotate](images/lib3x-rotate_p-1.JPG)
+![ptf_rotate](images/lib3x-ptf_rotate-1.JPG)
 
     use <ptf/ptf_rotate.scad>;
 
@@ -48,7 +48,7 @@ Rotates a point `a` degrees around the axis of the coordinate system or an arbit
 	
 	%sphere(radius);
 
-![ptf_rotate](images/lib3x-rotate_p-2.JPG)
+![ptf_rotate](images/lib3x-ptf_rotate-2.JPG)
 
 	use <ptf/ptf_rotate.scad>;
 
@@ -66,4 +66,4 @@ Rotates a point `a` degrees around the axis of the coordinate system or an arbit
 			sphere(1);  
 	}
 	
-![ptf_rotate](images/lib3x-rotate_p-3.JPG)
+![ptf_rotate](images/lib3x-ptf_rotate-3.JPG)

docs/lib3x-ptf_sphere.md

@@ -15,7 +15,7 @@ Transforms a point inside a rectangle to a point of a sphere. It can create thin
 
 ## Examples
 
-    use <hull_polyline3d.scad>;
+    use <polyline_join.scad>;
     use <ptf/ptf_sphere.scad>;
 
     size = [20, 10];
@@ -23,23 +23,25 @@ Transforms a point inside a rectangle to a point of a sphere. It can create thin
     angle = [180, 270];
 
     rows = [
-        for(y = [0:size[1]])
+        for(y = [0:size.y])
-            [for(x = [0:size[0]]) [x, y]]
+            [for(x = [0:size.x]) [x, y]]
     ];
 
     columns = [
-        for(x = [0:size[0]])
+        for(x = [0:size.x])
-            [for(y = [0:size[1]]) [x, y]]
+            [for(y = [0:size.y]) [x, y]]
     ];
 
     for(line = rows) {
         transformed = [for(p = line) ptf_sphere(size, p, radius, angle)];
-        hull_polyline3d(transformed, thickness = .5);
+        polyline_join(transformed)
+            sphere(.25);
     }
 
     for(line = columns) {
         transformed = [for(p = line) ptf_sphere(size, p, radius, angle)];
-        hull_polyline3d(transformed, thickness = .5);
+        polyline_join(transformed)
+            sphere(.25);
     }
 
 ![ptf_sphere](images/lib3x-ptf_sphere-2.JPG)

docs/lib3x-ptf_torus.md

@@ -16,7 +16,7 @@ Transforms a point inside a rectangle to a point of a torus. It can create thing
 
 ## Examples
 
-    use <hull_polyline3d.scad>;
+    use <polyline_join.scad>;
     use <ptf/ptf_torus.scad>;
 
     size = [20, 10];
@@ -25,23 +25,25 @@ Transforms a point inside a rectangle to a point of a torus. It can create thing
     twist = 90;
 
     rows = [
-        for(y = [0:size[1]])
+        for(y = [0:size.y])
-            [for(x = [0:size[0]]) [x, y]]
+            [for(x = [0:size.x]) [x, y]]
     ];
 
     columns = [
-        for(x = [0:size[0]])
+        for(x = [0:size.x])
-            [for(y = [0:size[1]]) [x, y]]
+            [for(y = [0:size.y]) [x, y]]
     ];
 
     for(line = rows) {
         transformed = [for(p = line) ptf_torus(size, p, radius, angle, twist)];
-        hull_polyline3d(transformed, thickness = .5);
+        polyline_join(transformed)
+		    sphere(.25);
     }
 
     for(line = columns) {
         transformed = [for(p = line) ptf_torus(size, p, radius, angle, twist)];
-        hull_polyline3d(transformed, thickness = .5);
+        polyline_join(transformed)
+		    sphere(.25);
     }
 
 ![ptf_torus](images/lib3x-ptf_torus-2.JPG)

docs/lib3x-ptf_x_twist.md

@@ -14,29 +14,31 @@ Twist a point along the x-axis. You can use it to create something such as a [tw
 
 ## Examples
 
-    use <hull_polyline3d.scad>;
+    use <polyline_join.scad>;
     use <ptf/ptf_x_twist.scad>;
 
     size = [20, 10];
 
     rows = [
-        for(y = [0:size[1]])
+        for(y = [0:size.y])
-            [for(x = [0:size[0]]) [x, y]]
+            [for(x = [0:size.x]) [x, y]]
     ];
 
     columns = [
-        for(x = [0:size[0]])
+        for(x = [0:size.x])
-            [for(y = [0:size[1]]) [x, y]]
+            [for(y = [0:size.y]) [x, y]]
     ];
 
     for(line = rows) {
         twisted = [for(p = line) ptf_x_twist(size, p, 90)];
-        hull_polyline3d(twisted, thickness = .1);
+        polyline_join(twisted)
+		    sphere(.05);
     }
 
     for(line = columns) {
         twisted = [for(p = line) ptf_x_twist(size, p, 90)];
-        hull_polyline3d(twisted, thickness = .1);
+        polyline_join(twisted)
+		    sphere(.05);
     }
 
 ![ptf_x_twist](images/lib3x-ptf_x_twist-1.JPG)

docs/lib3x-ptf_y_twist.md

@@ -14,29 +14,31 @@ Twist a point along the y-axis. You can use it to create something such as a [tw
 
 ## Examples
 
-    use <hull_polyline3d.scad>;
+    use <polyline_join.scad>;
     use <ptf/ptf_y_twist.scad>;
 
     size = [10, 20];
 
     rows = [
-        for(y = [0:size[1]])
+        for(y = [0:size.y])
-            [for(x = [0:size[0]]) [x, y]]
+            [for(x = [0:size.x]) [x, y]]
     ];
 
     columns = [
-        for(x = [0:size[0]])
+        for(x = [0:size.x])
-            [for(y = [0:size[1]]) [x, y]]
+            [for(y = [0:size.y]) [x, y]]
     ];
 
     for(line = rows) {
         twisted = [for(p = line) ptf_y_twist(size, p, 90)];
-        hull_polyline3d(twisted, thickness = .1);
+        polyline_join(twisted)
+		    sphere(.05);
     }
 
     for(line = columns) {
         twisted = [for(p = line) ptf_y_twist(size, p, 90)];
-        hull_polyline3d(twisted, thickness = .1);
+        polyline_join(twisted)
+		    sphere(.05);
     }
 
 ![ptf_y_twist](images/lib3x-ptf_y_twist-1.JPG)

docs/lib3x-rails2sections.md

@@ -0,0 +1,69 @@
+# rails2sections
+
+Create sections along rails. Combined with the `sweep` module, you can describe a more complex model.
+
+Rails should be indexed count-clockwisely.
+
+**Since:** 3.2
+
+## Parameters
+
+- `rails` : A list of rails used to describe the surface of the model.
+
+## Examples
+
+	use <rails2sections.scad>;
+	use <polyline_join.scad>;
+	use <sweep.scad>;
+	
+	rails = [
+	    [[5, 0, 5], [15, 10, 10], [25, 20, 5]],
+	    [[-5, 0, 5], [-15, 10, 10], [-25, 20, 5]],
+	    [[-5, 0, -5], [-15, 10, -10], [-25, 20, -5]],  
+	    [[5, 0, -5], [15, 10, -10], [25, 20, -5]]
+	];
+	
+	sections = rails2sections(rails);
+	
+	sweep(sections);
+	
+	#for(path = rails) {
+	    polyline_join(path)
+		    sphere(.25);
+	}
+
+![rails2sections](images/lib3x-rails2sections-1.JPG)
+
+	use <bezier_curve.scad>;
+	use <rails2sections.scad>;
+	use <polyline_join.scad>;
+	use <sweep.scad>;
+	
+	t_step = 0.05;
+	
+	rails = [
+	    bezier_curve(t_step, 
+	        [[1.25, 0, 5], [5, 20, 5], [16, 20, -2], [18, 20, 10], [30, 15, 8]]
+	    ),
+	    bezier_curve(t_step, 
+	        [[-1.25, 0, 5], [0, 20, 5],  [16, 22, -2], [18, 20, 10], [30, 25, 8]]
+	    ),
+	    bezier_curve(t_step, 
+	        [[-1.25, 0, -5], [0, 20, -5], [16, 20, 1], [18, 27, -3], [20, 27, -5]]
+	    ),
+	    bezier_curve(t_step, 
+	        [[1.25, 0, -5], [5, 20, -5], [16, 20, 1], [18, 17.5, -3], [20, 17.5, -5]]
+	    )
+	];
+	
+	
+	sections = rails2sections(rails);
+	
+	sweep(sections);
+	
+	#for(path = rails) {
+	    polyline_join(path)
+		    sphere(.25);
+	}
+
+![rails2sections](images/lib3x-rails2sections-2.JPG)

docs/lib3x-rotate_p.md

@@ -1,82 +0,0 @@
-# rotate_p
-
-Rotates a point `a` degrees about the axis of the coordinate system or around an arbitrary axis. It behaves as the built-in `rotate` module
-
-## Parameters
-
-- `point` : A 3D point `[x, y, z]` or a 2D point `[x, y]`.
-- `a` : If it's `[deg_x, deg_y, deg_z]`, the rotation is applied in the order `x`, `y`, `z`. If it's `[deg_x, deg_y]`, the rotation is applied in the order `x`, `y`.  If it's`[deg_x]`, the rotation is only applied to the `x` axis. If it's an number, the rotation is only applied to the `z` axis or an arbitrary axis.
-- `v`: A vector allows you to set an arbitrary axis about which the object will be rotated. When `a` is an array, the `v` argument is ignored. **Since:** 1.1.
-
-## Examples
-    
-You can use the code below to create a line.
-
-    use <rotate_p.scad>;
-
-	hull() {
-	    sphere(1);
-	    rotate([0, -45, 45]) 
-	        translate([20, 0, 0]) 
-	            sphere(1);   
-	}  
-
-The following code has the same effect.
-
-    use <rotate_p.scad>;
-
-	point = [20, 0, 0];
-	a = [0, -45, 45];
-	
-	hull() {
-	    sphere(1);
-	    translate(rotate_p(point, a))    
-	       rotate(a)  
-	           sphere(1);   
-	}  
-
-![rotate_p](images/lib3x-rotate_p-1.JPG)
-
-The `rotate_p` function is useful in some situations. For example, you probably want to get all points on the path of a spiral around a sphere. 
-
-    use <rotate_p.scad>;
-
-	radius = 40;
-	step_angle = 10;
-	z_circles = 20;
-	
-	points = [for(a = [0:step_angle:90 * z_circles]) 
-	    rotate_p(
-	        [radius, 0, 0], 
-	        [0, -90 + 2 * a / z_circles, a]
-	    )
-	];
-	
-	// Once you get all points on the path, you can place anything at each point.
-	// I just place a sphere as a simple demonstration.
-	for(p = points) {
-	    translate(p) 
-	        sphere(1);
-	}
-	
-	%sphere(radius);
-
-![rotate_p](images/lib3x-rotate_p-2.JPG)
-
-	use <rotate_p.scad>;
-
-	v = [10, 10, 10];
-
-	hull() {
-		sphere(1);
-		translate(v)
-		sphere(1);   
-	}
-
-	p = [10, 10, 0];
-	for(i = [0:20:340]) {
-		translate(rotate_p(p, a = i, v = v)) 
-			sphere(1);  
-	}
-	
-![rotate_p](images/lib3x-rotate_p-3.JPG)

docs/lib3x-select.md

@@ -0,0 +1,37 @@
+# select
+
+Selects module objects. 
+
+**Since:** 3.2
+
+## Parameters
+
+- `i` : An index value, range, or list. Select all module objects if `i` is ignored.
+
+## Examples
+
+If you write code like this:
+	
+	i = 0;
+
+	if(i == 0) {
+		sphere(1);
+	}
+	else if(i == 1) {
+		cube(1);
+	}
+	else if(i == 2) {
+		cylinder(1, 1);
+	}
+
+You may use `select`:
+
+	use <select.scad>;
+
+	i = 0;
+
+	select(i) {
+		sphere(1);
+		cube(1);
+		cylinder(1, 1);
+	}

docs/lib3x-sf_curve.md

@@ -20,7 +20,7 @@ Follow the steps described in [img2gray](https://github.com/JustinSDK/img2gray).
 
 ## Examples
 
-    use <hull_polyline3d.scad>;
+    use <polyline_join.scad>;
     use <bezier_curve.scad>;
     use <surface/sf_curve.scad>;
 
@@ -146,4 +146,5 @@ Follow the steps described in [img2gray](https://github.com/JustinSDK/img2gray).
 
     sf_curve(levels, curve_path, thickness, depth, invert);
 
-    #hull_polyline3d(curve_path, 5);      
+    #polyline_join(curve_path)
+	    sphere(2.5);      

docs/lib3x-sf_solidifyT.md

@@ -18,8 +18,8 @@ It solidifies two surfaces with triangular mesh.
     points = [for(i = [0:50]) rands(-300, 300, 2)]; 
     triangles = tri_delaunay(points);
 
-    pts = [for(p = points) [p[0], p[1], rands(100, 150, 1)[0]]];
+    pts = [for(p = points) [p.x, p.y, rands(100, 150, 1)[0]]];
-    pts2 = [for(p = pts) [p[0], p[1], p[2] - 100]];
+    pts2 = [for(p = pts) [p.x, p.y, p.z - 100]];
 
     sf_solidifyT(pts, pts2, triangles = triangles);	
 
@@ -45,8 +45,8 @@ It solidifies two surfaces with triangular mesh.
             [x, y] 
     ];
 
-    points1 = [for(p = pts2d) scale * [p[0], p[1], f(p[0], p[1])]];
+    points1 = [for(p = pts2d) scale * [p.x, p.y, f(p.x, p.y)]];
-    points2 = [for(p = points1) [p[0], p[1], p[2] - scale * thickness]];
+    points2 = [for(p = points1) [p.x, p.y, p.z - scale * thickness]];
     triangles = tri_delaunay(pts2d);
 
 

docs/lib3x-shape_star.md

@@ -0,0 +1,22 @@
+# shape_star 
+
+Create a star. Default to a pentagram.
+
+**Since:** 3.2
+
+## Parameters
+
+- `outer_radius`: the outer radius of the star. Default to 1.
+- `inner_radius`: the inner radius of the star. Default to 0.381966.
+- `n`: the burst number. Default to 5.
+
+## Examples
+
+	use <shape_star.scad>;
+
+	polygon(shape_star());
+	translate([3, 0, 0]) 
+	    polygon(shape_star(n = 8));
+
+![shape_star](images/lib3x-shape_star-1.JPG)
+

docs/lib3x-sphere_spiral.md

@@ -14,7 +14,7 @@ Creates all points and angles on the path of a spiral around a sphere. It return
 
 ## Examples
     
-	use <hull_polyline3d.scad>;
+	use <polyline_join.scad>;
 	use <sphere_spiral.scad>;
 	
 	points_angles = sphere_spiral(
@@ -25,7 +25,8 @@ Creates all points and angles on the path of a spiral around a sphere. It return
 	    end_angle = 90
 	);
 	
-	hull_polyline3d([for(pa = points_angles) pa[0]], 1);
+	polyline_join([for(pa = points_angles) pa[0]])
+	    sphere(.5);
 	
 	%sphere(40);
 
@@ -54,7 +55,7 @@ Creates all points and angles on the path of a spiral around a sphere. It return
 
 ![sphere_spiral](images/lib3x-sphere_spiral-5.JPG)
 
-	use <hull_polyline3d.scad>;
+	use <polyline_join.scad>;
 	use <sphere_spiral.scad>;
 	
 	points_angles = sphere_spiral(
@@ -64,7 +65,8 @@ Creates all points and angles on the path of a spiral around a sphere. It return
 	
 	for(a = [0:30:360]) {
 	    rotate(a) 
-	        hull_polyline3d([for(pa = points_angles) pa[0]], 2);
+		polyline_join([for(pa = points_angles) pa[0]])
+			sphere(1);
 	}
 
 ![sphere_spiral](images/lib3x-sphere_spiral-6.JPG)

docs/lib3x-sweep.md

@@ -40,7 +40,7 @@ The indexes of the above triangles is:
 
 ## Examples
 
-	use <rotate_p.scad>;
+	use <ptf/ptf_rotate.scad>;
 	use <sweep.scad>;
 
 	section1 = [
@@ -55,8 +55,8 @@ The indexes of the above triangles is:
 		for(i = [0:55]) 
 			[
 				for(p = section1)
-					let(pt = rotate_p(p, [90, 0, 10 * i]))
+					let(pt = ptf_rotate(p, [90, 0, 10 * i]))
-					[pt[0], pt[1] , pt[2] + i]
+					[pt.x, pt.y , pt.z + i]
 			]
 	];
 
@@ -64,7 +64,7 @@ The indexes of the above triangles is:
 
 ![sweep](images/lib3x-sweep-7.JPG)
 
-	use <rotate_p.scad>;
+	use <ptf/ptf_rotate.scad>;
 	use <sweep.scad>;
 	
 	section1 = [
@@ -85,8 +85,8 @@ The indexes of the above triangles is:
 	    for(i = [0:55]) 
 	        [
 	            for(p = section1)
-	                let(pt = rotate_p(p, [90, 0, 10 * i]))
+	                let(pt = ptf_rotate(p, [90, 0, 10 * i]))
-	                [pt[0], pt[1] , pt[2] + i]
+	                [pt.x, pt.y , pt.z + i]
 	        ]
 	];
 	    
@@ -94,7 +94,7 @@ The indexes of the above triangles is:
 
 ![sweep](images/lib3x-sweep-8.JPG)
 
-	use <rotate_p.scad>;
+	use <ptf/ptf_rotate.scad>;
 	use <sweep.scad>;
 	
 	section1 = [
@@ -113,8 +113,8 @@ The indexes of the above triangles is:
 	    for(i = [0:55]) 
 	        [
 	            for(p = section1)
-	                let(pt = rotate_p(p, [90, 0, 10 * i]))
+	                let(pt = ptf_rotate(p, [90, 0, 10 * i]))
-	                [pt[0], pt[1] , pt[2] + i]
+	                [pt.x, pt.y , pt.z + i]
 	        ]
 	];
 	    

docs/lib3x-t2d.md

@@ -81,7 +81,7 @@ The code below creates the same drawing.
 
 ![t2d](images/lib3x-t2d-1.JPG)
 	
-	use <hull_polyline2d.scad>;
+	use <polyline_join.scad>;
 	use <turtle/t2d.scad>;
 	
 	side_leng = 100;
@@ -100,10 +100,8 @@ The code below creates the same drawing.
 	        ["forward", side_leng]
 	    ]);
 	
-	    hull_polyline2d(
+	    polyline_join([for(turtle = [t, t2, t3, t]) t2d(turtle, "point")]) 
-	        [for(turtle = [t, t2, t3, t]) t2d(turtle, "point")], 
+		    circle(thickness / 2);
-	        thickness
-	    );
 	}
 	
 	module sierpinski_triangle(t, side_leng, min_leng, thickness) {

docs/lib3x-t3d.md

@@ -20,7 +20,7 @@ For more details, please see [3D turtle graphics](https://openhome.cc/eGossip/Op
 ## Examples
 	    
 	use <turtle/t3d.scad>;
-	use <hull_polyline3d.scad>;
+	use <polyline_join.scad>;
 	
 	leng = 10;
 	angle = 120;
@@ -37,10 +37,9 @@ For more details, please see [3D turtle graphics](https://openhome.cc/eGossip/Op
         ["xforward", leng]
     ]);   
     
-	hull_polyline3d(
+	polyline_join(
-        [for(turtle = [t, t2, t3, t4]) t3d(turtle, "point")],
+        [for(turtle = [t, t2, t3, t4]) t3d(turtle, "point")]
-	    thickness
+	) sphere(thickness / 2);
-	);
 
 ![t3d](images/lib3x-t3d-1.JPG)
 	

docs/lib3x-tri_delaunay.md

@@ -12,7 +12,7 @@ Join a set of points to make a [Delaunay triangulation](https://en.wikipedia.org
 ## Examples
 
     use <triangle/tri_delaunay.scad>;
-    use <hull_polyline2d.scad>;
+    use <polyline_join.scad>;
 
     points = [for(i = [0:20]) rands(-100, 100, 2)]; 
 
@@ -32,7 +32,8 @@ Join a set of points to make a [Delaunay triangulation](https://en.wikipedia.org
 	color("red")
 	linear_extrude(3)
 	for(t = tri_delaunay(points, ret = "VORONOI_CELLS")) {
-	    hull_polyline2d(concat(t, [t[0]]), 2);
+	    polyline_join(concat(t, [t[0]]))
+		    circle(1);
 	}
 
 ![tri_delaunay](images/lib3x-tri_delaunay-1.JPG)

docs/lib3x-tri_delaunay_indices.md

@@ -14,7 +14,7 @@ A method of [`tri_delaunay`](lib3x-tri_delaunay.html). Returns the indices from
 	use <triangle/tri_delaunay_indices.scad>;
 	use <triangle/tri_delaunay_shapes.scad>;
 	use <triangle/tri_delaunay_voronoi.scad>;
-	use <hull_polyline2d.scad>;
+	use <polyline_join.scad>;
 
 	points = [for(i = [0:20]) rands(-100, 100, 2)]; 
 
@@ -36,7 +36,8 @@ A method of [`tri_delaunay`](lib3x-tri_delaunay.html). Returns the indices from
 	color("red")
 	linear_extrude(3)
 	for(t = tri_delaunay_voronoi(delaunay)) {
-		hull_polyline2d(concat(t, [t[0]]), 2);
+		polyline_join(concat(t, [t[0]]))
+		    circle(1);
 	}
 
 ![tri_delaunay_indices](images/lib3x-tri_delaunay_indices-1.JPG)

docs/lib3x-tri_delaunay_shapes.md

@@ -14,7 +14,7 @@ A method of [`tri_delaunay`](lib3x-tri_delaunay.html). Returns triangle shapes f
 	use <triangle/tri_delaunay_indices.scad>;
 	use <triangle/tri_delaunay_shapes.scad>;
 	use <triangle/tri_delaunay_voronoi.scad>;
-	use <hull_polyline2d.scad>;
+	use <polyline_join.scad>;
 
 	points = [for(i = [0:20]) rands(-100, 100, 2)]; 
 
@@ -36,7 +36,8 @@ A method of [`tri_delaunay`](lib3x-tri_delaunay.html). Returns triangle shapes f
 	color("red")
 	linear_extrude(3)
 	for(t = tri_delaunay_voronoi(delaunay)) {
-		hull_polyline2d(concat(t, [t[0]]), 2);
+		polyline_join(concat(t, [t[0]]))
+		    circle(1);
 	}
 
 ![tri_delaunay_shapes](images/lib3x-tri_delaunay_shapes-1.JPG)

docs/lib3x-tri_delaunay_voronoi.md

@@ -14,7 +14,7 @@ A method of [`tri_delaunay`](lib3x-tri_delaunay.html). Returns voronoi cells fro
 	use <triangle/tri_delaunay_indices.scad>;
 	use <triangle/tri_delaunay_shapes.scad>;
 	use <triangle/tri_delaunay_voronoi.scad>;
-	use <hull_polyline2d.scad>;
+	use <polyline_join.scad>;
 
 	points = [for(i = [0:20]) rands(-100, 100, 2)]; 
 
@@ -36,7 +36,8 @@ A method of [`tri_delaunay`](lib3x-tri_delaunay.html). Returns voronoi cells fro
 	color("red")
 	linear_extrude(3)
 	for(t = tri_delaunay_voronoi(delaunay)) {
-		hull_polyline2d(concat(t, [t[0]]), 2);
+		polyline_join(concat(t, [t[0]]))
+		    circle(1);
 	}
 
 ![tri_delaunay_voronoi](images/lib3x-tri_delaunay_voronoi-1.JPG)

docs/lib3x-trim_shape.md

@@ -13,7 +13,7 @@ Given a tangled-edge shape. This function trims the shape to a non-tangled shape
 
 ## Examples
 
-    use <hull_polyline2d.scad>;
+    use <polyline_join.scad>;
     use <trim_shape.scad>;
     use <shape_taiwan.scad>;
     use <bijection_offset.scad>;
@@ -24,10 +24,13 @@ Given a tangled-edge shape. This function trims the shape to a non-tangled shape
     trimmed = trim_shape(offseted, 3, len(offseted) - 6);
     smoothed = midpt_smooth(trimmed, 3);
 
-    #hull_polyline2d(taiwan, .1); 
+    #polyline_join(taiwan)
+	    circle(.05); 
     %translate([25, 0, 0]) 
-        hull_polyline2d(offseted, .2);
+	 polyline_join(offseted)
-    hull_polyline2d(smoothed, .1); 
+		circle(.1);
+    polyline_join(smoothed)
+	    circle(.05); 
 
 ![trim_shape](images/lib3x-trim_shape-1.JPG)
 

docs/lib3x-vrn2_cells_from.md

@@ -10,7 +10,7 @@ Create cell shapes of Voronoi from a list of points.
 
 ## Examples
 
-    use <hull_polyline2d.scad>;
+    use <polyline_join.scad>;
     use <voronoi/vrn2_cells_from.scad>;
 
     points = [for(i = [0:50]) rands(-100, 100, 2)]; 
@@ -21,7 +21,8 @@ Create cell shapes of Voronoi from a list of points.
         cell = cells[i];
         
         linear_extrude(1)
-            hull_polyline2d(concat(cell, [cell[0]]), width = 1);
+        polyline_join(concat(cell, [cell[0]]))
+		    circle(.5);
         
         color(rands(0, 1, 3))
         translate(pt)    

docs/lib3x-vrn2_cells_space.md

@@ -12,7 +12,7 @@ Create cell shapes of Voronoi in the first quadrant. You specify a space and a g
 
 ## Examples
 
-    use <hull_polyline2d.scad>;
+    use <polyline_join.scad>;
     use <voronoi/vrn2_cells_space.scad>;
 
     size = [20, 20];
@@ -24,7 +24,8 @@ Create cell shapes of Voronoi in the first quadrant. You specify a space and a g
         cell_poly = cell[1];
 
         linear_extrude(1)
-            hull_polyline2d(concat(cell_poly, [cell_poly[0]]), width = 1);
+		polyline_join(concat(cell_poly, [cell_poly[0]]))
+			circle(.5);
         
         color(rands(0, 1, 3))
         translate(cell_pt)    
@@ -35,7 +36,7 @@ Create cell shapes of Voronoi in the first quadrant. You specify a space and a g
 
 ![vrn2_cells_space](images/lib3x-vrn2_cells_space-1.JPG)
 
-    use <hull_polyline3d.scad>;
+    use <polyline_join.scad>;
     use <ptf/ptf_torus.scad>;
     use <voronoi/vrn2_cells_space.scad>;
     
@@ -48,7 +49,8 @@ Create cell shapes of Voronoi in the first quadrant. You specify a space and a g
     for(cell = cells) {
         cell_poly = [for(p = cell[1]) ptf_torus(size, p, [10, 5], [360, 360])];
 
-        hull_polyline3d(cell_poly, thickness = 1);
+        polyline_join(cell_poly)
+		    sphere(.5);
     }
     
 ![vrn2_cells_space](images/lib3x-vrn2_cells_space-2.JPG)

docs/lib3x-vx_curve.md

@@ -12,7 +12,7 @@ Draws a voxel-by-voxel curve from control points. The curve is drawn only from t
 ## Examples
 
     use <voxel/vx_curve.scad>;
-    use <hull_polyline3d.scad>;
+    use <polyline_join.scad>;
 
     pts = [
         [28, 2, 1],
@@ -32,6 +32,7 @@ Draws a voxel-by-voxel curve from control points. The curve is drawn only from t
         translate(pt)
             sphere(1);
     }
-    #hull_polyline3d(pts, .1);  
+    #polyline_join(pts)
+	    sphere(.05);  
 
 ![vx_curve](images/lib3x-vx_curve-1.JPG)

docs/lib3x-vx_polygon.md

@@ -16,7 +16,7 @@ Returns points that can be used to draw a voxel-style polygon.
 
 	pentagram = [
 		for(pt = shape_pentagram(15)) 
-			[round(pt[0]), round(pt[1])]
+			[round(pt.x), round(pt.y)]
 	];
 
 	for(pt = vx_polygon(pentagram)) {

docs/lib3x-vx_polyline.md

@@ -15,7 +15,7 @@ Given a list of points. `vx_polyline` returns points that can be used to draw a
 
 	pentagram = [
 		for(pt = shape_pentagram(15)) 
-			[round(pt[0]), round(pt[1])]
+			[round(pt.x), round(pt.y)]
 	];
 
 	for(pt = vx_polyline(concat(pentagram, [pentagram[0]]))) {
@@ -37,7 +37,7 @@ Given a list of points. `vx_polyline` returns points that can be used to draw a
 	points = [
 		for(pa = points_angles) 
 		let(pt = pa[0])
-		[round(pt[0]), round(pt[1]), round(pt[2])]
+		[round(pt.x), round(pt.y), round(pt.z)]
 	];
 
 	for(a = [0:30:330]) { 

examples/caterpillar.scad

@@ -0,0 +1,220 @@
+use <arc.scad>;
+use <pie.scad>;
+use <hollow_out.scad>;
+
+$fn = 96;
+
+module track(radius) {
+	module wheels(radius) {
+		module wheel() {
+			rotate_extrude() 
+			translate([radius, 0, 0]) 
+				circle(radius / 2);
+		}
+		
+		for(i = [0:4:8]) {
+			translate([radius * i, 0, 0])
+				wheel();
+		}
+	}
+	
+    module track_profile() {
+        hull() {
+			circle(1.7 * radius );
+			translate([radius * 8, 0, 0]) 
+				circle(1.7 * radius);
+		}
+	}
+
+    translate([-radius * 4, 0, -radius])
+	scale([1, 1, 1.5]) {
+		color("black")
+		linear_extrude(radius * 1.5)
+		hollow_out(shell_thickness = 0.45 * radius)
+		    track_profile();
+
+		color("white") 
+		translate([0, 0, radius * 0.75]) 
+		scale([1, 1, 1.5]) 
+		    wheels(radius);
+	}
+}
+
+module body(radius) {
+	module eye() {
+		translate([-radius / 15, 0, 0]) 
+		rotate([0, 0, 90]) 
+			arc(radius / 2, [0, 180], radius / 5, width_mode = "LINE_OUTWARD");
+				
+		translate([0, radius / 3, 0]) 
+			circle(radius / 3);
+	}
+
+	module eyebrow() {
+		rotate([0, 0, 90]) 
+			arc(radius / 1.25, [25, 155], radius / 10, width_mode = "LINE_OUTWARD");
+	}
+
+    scale([1, 1, 0.9]) {
+		color("yellow") 
+		    sphere(radius * 4);
+		
+		color("Aqua") 
+		rotate([85, 0, 90]) 
+		intersection() {
+			linear_extrude(radius * 4.5) 
+			    pie(radius * 3.5, [0, 180]);
+			difference() {
+				sphere(radius * 4 + radius / 5);
+				sphere(radius * 4);
+			}
+		}
+		
+		// eyes
+		color("black") {    
+			rotate([0, 65, 16]) 
+				linear_extrude(radius * 4.25)
+					eye();
+			
+			rotate([0, 65, -16]) 
+				linear_extrude(radius * 4.25) 
+					eye();
+		}
+		
+		// eyebrows
+		color("black") {
+			rotate([0, 55, 20]) 
+				linear_extrude(radius * 4.25)
+  				    eyebrow();
+				
+			rotate([0, 55, -20]) 
+				linear_extrude(radius * 4.25) 
+				    eyebrow();				
+		}
+	}
+}
+
+module arm(radius) {
+    translate([0, 0, -radius]) {
+		translate([0, 0, radius / 2]) 
+		linear_extrude(radius) {
+			translate([0, -radius * 0.75, 0]) 
+			    square([radius * 9, radius * 1.5]);
+			rotate(80) 
+			translate([0, -radius * 0.5, 0]) 
+			    square([radius * 9, radius]);
+		}
+
+		translate([0, 0, radius * 0.25]) 
+		linear_extrude(radius * 1.5) 
+			circle(radius);
+			
+		linear_extrude(radius * 2)  
+		translate([radius * 9, 0, 0]) 
+			circle(radius);
+	}
+}
+
+module glove(radius) {
+    scale([0.8, 0.8, 1.2]) {
+		color("white") {
+			hull() {
+				scale([1.1, 1, 0.5]) 
+				    sphere(radius * 2.5);
+					
+				translate([-radius * 1.75, 0, radius / 1.5]) 
+				scale([1, 1.75, 0.8]) 
+				    sphere(radius);
+			}
+
+			translate([-radius * 2.5, 0, radius / 1.5]) 
+			scale([1.2, 2, 1]) 
+			    sphere(radius);
+
+			rotate(-10)
+			translate([0, -radius * 2.5, 0])  
+			scale([1.75, 1, 0.8]) 
+			    sphere(radius / 1.5);	
+		}   
+		
+		color("black") 
+		intersection() {
+			scale([1.1, 1, 0.55]) 
+			    sphere(radius * 2.5);
+			
+			union() {
+				translate([0, radius * 0.75, -radius * 2])  
+				linear_extrude(radius) 
+					square([radius * 2, radius / 4], center = true);
+				
+				translate([0, -radius * 0.75, -radius * 2])  
+				linear_extrude(radius) 
+					square([radius * 2, radius / 4], center = true);				
+			}
+		}
+	}
+}
+
+module big_caterpillar(radius) {
+	translate([0, -radius * 4, 0]) 
+	rotate([90, 0, 0]) 
+	    track(radius);
+	
+	translate([0, 0, radius * 3]) 
+	    body(radius);
+	
+	translate([0, radius * 4, 0]) 
+	rotate([90, 0, 0]) 
+	    track(radius);
+	
+	color("yellow") 
+	translate([radius * 6, -radius * 4.5, radius * 9.5]) 
+	rotate([90, 135, 0]) 
+	    arm(radius);
+	
+	translate([radius * 10.75, -radius * 4.5, radius / 2.325]) 
+	rotate([0, 70, 180]) 
+	    glove(radius);
+}
+
+module small_caterpillar(radius) {
+	body_pts = [
+	    [0, 0, -radius / 3],
+		[radius * 1.5, 0, 0],
+		[radius * 3, 0, radius],
+		[radius * 4.25, 0, radius * 2]
+	];
+	
+	color("LimeGreen")
+	for(p = body_pts) {
+	    translate(p) 
+		    sphere(radius);
+	}
+
+    module eye() {
+		color("white") 
+		translate([0, 0, 0]) 
+		    sphere(radius / 1.5);
+		color("black") 
+		translate([.5 * radius, radius / 4, 0]) 
+		    sphere(radius / 3);
+		color("white") 
+		translate([.655 * radius, radius / 2.75, 0])
+		sphere(radius / 6);
+	}
+	
+	half_r = radius / 2;
+	translate([radius * 4.75, 0, radius * 3]) {
+	    translate([0, half_r, 0]) eye();
+		translate([0, -half_r, 0]) eye();
+	}
+}
+
+module caterpillars(radius) {
+	big_caterpillar(radius);
+	translate([radius * 3.5, -radius * 4.5, radius * 9.75]) 
+		rotate([0, -15, 0]) 
+			scale([0.8, 0.8, 0.8]) small_caterpillar(radius);
+}
+
+caterpillars(5);

examples/daruma.scad

@@ -0,0 +1,225 @@
+use <shear.scad>;
+
+text = "順暢";
+font = "思源黑體 Heavy";
+font_size = 15;
+nose = true;
+smoothing = false; // warning: previewing is slow if it's true.
+
+scale(smoothing ? 0.985 : 1)
+    daruma(nose);
+
+wish_decoration(text, font, font_size);
+
+module daruma(nose) {
+    radius = 10;
+
+	module body() {
+		translate([0, 0, radius * 2.75])
+		shear(sy = [.025, 0])
+		minkowski() {
+			linear_extrude(radius * 2, scale = 0.4)
+			translate([0, -radius / 4])
+				circle(radius);
+				
+			sphere(radius * 4, $fn = 48);
+		}
+	}
+
+	module mask_face() {
+		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;
+				translate([0, y / 2, 0]) 
+				linear_extrude(thickness, scale = s) 
+					translate([-offsetX - half_frag_width, -y / 2, 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(angle - 90)
+			mirror([0, 1, 0])
+			mirror([0, 0, 1])
+				for(i = [0 : frags - 1]) {
+				rotate(i * frag_angle + half_frag_angle) 
+					translate([0, offsetY, 0])
+					rotate([-90, 0, 0]) 
+						get_frag(i) 
+							children();  
+				}
+		}
+		
+		translate([0, -radius, radius * 1.4])
+		scale([1.27, 1, 1])
+		rotate([-24, 0, 0])
+		rotate(225)
+		bend_extrude(size = [radius * 16, radius * 8], thickness = radius, angle = 180, frags = 36)
+		translate([radius * 4, radius * 2.5])
+		hull() {
+			$fn = 12;
+			translate([0, radius * 1.75])
+				circle(radius * 1.2);
+				
+			translate([radius * 1.45, radius * 1.5])
+				circle(radius * 1.25, $fn = 24);
+
+			translate([-radius * 1.45, radius * 1.5])
+				circle(radius * 1.25, $fn = 24);
+				
+			translate([radius * 1.85, radius * 0.25])
+			rotate(25)
+			scale([1, 1.3])
+				circle(radius * 1.3);
+				
+			translate([-radius * 1.85, radius * 0.25])
+			rotate(-25)
+			scale([1, 1.3])
+				circle(radius * 1.3);
+				
+			translate([radius * 2.75, -radius * 1.2])
+				circle(radius / 2);
+
+			translate([-radius * 2.75, -radius * 1.2])
+				circle(radius / 2);
+		}	
+	}
+
+	module eyes_nose() {
+		module eye() {
+			translate([radius * 1.4, -3.1 * radius, radius * 5.9])
+			rotate([66, 0, 15])
+			linear_extrude(radius / 4, scale = 0.9)
+				circle(radius * 1.15);
+		}
+
+		eye();
+
+		mirror([1, 0, 0])
+			eye();
+			
+		// nose
+		if(nose) {
+			translate([0, -3.75 * radius, radius * 4.85])
+			rotate([67.5, 0, 0])
+			linear_extrude(radius / 4, scale = 0.9)
+				circle(radius * 0.4);
+		}
+	}
+	
+	if(smoothing) {
+		minkowski() {
+			union() {
+				difference() {
+					body();
+					mask_face();	
+				}
+				eyes_nose();
+			}
+			sphere(radius / 9.5, $fn = 8);
+		}
+	} else {	
+		difference() {
+			body();
+			mask_face();	
+		}
+		eyes_nose();
+	}
+}
+
+module wish_decoration(text, font, font_size) {
+    $fn = 48;
+	
+	translate([0, -2, 0])
+	intersection() {
+		union() {
+			wish();
+
+			decoration();
+			mirror([1, 0, 0])
+				decoration();
+		}
+
+		translate([0, 0, 31])
+			sphere(52.25);
+	}
+
+	module wish() {
+		if(len(text) == 1) {
+			translate([0, -43, 21])
+			rotate([90, 0, 0])
+			linear_extrude(10, scale = .8)
+				text(
+					text, 
+					font = font,
+					size = font_size,
+					valign = "center", 
+					halign = "center"
+				);
+		}
+		else {
+			translate([0, -43, 29.5])
+			rotate([85, 0, 0])
+			linear_extrude(10, scale = .8)
+				text(
+					text[0], 
+					font = font,
+					size = font_size,
+					valign = "center", 
+					halign = "center"
+				);
+				
+			translate([0, -42.5, 12])
+			rotate([105, 0, 0])
+			linear_extrude(10, scale = .8)
+				text(
+					text[1], 
+					font = font,
+					size = font_size,
+					valign = "center", 
+					halign = "center"
+				);
+	    }
+	}
+
+	module decoration() {
+		translate([18, -38, 21])
+		rotate([100, 0, 0])
+		linear_extrude(10, scale = .8)
+		scale(.85)
+		scale([1, 1.825])
+		offset(.5)
+		difference() {
+			circle(10);
+			translate([-9, 0])
+				circle(11.5);
+		}
+
+		translate([28, -30, 21])
+		rotate([100, 0, 30])
+		linear_extrude(10, scale = .8)
+		scale(.7)
+		scale([1, 1.825])
+		offset(.5)
+		difference() {
+			circle(10);
+			translate([-9, 0])
+				circle(11.5);
+		}
+	}
+}

examples/distorted_vase.scad

@@ -11,11 +11,11 @@ beginning_radius = 15;
 thickness = 2;
 fn = 180;
 amplitude = 10;
-curve_step = 0.02;
+curve_step = 0.01;
 smoothness = 15;
 // Perlin noise 2D or 3D
 perlin = 2; // [2, 3]
-bottom = "NO"; // ["YES", "NO"]
+bottom = "YES"; // ["YES", "NO"]
 epsilon = 0.000001;
 
 distorted_vase(beginning_radius, thickness, fn, amplitude, curve_step, smoothness, perlin, epsilon);
@@ -77,7 +77,10 @@ module distorted_vase(beginning_radius, thickness, fn, amplitude,curve_step, smo
 	sweep(all, triangles = "HOLLOW");
 	
 	if(bottom == "YES") {
-	    linear_extrude(thickness)
+	    sweep([
-	        polygon([for(p = offset_noisy[len(offset_noisy) - 1]) [p[0], p[1]]]);
+			for(section = noisy)
+			if(section[0][2] < thickness) 
+			section
+		]);
 	}
 }

examples/dragon/dragon_and_pearl.scad

@@ -0,0 +1,112 @@
+use <bezier_curve.scad>;
+use <shear.scad>;
+use <along_with.scad>;
+use <bezier_smooth.scad>;
+use <fibonacci_lattice.scad>;
+use <polyhedron_hull.scad>;
+use <dragon_head.scad>;
+use <dragon_scales.scad>;
+use <dragon_foot.scad>;
+
+dragon_and_perl();
+
+module one_segment(body_r, body_fn, one_scale_data) {
+    // scales
+    rotate([-90, 0, 0])
+        dragon_body_scales(body_r, body_fn, one_scale_data);
+
+    // dorsal fin
+    translate([0, 3.2, -3]) 
+    rotate([-61, 0, 0]) 
+    shear(sy = [0, 2.25])
+    linear_extrude(3.25, scale = 0.3)
+        square([1.5, 10], center = true);            
+            
+    // belly    
+    translate([0, -2.5, .8]) 
+    rotate([-5, 0, 0]) 
+    scale([1, 1, 1.4])  
+        sphere(body_r * 0.966, $fn = 8); 
+    
+}
+
+module tail() {
+    $fn = 4;
+    tail_scales(75, 2.5, 4.25, -4, 1.25);
+    tail_scales(100, 1.25, 4.5, -7, 1);
+    tail_scales(110, 1.25, 3, -9, 1);
+    tail_scales(120, 2.5, 2, -9, 1);   
+}
+
+module dragon_and_perl() {
+    function __angy_angz(p1, p2) = 
+        let(
+            dx = p2.x - p1.x,
+            dy = p2.y - p1.y,
+            dz = p2.z - p1.z,
+            ya = atan2(dz, sqrt(pow(dx, 2) + pow(dy, 2))),
+            za = atan2(dy, dx)
+        ) [ya, za];
+        
+    body_path = bezier_curve(0.02, [
+        [0, 7.5, 15],
+        [0, 30, 0],
+        [-30, 50, -55],
+        [-50, 70, 0],
+        [20, 90, 60],
+        [50, 110, 0],
+        [0, 130, -30],
+        [-10, 150, 0],
+        [-5, 170, 0]
+    ]);
+    leng_body_path = len(body_path);
+    angy_angz = __angy_angz(body_path[0], body_path[1]);
+
+    translate([1, 7, 14])
+    rotate([-135, 0, 3])
+    scale(1.15)
+    rotate([0, angy_angz[0], angy_angz[1]])
+        dragon_head();
+
+    body_r = 6;
+    body_fn = 12;
+    scale_fn = 4;
+    scale_tilt_a = 6;
+    one_body_scale_data = one_body_scale(body_r, body_fn, scale_fn, scale_tilt_a);
+
+    along_with(body_path, scale = [0.25, 0.25, 0.5], method = "EULER_ANGLE")    
+        one_segment(body_r, body_fn, one_body_scale_data);
+
+    ayz = __angy_angz(body_path[leng_body_path - 2], body_path[leng_body_path - 1]);
+
+    translate(body_path[leng_body_path - 1])
+    rotate([0, ayz[0] + 82, ayz[1]])
+    mirror([0, 0, 1])
+    rotate(-12)
+    scale([0.3, 0.3, 0.6])
+        tail();
+
+    translate([-5, 25, -12.5]) 
+    rotate([-20, 0, -15]) 
+        foot();
+
+    translate([-10, 15, -6.5]) 
+    rotate([-60, 45, 25]) 
+    mirror([1, 0, 0])
+        foot();
+
+    translate([11.5, 107, -.5]) 
+    rotate([-10, 20, -50]) 
+    scale(0.65)
+        foot();
+
+    translate([7, 108, .25]) 
+    rotate([5, 20, 60]) 
+    rotate([10, -30, 0]) 
+    scale(0.65)
+    mirror([1, 0, 0])
+        foot();
+
+    translate([-27.5, 11.75, -14])
+        polyhedron_hull(fibonacci_lattice(66, 7));
+}

examples/dragon/dragon_claw.scad

@@ -0,0 +1,42 @@
+use <curve.scad>;
+use <polyline2d.scad>;
+use <ptf/ptf_rotate.scad>;
+use <util/dedup.scad>;
+
+module dragon_claw() {
+	pts = [
+		[0, 0.55], [1, 0.45], [2.5, 0.375], [6, 0.825], [8, -0.375], 
+		[8, -0.375], [6, 1.875], [4, 1.6], [1.8, 2.5], [1.5, 2.8], [1.2, 3.3], [1.05, 3.8], [1, 4], [0, 8]
+	];
+
+	$fn = 16;
+
+	a = 360 / $fn;
+	x = 6.2 * cos(a);
+	y = 6.2 * sin(a);
+	path = [
+		[0, 0], [2.5, 0], [x, y], [x + 1, y + 1]
+	];
+	path2 = [
+		for(i = len(path) - 1; i > -1; i = i - 1) 
+			ptf_rotate([path[i][0], -path[i][1]], a * 2)
+	];
+
+	t_step = 0.25;
+	claw_path_basic = concat(curve(t_step, path), curve(t_step, path2));
+	claw_path1 = [for(p = claw_path_basic) [p[0] * 1.15, p[1] * 1.1]];
+	claw_path2 = [for(p = claw_path_basic) ptf_rotate(p * 1.2, a * 2)];
+	claw_path3 = [for(p = claw_path_basic) ptf_rotate(p * 1.15, a * 4)];
+	claw_path4 = [for(p = claw_path_basic) ptf_rotate(p * 1.1, a * 6)];
+	claw_path5 = [for(p = claw_path_basic) ptf_rotate(p, a * 11)];
+
+	rotate(-15)
+	scale([1.15, 1.3, 1]) 
+	rotate(15)
+	intersection() {
+		rotate_extrude($fn = 7)
+			polygon(pts);
+		linear_extrude(5)
+			polygon(dedup(concat(claw_path1, claw_path2, claw_path3, claw_path4, [[-2, -.75], [-1.45, -1.45]], claw_path5, [[1.45, -1.45], [2, -.75]])));
+	}
+}

examples/dragon/dragon_foot.scad

@@ -0,0 +1,44 @@
+use <along_with.scad>;
+use <dragon_scales.scad>;
+use <dragon_claw.scad>;
+
+module knee() {
+    $fn = 4;
+    scale([1,0.85, 1]) union() {
+        knee_scales(75, 2.5, 4.25, -4, 1.25);
+        knee_scales(100, 1.25, 4.5, -7, 1);
+        knee_scales(110, 1.25, 3, -9, 1);
+        knee_scales(120, 2.5, 2, -9, 1);   
+    }
+}
+
+module foot() {
+    upper_arm_r = 3.6;
+    lower_arm_r = 2.7;
+    arm_fn = 6;
+    scale_fn = 4;
+    scale_tilt_a = 6;
+
+    upper_arm_path = [[.5, 1, 10], [1.25, 6.25, 11.25], [2, 11.5, 12.5], [2, 16.75, 13.75], [1.9, 20, 14.25]];
+    lower_arm_path = [[2, 22, 14],  [3.5, 21, 10], [4.5, 20.3, 7]];
+
+    upper_arm_scale_data = one_body_scale(upper_arm_r, arm_fn, scale_fn, scale_tilt_a);
+    lower_arm_scale_data = one_body_scale(lower_arm_r, arm_fn, scale_fn, scale_tilt_a);
+
+    along_with(upper_arm_path, scale = 0.75, method = "EULER_ANGLE") 
+        rotate([-90, 0, 0])
+            dragon_body_scales(upper_arm_r, arm_fn, upper_arm_scale_data);
+    along_with(lower_arm_path, scale = 0.7, method = "EULER_ANGLE") 
+        rotate([-90, 0, 0])
+            dragon_body_scales(lower_arm_r, arm_fn, lower_arm_scale_data);
+    
+    translate([2.25, 14.5, 12.75])
+    scale([0.7, 1.15, .8])
+    rotate([108, 9, 1])
+        knee();
+
+    translate([6.4, 18.95, .25])
+    rotate([11, 13, 185])
+    scale([1.2, 1.2, 1.2])
+        dragon_claw();
+}

examples/dragon/dragon_head.scad

@@ -0,0 +1,138 @@
+use <ellipse_extrude.scad>;
+use <curve.scad>;
+use <sweep.scad>;
+use <rails2sections.scad>;
+use <shape_trapezium.scad>;
+use <ptf/ptf_rotate.scad>;
+
+module dragon_head() {
+    module hair() {
+        for(i = [16:36]) {
+            rotate(i * 10 + rands(0, 5, 1, i)[0]) 
+            translate([0, -13, 0]) 
+            rotate([8 + rands(0, 2, 1, i)[0], 0, 0]) 
+            linear_extrude(12 + rands(0, 5, 1, i)[0], scale = 0.05, twist = 50 - rands(0, 100, 1, seed = i)[0]) 
+            translate([0, 10, 0]) 
+                circle(3, $fn = 5);    
+        }       
+
+        for(i = [0:35]) {
+            rotate(i * 12 + rands(0, 5, 1, i)[0]) 
+            translate([0, -11.5, 0]) 
+            rotate([4 + rands(0, 2, 1, i)[0], 0, 0]) 
+            linear_extrude(14 + rands(0, 5, 1, i)[0], scale = 0.05, twist = 50 - rands(0, 100, 1, seed = i + 1)[0]) 
+            translate([0, 10, 0]) 
+                circle(3.5, $fn = 6);    
+        }
+        
+        for(i = [0:35]) {
+            rotate(i * 10) 
+            translate([0, -10, 0]) 
+            rotate([2, 0, 0]) 
+            linear_extrude(16 + rands(0, 5, 1, i)[0], scale = 0.05, twist = 50 - rands(0, 100, 1, seed = i + 2)[0]) 
+            translate([0, 10, 0]) 
+                circle(3.5, $fn = 5);    
+        }         
+    }
+    
+    module one_horn() {        
+        translate([-9, -4, -2]) 
+        rotate([45, -25, 0]) 
+        linear_extrude(27.5, scale = 0.1, twist = -90) 
+        translate([7.5, 0, 0]) 
+            circle(3, $fn = 4);    
+    }
+    
+    module mouth() {
+        path1 = curve(0.4, [[0, -8, -1], [0, -11, .25], [0, -12, 5], [0, -9, 5], [0, -4, 6], [0, -0.5, 8], [0, 5, 6.5], [0, 8, 6], [0, 12, 1], [0, 16, 0]]);
+        path2 = [for(p = path1) ptf_rotate(p, [0, -12, 0]) * 0.9 + [-2, 0, 0]];
+        path3 = [for(i = [0:len(path1) - 1]) [-i / 6 - 1.5, i / 1.65 - 9, 0]];
+        path4 = [for(p = path3) [-p[0], p[1], p[2]]];
+        path5 = [for(p = path2) [-p[0], p[1], p[2]]];
+
+        translate([0, 0, -2]) 
+        rotate([90, 0, -90]) 
+            sweep(rails2sections([path1, path2, path3, path4, path5]));
+
+        translate([0, 0, -3.25]) 
+        rotate([90, 0, -90]) 
+            ellipse_extrude(5.5, slices = 2) 
+                polygon(
+                    shape_trapezium([5, 18], 
+                    h = 20,
+                    corner_r = 2, $fn = 4)
+                );    
+
+        scale([1.5, 1, 1])
+        intersection() {       
+            mirror([1, 0, 0]) 
+            translate([0, 0, -2.25]) 
+            rotate([85, 0, -90])
+            ellipse_extrude(4, slices = 2) 
+                polygon(
+                    shape_trapezium([5, 18], 
+                    h = 20,
+                    corner_r = 2, $fn = 5)
+                );       
+
+            
+            jpath1 = curve(0.4, [[-10, 16], [0, 8], [4, 5],  [3, 0], [2, -5], [2, -10], [0, -13.5], [-3, -14]]);
+            rotate([90, -4, 0])
+            linear_extrude(25, center = true)
+                polygon(jpath1);
+        }
+    
+        translate([0, -2.5, -11])
+        rotate([0, 95, 0])
+        linear_extrude(1.4, scale = 0.1)
+        translate([.4, 0, 0])
+            circle(.5, $fn = 6);
+
+        translate([0, 2.5, -11])
+        rotate([0, 95, 0])
+        linear_extrude(1.5, scale = 0.1)
+        translate([.4, 0, 0])
+            circle(.5, $fn = 6);
+    }
+    
+    module one_eye() {
+        translate([-5, 2.5, -2]) 
+        rotate([-5, -8, -10]) 
+        scale([1, 1, 1.75]) 
+            sphere(1.75, $fn = 6);      
+
+        translate([-5.1, 3.75, -2.25]) 
+        rotate([-25, 0, 75]) 
+            sphere(0.65, $fn = 6);                      
+    }
+    
+    module one_beard() {
+        translate([-10, -12, -10])
+        rotate(180) 
+        linear_extrude(8, scale = 0.15, twist = 35) 
+        translate([-9, -10, 0]) 
+            circle(1, $fn = 8);    
+    }
+    // mouth();
+    rotate([0, 15, 0]) 
+    translate([0, 0, -25 / 2]) 
+    scale(1.15) {
+        scale([0.8, 0.9, 1]) hair();
+
+        translate([0, 0, 2]) 
+        {
+            rotate(-90) {
+                    one_horn();
+                    mirror([-1, 0, 0]) one_horn();       
+            }
+            
+            mouth();
+
+            one_eye();
+            mirror([0, 1, 0]) one_eye();
+            
+            one_beard();
+            mirror([0, 1, 0]) one_beard();
+        }        
+    }
+}

examples/dragon/dragon_head_low_poly.scad

@@ -1,50 +1,8 @@
 use <bezier_curve.scad>;
-use <ellipse_extrude.scad>;
 use <path_extrude.scad>;
 use <shape_circle.scad>;
-use <torus_knot.scad>;
-use <util/reverse.scad>;
 
-torus_knot_dragon();
+module dragon_head_low_poly() {
-
-module torus_knot_dragon() {
-    phi_step = 0.04;
-
-    knot = torus_knot(2, 3, phi_step);
-    dragon_body_path = reverse([for(i = [9:len(knot) - 3]) knot[i]]);
-
-    body_shape = concat(
-        bezier_curve(0.25, 
-            [
-                [30, -35], [16, 0], [4, 13], 
-                [3, -5], [0, 26], [-3, -5],
-                [-4, 13],  [-16, 0], [-30, -35]
-            ]
-        ),
-        bezier_curve(0.25, 
-            [[-22, -35], [-15, -45], [0, -55], [15, -45], [22, -35]]
-        )
-    );    
-
-    
-    pts = [for(p = body_shape) p * 0.015];
-    p = dragon_body_path[0];
-    
-    path_extrude(pts, concat([p + [0.00001, 0.0000055, 0.000008]], dragon_body_path), scale = 0.9);
-
-    translate([2.975, -0.75, -0.75])      
-    scale(0.01825)
-    rotate([-52, -9, -25]) 
-    dragon_head(); 
-    
-    translate([1.84, 1.635, -0.885])
-    rotate([104.95, -154.35, 66.25])
-    ellipse_extrude(1.2, slices = 7, twist = 15)
-    scale(0.9 * 0.0150)
-        polygon(body_shape);
-}
-   
-module dragon_head() {
     module palate() {
         t_step = 0.15;