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@@ -45,105 +45,105 @@ These examples incubate dotSCAD and dotSCAD refactors these examples. See [examp
Signature | Description 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. [**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]`. [**hull_polyline2d**(points[, width])](https://openhome.cc/eGossip/OpenSCAD/lib3x-hull_polyline2d.html) | create a 2D polyline from a list of `[x, y]`.
[**line2d**(p1, p2, width = 1, p1Style = "CAP_SQUARE", p2Style = "CAP_SQUARE")](https://openhome.cc/eGossip/OpenSCAD/lib3x-line2d.html) | create a line from two points. [**line2d**(p1, p2[, width, p1Style, p2Style])](https://openhome.cc/eGossip/OpenSCAD/lib3x-line2d.html) | create a line from two points.
[**multi_line_text**(lines, line_spacing = 15, size = 10, font = "Arial", ...)](https://openhome.cc/eGossip/OpenSCAD/lib3x-multi_line_text.html) | create multi-line text from a list of strings. [**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.
[**pie**(radius, angle)](https://openhome.cc/eGossip/OpenSCAD/lib3x-pie.html) | create polyline2de a pie (circular sector). [**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. [**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 ## 3D Module
Signature | Description 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]`. [**hull_polyline3d**(points[, diameter])](https://openhome.cc/eGossip/OpenSCAD/lib3x-hull_polyline3d.html) | create a 3D polyline from a list of `[x, y, z]`.
[**line3d**(p1, p2, diameter = 1, p1Style = "CAP_CIRCLE", p2Style = "CAP_CIRCLE")](https://openhome.cc/eGossip/OpenSCAD/lib3x-line3d.html) | create a 3D line from two points. [**line3d**(p1, p2[, diameter, p1Style, p2Style])](https://openhome.cc/eGossip/OpenSCAD/lib3x-line3d.html) | create a 3D line from two points.
[**loft**(sections, slices = 1)](https://openhome.cc/eGossip/OpenSCAD/lib3x-loft.html) | develop a smooth skin between crosssections with different geometries. [**loft**(sections[, slices])](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. [**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). [**starburst**(r1, r2, n, height)](https://openhome.cc/eGossip/OpenSCAD/lib3x-starburst.html) | a 3D version of [`shape_starburst`](https://openhome.cc/eGossip/OpenSCAD/lib3x-starburst.html).
[**sweep**(sections, triangles = "SOLID")](https://openhome.cc/eGossip/OpenSCAD/lib3x-sweep.html) | develop a smooth skin from crosssections with the same umber of sides. [**sweep**(sections[, triangles])](https://openhome.cc/eGossip/OpenSCAD/lib3x-sweep.html) | develop a smooth skin from crosssections with the same umber of sides.
## Transformation ## Transformation
Signature | Description 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. [**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.
## 2D Function ## 2D Function
Signature | Description 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. [**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 ## 2D/3D Function
Signature | Description Signature | Description
--|-- --|--
[**angle_between**(vt1, vt2)](https://openhome.cc/eGossip/OpenSCAD/lib3x-angle_between.html) | return the angle between two vectors. [**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. [**paths2sections**(paths)](https://openhome.cc/eGossip/OpenSCAD/lib3x-paths2sections.html) | given a list of paths, this function returns all cross-sections described by those paths.
[**path_scaling_sections**(shape_pts, edge_path)](https://openhome.cc/eGossip/OpenSCAD/lib3x-path_scaling_sections.html) | given an edge path with the first point at the outline of a shape, this function uses the path to calculate scaling factors and returns all scaled sections in the reversed order of the edge path. [**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 ## Path
Signature | Description Signature | Description
--|-- --|--
[**arc_path**(radius, angle)](https://openhome.cc/eGossip/OpenSCAD/lib3x-arc_path.html) | create an arc path. [**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. [**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). [**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). [**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 ## Extrusion
Signature | Description 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. [**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 ## 2D Shape
Signature | Description 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_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_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_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_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_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_starburst**(r1, r2, n)](https://openhome.cc/eGossip/OpenSCAD/lib3x-shape_starburst.html) | returns shape points of a star.
[**shape_superformula**(phi_step, m1, m2, n1, n2 = 1, n3 = 1, a = 1, b = 1)](https://openhome.cc/eGossip/OpenSCAD/lib3x-shape_superformula.html) | return shape points of [Superformula](https://en.wikipedia.org/wiki/Superformula). [**shape_superformula**(phi_step, m1, m2, n1, n2 = 1[, 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 ## 2D Shape Extrusion
@@ -153,7 +153,7 @@ 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. [**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. [**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. [**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. [**sphere_spiral_extrude**(shape_pts, radius, za_step, ...)](https://openhome.cc/eGossip/OpenSCAD/lib3x-sphere_spiral_extrude.html) | extrude a 2D shape along the path of a sphere spiral.
## Util ## Util
@@ -163,13 +163,13 @@ These examples incubate dotSCAD and dotSCAD refactors these examples. See [examp
Signature | Description 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/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/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/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/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/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/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/swap**(lt, i, j)](https://openhome.cc/eGossip/OpenSCAD/lib3x-swap.html) | swap two elements in a list.
[**util/zip**(lts, combine)](https://openhome.cc/eGossip/OpenSCAD/lib3x-zip.html) | make a list that aggregates elements from each of the lists. [**util/zip**(lts, combine)](https://openhome.cc/eGossip/OpenSCAD/lib3x-zip.html) | make a list that aggregates elements from each of the lists.
@@ -181,8 +181,8 @@ These examples incubate dotSCAD and dotSCAD refactors these examples. See [examp
Signature | Description Signature | Description
--|-- --|--
[**util/choose**(choices, seed)](https://openhome.cc/eGossip/OpenSCAD/lib3x-choose.html) | choose an element from the given list. [**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 ### util/string
@@ -235,7 +235,7 @@ 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_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_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_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. [**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. [**maxtrix/m_transpose**(m)](https://openhome.cc/eGossip/OpenSCAD/lib3x-m_transpose.html) | transpose a matrix.
@@ -245,10 +245,10 @@ 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_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_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_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_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. [**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 +258,8 @@ 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_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_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_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_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. [**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 +270,10 @@ These examples incubate dotSCAD and dotSCAD refactors these examples. See [examp
Signature | Description 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/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`. [**turtle/t3d**(t, cmd, point, unit_vectors, leng, angle)](https://openhome.cc/eGossip/OpenSCAD/lib3x-t3d.html) | a 3D version of `t2d`.
@@ -281,40 +281,40 @@ These examples incubate dotSCAD and dotSCAD refactors these examples. See [examp
Signature | Description 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_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_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_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_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_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. [**voxel/vx_union**(points1, points2)](https://openhome.cc/eGossip/OpenSCAD/lib3x-vx_union.html) | create a union of two lists of points.
## Part ## Part
Signature | Description 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 ## Surface
Signature | Description 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_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_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. [**surface/sf_thicken**(points, thickness, ...)](https://openhome.cc/eGossip/OpenSCAD/lib3x-sf_thicken.html) | thicken a surface.
@@ -325,40 +325,40 @@ These examples incubate dotSCAD and dotSCAD refactors these examples. See [examp
Signature | Description 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, grid_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, grid_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 ## Voronoi
Signature | Description 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_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 ## Maze
Signature | Description 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_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_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_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_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. [**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.
---- ----
@@ -376,8 +376,8 @@ These examples incubate dotSCAD and dotSCAD refactors these examples. See [examp
Signature | Description Signature | Description
--|-- --|--
[**polyhedra/tetrahedron**(radius, detail = 0)](https://openhome.cc/eGossip/OpenSCAD/lib3x-tetrahedron.html) | Create a tetrahedron. [**polyhedra/tetrahedron**(radius[, detail])](https://openhome.cc/eGossip/OpenSCAD/lib3x-tetrahedron.html) | Create a tetrahedron.
[**polyhedra/hexahedron**(radius, detail = 0)](https://openhome.cc/eGossip/OpenSCAD/lib3x-hexahedron.html) | create a hexahedron. [**polyhedra/hexahedron**(radius[, detail])](https://openhome.cc/eGossip/OpenSCAD/lib3x-hexahedron.html) | create a hexahedron.
polyhedra/octahedron | create a octahedron. polyhedra/octahedron | create a octahedron.
polyhedra/dodecahedron | create a dodecahedron. polyhedra/dodecahedron | create a dodecahedron.
polyhedra/icosahedron | create a icosahedron. polyhedra/icosahedron | create a icosahedron.