Topics

Topic Index

An index of topics, with related functions, modules, and constants.

A: Affine, Angle, Area, Argument Handling, Arrays, Attachable, Attachment, Attachments

B: Bearings, Bezier Curves, Bezier Patches, Bezier Paths, Boolean Operations, Boolean Testing, Bottles, Bounding Boxes, Bounds

C: Calculus, Centroid, Chamfers, Circles, Clockwise, Closest, Collinearity, Collision, Colors, Colorspace, Comparators, Comparison, Comparisons, Complex Numbers, Constants, Convexity, Coordinates, Copiers, Coplanarity, CubeTruss, Cylinders

D: Data Structures, Debugging, Descriptions, Dictionaries, Distance, Distributors, Drawing Tools

E: Error Checking, Extrusion, Extrusions

F: FDM Optimized, Filters, Function Literals

G: Gears, Geometry

H: Hashing, Heightfield, Hinges, Hulling

I: Indexing, Interpolation, Intersection, Iteration

J: Joiners

K: Knurling

L: Linear Algebra, Lines, List Handling, Lists, Logic, Looping

M: Masking, Masks, Masks (2D), Math, Math Operators, Matrices, Mini-Language, Mirroring, Miscellaneous, Modifiers, Modular Hose, Motors

N: NURBS, NURBS Curves, NURBS Patches

O: Offsets

P: Partitions, Parts, Path Generators, Path Generators (2D), Path Generators (3D), Path Subdivision, Paths, Paths (2D), Paths (3D), Planes, Points, Polygon, Polygons, Polyhedra, Projection

Q: Quantization

R: Random, Reflection, Regions, Revolution, Rotation, Rounding

S: Scaling, Screws, Search, Searching, Segments, Set Handling, Shapes, Shapes (2D), Shapes (3D), Shapes2D, Shapes3D, Shearing, Shell, Skewing, Skin, Skinning, Sliders, Slop, Spheres, Spiral, Statistics, String Operators, Strings, Sweep

T: Tangents, Test, Testing, Text, Textures, Threading, Transformations, Transforms, Translation, Triangles, Triangulation, Trigonometry, Trusses, Type Checking, Type Conversion, Type Queries

U: Undef Handling

V: VNF Generators, VNF Manipulation, Vectors, Versioning

W: Walls, Wiring

Affine

• apply() Func – Applies a transformation matrix to a point, list of points, array of points, or a VNF. ^{[Path] [VNF] [Mat]}
• back() Func/Mod – Translates children backwards (Y+). ^{[Trans] [Path] [VNF] [Mat]}
• diagonal_matrix() Func – Make a diagonal matrix.
• down() Func/Mod – Translates children downwards (Z-). ^{[Trans] [Path] [VNF] [Mat]}
• frame_map() Func/Mod – Rotates and possibly skews children from one frame of reference to another. ^{[Trans] [Path] [VNF] [Mat]}
• fwd() Func/Mod – Translates children forwards (Y-). ^{[Trans] [Path] [VNF] [Mat]}
• IDENT Const – A constant containing the 3D identity transformation matrix. ^[Mat]
• ident() Func – Return identity matrix.
• is_rotation() Func – Check if a transformation matrix represents a rotation.
• left() Func/Mod – Translates children leftwards (X-). ^{[Trans] [Path] [VNF] [Mat]}
• mirror() Func/Mod – Reflects children across an arbitrary plane. ^{[Trans] [Path] [VNF] [Mat] [Ext]}
• move() Func/Mod – Translates children in an arbitrary direction. ^{[Trans] [Path] [VNF] [Mat]}
• right() Func/Mod – Translates children rightwards (X+). ^{[Trans] [Path] [VNF] [Mat]}
• rot() Func/Mod – Rotates children in various ways. ^{[Trans] [Path] [VNF] [Mat]}
• rot_decode() Func – Extract axis and rotation angle from a rotation matrix.
• rot_inverse() Func – Invert 2d or 3d rotation transformations.
• scale() Func/Mod – Scales children arbitrarily. ^{[Trans] [Path] [VNF] [Mat] [Ext]}
• skew() Func/Mod – Skews (or shears) children along various axes. ^{[Trans] [Path] [VNF] [Mat]}
• tilt() Func/Mod – Tilts children towards a direction ^{[Trans] [Path] [VNF] [Mat]}
• move() Func/Mod – Translates children in an arbitrary direction. ^{[Trans] [Path] [VNF] [Mat]}
• up() Func/Mod – Translates children upwards (Z+). ^{[Trans] [Path] [VNF] [Mat]}
• xflip() Func/Mod – Reflects children across the YZ plane. ^{[Trans] [Path] [VNF] [Mat]}
• right() Func/Mod – Translates children rightwards (X+). ^{[Trans] [Path] [VNF] [Mat]}
• xrot() Func/Mod – Rotates children around the X axis using the right-hand rule. ^{[Trans] [Path] [VNF] [Mat]}
• xscale() Func/Mod – Scales children along the X axis. ^{[Trans] [Path] [VNF] [Mat]}
• yflip() Func/Mod – Reflects children across the XZ plane. ^{[Trans] [Path] [VNF] [Mat]}
• back() Func/Mod – Translates children backwards (Y+). ^{[Trans] [Path] [VNF] [Mat]}
• yrot() Func/Mod – Rotates children around the Y axis using the right-hand rule. ^{[Trans] [Path] [VNF] [Mat]}
• yscale() Func/Mod – Scales children along the Y axis. ^{[Trans] [Path] [VNF] [Mat]}
• zflip() Func/Mod – Reflects children across the XY plane. ^{[Trans] [Path] [VNF] [Mat]}
• up() Func/Mod – Translates children upwards (Z+). ^{[Trans] [Path] [VNF] [Mat]}
• zrot() Func/Mod – Rotates children around the Z axis using the right-hand rule. ^{[Trans] [Path] [VNF] [Mat]}
• zscale() Func/Mod – Scales children along the Z axis. ^{[Trans] [Path] [VNF] [Mat]}

Angle

• plane_line_angle() Func – Returns the angle between a plane and a 3d line.

Area

• polygon_area() Func – Calculate area of a 2d or 3d polygon.
• region_area() Func – Computes the area of the specified valid region.

Argument Handling

• get_anchor() Func – Returns the correct anchor from anchor and center.
• get_radius() Func – Given various radii and diameters, returns the most specific radius.
• scalar_vec3() Func – Expands a scalar or a list with length less than 3 to a length 3 vector.

Arrays

• block_matrix() Func – Make a new matrix from a block of matrices.
• column() Func – Extract a column from a matrix.
• hstack() Func – Make a new matrix by stacking matrices horizontally.
• submatrix() Func – Extract a submatrix from a matrix
• submatrix_set() Func – Takes a matrix as input and change values in a submatrix.

Attachable

• cube() Func/Mod – Creates a cube with anchors for attaching children. ^{[Geom] [VNF] [Ext]}
• cuboid() Mod – Creates a cube with chamfering and roundovers. ^[Geom]
• cylinder() Func/Mod – Creates an attachable cylinder. ^{[Geom] [VNF] [Ext]}
• egg() Func/Mod – Creates an egg-shaped 2d object. ^{[Geom] [Path]}
• ellipse() Func/Mod – Creates the approximation of an ellipse or a circle. ^{[Geom] [Path]}
• fillet() Mod – Creates a smooth fillet between two faces. ^{[Geom] [VNF]}
• glued_circles() Func/Mod – Creates a shape of two circles joined by a curved waist. ^{[Geom] [Path]}
• hexagon() Func/Mod – Creates a regular hexagon. ^{[Geom] [Path]}
• keyhole() Func/Mod – Creates a 2D keyhole shape. ^{[Geom] [Path]}
• mask2d_chamfer() Func/Mod – Produces a 2D chamfer mask shape. ^{[Geom] [Path]}
• mask2d_cove() Func/Mod – Creates a 2D cove (quarter-round) mask shape. ^{[Geom] [Path]}
• mask2d_dovetail() Func/Mod – Creates a 2D dovetail mask shape. ^{[Geom] [Path]}
• mask2d_ogee() Func/Mod – Creates a 2D ogee mask shape. ^{[Geom] [Path]}
• mask2d_rabbet() Func/Mod – Creates a rabbet mask shape. ^{[Geom] [Path]}
• mask2d_roundover() Func/Mod – Creates a circular mask shape for rounding edges or beading. ^{[Geom] [Path]}
• mask2d_teardrop() Func/Mod – Creates a 2D teardrop shape with specified max angle from vertical. ^{[Geom] [Path]}
• octagon() Func/Mod – Creates a regular octagon. ^{[Geom] [Path]}
• octahedron() Func/Mod – Creates an octahedron with axis-aligned points. ^{[Geom] [VNF]}
• onion() Func/Mod – Creates an attachable onion-like shape. ^{[Geom] [VNF]}
• pentagon() Func/Mod – Creates a regular pentagon. ^{[Geom] [Path]}
• pie_slice() Func/Mod – Creates a pie slice shape. ^{[Geom] [VNF]}
• prismoid() Func/Mod – Creates a rectangular prismoid shape with optional roundovers and chamfering. ^{[Geom] [VNF]}
• rect() Func/Mod – Creates a 2d rectangle with optional corner rounding. ^{[Geom] [Path]}
• rect_tube() Mod – Creates a rectangular tube. ^[Geom]
• regular_ngon() Func/Mod – Creates a regular N-sided polygon. ^{[Geom] [Path]}
• reuleaux_polygon() Func/Mod – Creates a constant-width shape that is not circular. ^{[Geom] [Path]}
• right_triangle() Func/Mod – Creates a right triangle. ^{[Geom] [Path]}
• ring() Func/Mod – Draws a 2D ring or partial ring or returns a region or path ^{[Geom] [Region] [Path]}
• sphere() Func/Mod – Creates an attachable spherical object. ^{[Geom] [VNF] [Ext]}
• spheroid() Func/Mod – Creates an attachable spherical object with controllable triangulation. ^{[Geom] [VNF]}
• squircle() Func/Mod – Creates a shape between a circle and a square, centered on the origin. ^{[Geom] [Path]}
• star() Func/Mod – Creates a star-shaped polygon or returns a star-shaped region. ^{[Geom] [Path]}
• supershape() Func/Mod – Creates a 2D Superformula shape. ^{[Geom] [Path]}
• teardrop() Func/Mod – Creates a teardrop shape. ^{[Geom] [VNF]}
• teardrop2d() Func/Mod – Creates a 2D teardrop shape. ^{[Geom] [Path]}
• torus() Func/Mod – Creates an attachable torus. ^{[Geom] [VNF]}
• trapezoid() Func/Mod – Creates a trapezoid with parallel top and bottom sides. ^{[Geom] [Path]}
• tube() Mod – Creates a cylindrical or conical tube. ^[Geom]
• wedge() Func/Mod – Creates a 3d triangular wedge. ^{[Geom] [VNF]}

Attachment

• EDGE() Func – Named edge anchor constants
• FACE() Func – Named face anchor constants

Attachments

• align() Mod – Position children with alignment to parent edges. ^[Trans]
• anchor_arrow() Mod – Shows a 3d anchor orientation arrow. ^[Geom]
• anchor_arrow2d() Mod – Shows a 2d anchor orientation arrow. ^[Geom]
• attach() Mod – Attaches children to a parent object at an anchor point and with anchor orientation. ^[Trans]
• attach_geom() Func – Returns the internal geometry description of an attachable object.
• attachable() Mod – Manages the anchoring, spin, orientation, and attachments for an object.
• color_this() Mod – Sets the color for children at the current level only. ^[Trans]
• conv_hull() Mod – Performs a hull operation on the children using tags to determine what happens.
• corner_mask() Mod – Attaches a 3d mask shape to the given corners of the parent. ^[Trans]
• corner_profile() Mod – Rotationally extrudes a 2d edge profile into corner mask on the given corners of the parent. ^[Geom]
• default_tag() Mod – Sets a default tag for all children.
• diff() Mod – Performs a differencing operation using tags rather than hierarchy to control what happens.
• edge_mask() Mod – Attaches a 3D mask shape to the given edges of the parent. ^[Trans]
• edge_profile() Mod – Extrudes a 2d edge profile into a mask on the given edges of the parent. ^[Geom]
• edge_profile_asym() Mod – Extrudes an asymmetric 2D profile into a mask on the given edges and corners of the parent. ^[Geom]
• expose_anchors() Mod – Used to show a transparent object with solid color anchor arrows.
• face_mask() Mod – Ataches a 3d mask shape to the given faces of the parent. ^[Trans]
• face_profile() Mod – Extrudes a 2D edge profile into a mask for all edges and corners of the given faces on the parent. ^[Geom]
• force_tag() Mod – Assigns a tag to a non-attachable object.
• frame_ref() Mod – Shows axis orientation arrows. ^[Geom]
• generic_airplane() Mod – Shows a generic airplane shape, useful for viewing orientations. ^[Geom]
• ghost() Mod – Sets % modifier for attachable children and their descendents. ^[Trans]
• ghost_this() Mod – Apply % modifier to children at a single level. ^[Trans]
• hide() Mod – Hides attachable children with the given tags.
• hide_this() Mod – Hides attachable children at the current level
• highlight() Mod – Sets # modifier for attachable children and their descendents. ^[Trans]
• highlight_this() Mod – Apply # modifier to children at a single level. ^[Trans]
• intersect() Mod – Perform an intersection operation on children using tags rather than hierarchy to control what happens.
• named_anchor() Func – Creates an anchor data structure.
• orient() Mod – Orients children's tops in the directon of the specified anchor. ^[Trans]
• parent() Func – Returns a description (transformation state and attachment geometry) of the parent
• position() Mod – Attaches children to a parent object at an anchor point. ^[Trans]
• recolor() Mod – Sets the color for attachable children and their descendants. ^[Trans]
• reorient() Func – Calculates the transformation matrix needed to reorient an object. ^{[Trans] [Path] [VNF]}
• restore() Mod – Restores transformation state and attachment geometry from a description ^[Trans]
• show_all() Mod – Shows all children and clears tags.
• show_anchors() Mod – Shows anchors for the parent object. ^[Geom]
• show_int() Mod – Shows children with the listed tags which were already shown in the parent context.
• show_only() Mod – Show only the children with the listed tags.
• show_transform_list() Mod – Shows a list of transforms and how they connect. ^[Geom]
• tag() Mod – Assigns a tag to an object
• tag_conv_hull() Mod – Performs a conv_hull() and then sets a tag on the result.
• tag_diff() Mod – Performs a diff() and then sets a tag on the result.
• tag_intersect() Mod – Performs an intersect() and then tags the result.
• tag_scope() Mod – Creates a new tag scope.
• tag_this() Mod – Assigns a tag to an object at the current level only.
• text() Mod – Creates an attachable block of text. ^[Geom]
• text3d() Mod – Creates an attachable 3d text block. ^[Geom]

Bearings

• ball_bearing() Mod – Creates a standardized ball bearing assembly. ^[Geom]
• ball_bearing_info() Func – Returns size info for a standardized ball bearing assembly.
• linear_bearing() Mod – Creates a generic linear bearing cartridge. ^[Geom]
• linear_bearing_housing() Mod – Creates a generic linear bearing mount clamp. ^[Geom]
• lmXuu_bearing() Mod – Creates a standardized LM*UU linear bearing cartridge. ^[Geom]
• lmXuu_housing() Mod – Creates a standardized LM*UU linear bearing mount clamp. ^[Geom]
• lmXuu_info() Func – Returns the sizes of a standard LM*UU linear bearing cartridge.

Bezier Curves

• bezier_closest_point() Func – Finds the closest position on a bezier curve to a given point.
• bezier_curvature() Func – Returns the curvature at one or more given positions along a bezier curve.
• bezier_curve() Func – Computes a specified number of points on a bezier curve. ^[Path]
• bezier_derivative() Func – Evaluates the derivative of the bezier curve at the given point or points.
• bezier_length() Func – Approximate the length of part of a bezier curve.
• bezier_line_intersection() Func – Calculates where a bezier curve intersects a line.
• bezier_points() Func – Computes one or more specified points along a bezier curve. ^[Path]
• bezier_tangent() Func – Calculates unit tangent vectors along the bezier curve at one or more given positions.

Bezier Patches

• bezier_patch_flat() Func – Creates a flat bezier patch.
• bezier_patch_normals() Func – Computes surface normals for one or more places on a bezier surface patch.
• bezier_patch_points() Func – Computes one or more specified points across a bezier surface patch.
• bezier_patch_reverse() Func – Reverses the orientation of a bezier patch.
• bezier_sheet() Func – Creates a thin sheet from a bezier patch by extruding in normal to the patch ^[VNF]
• bezier_vnf() Func – Generates a (probably non-manifold) VNF for one or more bezier surface patches. ^[VNF]
• bezier_vnf_degenerate_patch() Func – Generates a VNF for a degenerate bezier surface patch. ^[VNF]
• debug_bezier_patches() Mod – Shows a bezier surface patch and its associated control points. ^[Geom]
• is_bezier_patch() Func – Returns true if the given item is a bezier patch.

Bezier Paths

• bez_begin() Func – Calculates starting bezier path control points.
• bez_end() Func – Calculates ending bezier path control points.
• bez_joint() Func – Calculates control points for a disjointed corner bezier path joint.
• bez_tang() Func – Calculates control points for a smooth bezier path joint.
• bezpath_close_to_axis() Func – Closes a 2D bezier path to the specified axis. ^[Path]
• bezpath_closest_point() Func – Finds the closest point on a bezier path to a given point.
• bezpath_curve() Func – Converts bezier path into a path of points. ^[Path]
• bezpath_length() Func – Approximate the length of a bezier path.
• bezpath_offset() Func – Forms a closed bezier path loop with a translated and reversed copy of itself. ^[Path]
• bezpath_points() Func – Computes one or more specified points along a bezier path. ^[Path]
• debug_bezier() Mod – Shows a bezier path and its associated control points. ^[Geom]
• path_to_bezpath() Func – Generates a bezier path that passes through all points in a given linear path. ^[Path]

Boolean Operations

• difference() Func/Mod – Performs a Boolean difference operation. ^{[Geom] [Region]}
• exclusive_or() Func/Mod – Performs a Boolean exclusive-or operation. ^{[Geom] [Region]}
• f_and() Func – Returns a function to check if both a and b are true.
• f_nand() Func – Returns a function to check if a and b are not both true.
• f_nor() Func – Returns a function to check if neither a nor b are true.
• f_not() Func – Returns a function to check if a is not true.
• f_or() Func – Returns a function to check if either a or b is true.
• f_xor() Func – Returns a function to check if either a or b, but not both, are true.
• intersection() Func/Mod – Performs a Boolean intersection operation. ^{[Geom] [Region]}
• union() Func/Mod – Performs a Boolean union operation. ^{[Geom] [Region]}

Boolean Testing

• is_bool_list() Func – Returns true if the argument list contains only booleans.
• num_true() Func – Returns the number of true entries in the arguemnt list.

Bottles

• bottle_adapter_cap_to_cap() Mod – Creates a generic adaptor between a cap and a cap. ^[Geom]
• bottle_adapter_neck_to_cap() Mod – Creates a generic adaptor between a neck and a cap. ^[Geom]
• bottle_adapter_neck_to_neck() Mod – Creates a generic adaptor between a neck and a neck. ^[Geom]
• generic_bottle_cap() Mod – Creates a generic cap for a bottle. ^[Geom]
• generic_bottle_neck() Mod – Creates a generic neck for a bottle. ^[Geom]
• pco1810_cap() Mod – Creates a cap for a PCO1810 standard bottle. ^[Geom]
• pco1810_neck() Mod – Creates a neck for a PCO1810 standard bottle. ^[Geom]
• pco1881_cap() Mod – Creates a cap for a PCO1881 standard bottle. ^[Geom]
• pco1881_neck() Mod – Creates a neck for a PCO1881 standard bottle. ^[Geom]
• sp_cap() Mod – Creates an SPI threaded bottle cap. ^[Geom]
• sp_diameter() Func – Returns the base diameter of an SPI bottle neck from the nominal diameter and type number.
• sp_neck() Mod – Creates an SPI threaded bottle neck. ^[Geom]

Bounding Boxes

• bounding_box() Mod – Creates the smallest bounding box that contains all the children. ^[Geom]
• pointlist_bounds() Func – Returns the min and max bounding coordinates for the given list of points.

Bounds

• bounding_box() Mod – Creates the smallest bounding box that contains all the children. ^[Geom]
• pointlist_bounds() Func – Returns the min and max bounding coordinates for the given list of points.

Calculus

• deriv() Func – Returns the first derivative estimate of a list of data.
• deriv2() Func – Returns the second derivative estimate of a list of data.
• deriv3() Func – Returns the third derivative estimate of a list of data.

Centroid

• centroid() Func – Compute centroid of a 2d or 3d polygon or a VNF.

Chamfers

• chamfer_corner_mask() Mod – Creates a shape to chamfer a 90° corner. ^[Geom]
• chamfer_cylinder_mask() Mod – Creates a shape to chamfer the end of a cylinder. ^[Geom]
• chamfer_edge_mask() Mod – Creates a shape to chamfer a 90° edge. ^[Geom]
• cyl() Func/Mod – Creates an attachable cylinder with roundovers and chamfering. ^{[Geom] [VNF]}
• regular_prism() Func/Mod – Creates a regular prism with roundovers and chamfering ^{[Geom] [VNF]}
• xcyl() Mod – creates a cylinder oriented along the X axis. ^[Geom]
• ycyl() Mod – Creates a cylinder oriented along the y axis. ^[Geom]
• zcyl() Mod – Creates a cylinder oriented along the Z axis. ^[Geom]

Circles

• circle_2tangents() Func – Given two 2d or 3d rays, find a circle tangent to both.
• circle_3points() Func – Find a circle passing through three 2d or 3d points.
• circle_circle_intersection() Func – Find the intersection points of two 2d circles.
• circle_circle_tangents() Func – Find tangents to a pair of circles in 2d.
• circle_line_intersection() Func – Find the intersection points between a 2d circle and a line, ray or segment.
• circle_point_tangents() Func – Given a circle and point, find tangents to circle passing through the point.

Clockwise

• ccw_polygon() Func – Return counter-clockwise version of a polygon.
• clockwise_polygon() Func – Return clockwise version of a polygon.
• is_polygon_clockwise() Func – Determine if a 2d polygon winds clockwise.
• reverse_polygon() Func – Reverse winding direction of polygon.

Closest

• vector_nearest() Func – Finds the k nearest points in a list to a given point.
• vector_search() Func – Finds points in a list that are close to a given point.
• vector_search_tree() Func – Makes a distance search tree for a list of points.

Collinearity

• is_collinear() Func – Determine if points are collinear.

Collision

• convex_collision() Func – Check whether the convex hulls of two point lists intersect.

Colors

• hsl() Func/Mod – Sets the color of children to a specified hue, saturation, lightness and optional alpha channel value. ^[Trans]
• hsv() Func/Mod – Sets the color of children to a hue, saturation, value and optional alpha channel value. ^[Trans]

Colorspace

• hsl() Func/Mod – Sets the color of children to a specified hue, saturation, lightness and optional alpha channel value. ^[Trans]
• hsv() Func/Mod – Sets the color of children to a hue, saturation, value and optional alpha channel value. ^[Trans]

Comparators

• are_polygons_equal() Func – Check if two polygons (not necessarily in the same point order) are equal.
• f_approx() Func – Returns a function to compare if a is approximately equal to b.
• f_cmp() Func – Returns a function to compare values.
• f_eq() Func – Returns a function to compare if a is exactly equal to b.
• f_gt() Func – Returns a function to compare if a is greater than b.
• f_gte() Func – Returns a function to compare if a is greater than or equal to b.
• f_lt() Func – Returns a function to compare if a is less than b.
• f_lte() Func – Returns a function to compare if a is less than or equal to b.
• f_napprox() Func – Returns a function to compare if a is not approximately equal to b.
• f_neq() Func – Returns a function to compare if a is not exactly equal to b.

Comparison

• are_regions_equal() Func – Returns true if given regions are the same polygons.
• point_in_region() Func – Tests if a point is inside, outside, or on the border of a region.

Comparisons

• all_equal() Func – Returns true if all items in a list are approximately equal to each other.
• all_negative() Func – Returns true if the value(s) given are less than zero.
• all_nonnegative() Func – Returns true if the value(s) given are greater than or equal to zero.
• all_nonpositive() Func – Returns true if the value(s) given are less than or equal to zero.
• all_nonzero() Func – Returns true if the value(s) given are not aproximately zero.
• all_positive() Func – Returns true if the value(s) given are greater than zero.
• all_zero() Func – Returns true if the value(s) given are aproximately zero.
• approx() Func – Returns true if two values are equal to within a small epsilon value.
• are_ends_equal() Func – Returns true if the first and last items in a list are approximately equal.
• compare_lists() Func – Compares two lists of values, possibly of different type.
• compare_vals() Func – Compares two values, possibly of different type.
• is_decreasing() Func – Returns true if exery item in a list is less than the previous item.
• is_increasing() Func – Returns true if every item in a list is greater than the previous item.

Complex Numbers

• c_conj() Func – Returns the complex conjugate of the input.
• c_div() Func – Divides two complex numbers.
• c_ident() Func – Returns an n by n complex identity matrix.
• c_imag() Func – Returns the imaginary part of a complex number, vector or matrix..
• c_mul() Func – Multiplies two complex numbers.
• c_norm() Func – Returns the norm of a complex number or vector.
• c_real() Func – Returns the real part of a complex number, vector or matrix..
• complex() Func – Replaces scalars in a list or matrix with complex number 2-vectors.
• poly_roots() Func – Returns all complex valued roots of the given real polynomial.
• polynomial() Func – Evaluate a polynomial at a real or complex value.
• quadratic_roots() Func – Computes roots for the quadratic equation.
• real_roots() Func – Returns all real roots of the given real polynomial.

Constants

• $slop Const – The slop amount to make printed items fit closely. 0.0 by default.
• BACK Const – The backwards (Y+) direction vector constant [0,1,0].
• BOTTOM Const – The down-wards (Z-) direction vector constant [0,0,-1].
• BOTTOM Const – The down-wards (Z-) direction vector constant [0,0,-1].
• CENTER Const – The center vector constant [0,0,0].
• CENTER Const – The center vector constant [0,0,0].
• CENTER Const – The center vector constant [0,0,0].
• BOTTOM Const – The down-wards (Z-) direction vector constant [0,0,-1].
• EDGE() Func – Named edge anchor constants
• EPSILON Const – A tiny value to compare floating point values. 1e-9
• FACE() Func – Named face anchor constants
• FRONT Const – The front-wards (Y-) direction vector constant [0,-1,0].
• FRONT Const – The front-wards (Y-) direction vector constant [0,-1,0].
• FRONT Const – The front-wards (Y-) direction vector constant [0,-1,0].
• IDENT Const – A constant containing the 3D identity transformation matrix. ^[Mat]
• INCH Const – A constant containing the number of millimeters in an inch. 25.4
• INF Const – The floating point value for Infinite.
• LEFT Const – The left-wards (X-) direction vector constant [-1,0,0].
• LINE Const – A constant for specifying an unbounded line in various geometry.scad functions. [false,false]
• NAN Const – The floating point value for Not a Number.
• PHI Const – The golden ratio φ (phi). Approximately 1.6180339887
• RAY Const – A constant for specifying a ray line in various geometry.scad functions. [true,false]
• RIGHT Const – The right-wards (X+) direction vector constant [1,0,0].
• SEGMENT Const – A constant for specifying a line segment in various geometry.scad functions. [true,true]
• TOP Const – The top-wards (Z+) direction vector constant [0,0,1].
• TOP Const – The top-wards (Z+) direction vector constant [0,0,1].

Convexity

• convex_collision() Func – Check whether the convex hulls of two point lists intersect.
• convex_distance() Func – Compute distance between convex hull of two point lists.
• is_polygon_convex() Func – Check if a polygon is convex.

Coordinates

• altaz_to_xyz() Func – Convert altitude/azimuth/range to 3D cartesian coordinates. ^[Path]
• cylindrical_to_xyz() Func – Convert cylindrical coordinates to cartesian coordinates. ^[Path]
• lift_plane() Func – Map a list of 2D points onto a plane in 3D. ^[Path]
• path2d() Func – Convert a path to 2D. ^[Path]
• path3d() Func – Convert a path to 3D. ^[Path]
• path4d() Func – Convert a path to 4d. ^[Path]
• point2d() Func – Convert a vector to 2D.
• point3d() Func – Convert a vector to 3D.
• point4d() Func – Convert a vector to 4d.
• polar_to_xy() Func – Convert 2D polar coordinates to cartesian coordinates. ^[Path]
• project_plane() Func – Project a set of points onto a specified plane, returning 2D points. ^[Path]
• spherical_to_xyz() Func – Convert spherical coordinates to 3D cartesian coordinates. ^[Path]
• xy_to_polar() Func – Convert 2D cartesian coordinates to polar coordinates (radius and angle)
• xyz_to_altaz() Func – Convert 3D cartesian coordinates to [altitude,azimuth,range].
• xyz_to_cylindrical() Func – Convert 3D cartesian coordinates to cylindrical coordinates.
• xyz_to_spherical() Func – Convert 3D cartesian coordinates to spherical coordinates.

Copiers

• arc_copies() Func/Mod – Distributes duplicates of children along an arc. ^{[MatList] [Trans]}
• grid_copies() Func/Mod – Places copies of children in an [X,Y] grid. ^{[MatList] [Trans]}
• line_copies() Func/Mod – Places copies of children along an arbitrary line. ^{[MatList] [Trans]}
• mirror_copy() Func/Mod – Makes a copy of children mirrored across a given plane. ^{[MatList] [Trans]}
• move_copies() Func/Mod – Translates copies of all children. ^{[MatList] [Trans]}
• path_copies() Func/Mod – Uniformly distributes copies of children along a path. ^{[MatList] [Trans]}
• rot_copies() Func/Mod – Rotates copies of children. ^{[MatList] [Trans]}
• sphere_copies() Func/Mod – Distributes copies of children over the surface of a sphere. ^{[MatList] [Trans]}
• xcopies() Func/Mod – Places copies of children along the X axis. ^{[MatList] [Trans]}
• xflip_copy() Func/Mod – Makes a copy of children mirrored across the X axis. ^{[MatList] [Trans]}
• xrot_copies() Func/Mod – Rotates copies of children around the X axis. ^{[MatList] [Trans]}
• ycopies() Func/Mod – Places copies of children along the Y axis. ^{[MatList] [Trans]}
• yflip_copy() Func/Mod – Makes a copy of children mirrored across the Y axis. ^{[MatList] [Trans]}
• yrot_copies() Func/Mod – Rotates copies of children around the Y axis. ^{[MatList] [Trans]}
• zcopies() Func/Mod – Places copies of children along the Z axis. ^{[MatList] [Trans]}
• zflip_copy() Func/Mod – Makes a copy of children mirrored across the Z axis. ^{[MatList] [Trans]}
• zrot_copies() Func/Mod – Rotates copies of children around the Z axis. ^{[MatList] [Trans]}

Coplanarity

• is_coplanar() Func – Check if 3d points are coplanar and not collinear.

CubeTruss

• cubetruss() Mod – Creates a multi-cube straight cubetruss shape. ^[Geom]
• cubetruss_clip() Mod – Creates a clip for the end of a cubetruss to snap-lock it to another cubetruss. ^[Geom]
• cubetruss_corner() Mod – Creates a multi-cube corner cubetruss shape. ^[Geom]
• cubetruss_dist() Func – Returns the length of a cubetruss truss.
• cubetruss_foot() Mod – Creates a foot that can connect two cubetrusses. ^[Geom]
• cubetruss_joiner() Mod – Creates a joiner that can connect two cubetrusses end-to-end. ^[Geom]
• cubetruss_segment() Mod – Creates a single cubetruss cube. ^[Geom]
• cubetruss_support() Mod – Creates a cubetruss support structure shape. ^[Geom]
• cubetruss_uclip() Mod – Creates a joiner that can connect two cubetrusses end-to-end. ^[Geom]

Cylinders

• chamfer_cylinder_mask() Mod – Creates a shape to chamfer the end of a cylinder. ^[Geom]
• cyl() Func/Mod – Creates an attachable cylinder with roundovers and chamfering. ^{[Geom] [VNF]}
• rounding_cylinder_mask() Mod – Creates a shape to round the end of a cylinder. ^[Geom]
• xcyl() Mod – creates a cylinder oriented along the X axis. ^[Geom]
• ycyl() Mod – Creates a cylinder oriented along the y axis. ^[Geom]
• zcyl() Mod – Creates a cylinder oriented along the Z axis. ^[Geom]

Data Structures

• binsearch() Func – Does a binary search of a sorted list to find the index of a given value.
• echo_struct() Func/Mod – Echoes the struct to the console in a formatted manner.
• hashmap() Func – Creates a hashmap manipulation function.
• is_struct() Func – Returns true if the value is a struct.
• simple_hash() Func – Returns an integer hash of a given value.
• struct_keys() Func – Returns a list of keys for a struct.
• struct_remove() Func – Removes one or more keys from a struct.
• struct_set() Func – Sets one or more key-value pairs in a struct.
• struct_val() Func – Returns the value for an key in a struct.

Debugging

• assert_approx() Mod – Assert that a value is approximately what was expected.
• assert_equal() Mod – Assert that a value is expected.
• color_overlaps() Mod – Shows ghostly children, with overlaps highlighted in color. ^[Trans]
• debug_bezier() Mod – Shows a bezier path and its associated control points. ^[Geom]
• debug_bezier_patches() Mod – Shows a bezier surface patch and its associated control points. ^[Geom]
• debug_nurbs() Mod – Shows a NURBS curve and its control points, knots and weights ^[Geom]
• debug_vnf() Mod – A replacement for vnf_polyhedron() to help with debugging. ^[VNF]
• shape_compare() Mod – Compares two child shapes. ^[Geom]
• vnf_validate() Mod – Echos non-manifold VNF errors to the console. ^[VNF]

Descriptions

• parent() Func – Returns a description (transformation state and attachment geometry) of the parent
• restore() Mod – Restores transformation state and attachment geometry from a description ^[Trans]

Dictionaries

• echo_struct() Func/Mod – Echoes the struct to the console in a formatted manner.
• is_struct() Func – Returns true if the value is a struct.
• struct_keys() Func – Returns a list of keys for a struct.
• struct_remove() Func – Removes one or more keys from a struct.
• struct_set() Func – Sets one or more key-value pairs in a struct.
• struct_val() Func – Returns the value for an key in a struct.

Distance

• closest_point() Func – Finds the closest point in a list of points.
• convex_distance() Func – Compute distance between convex hull of two point lists.
• furthest_point() Func – Finds the furthest point in a list of points.
• line_closest_point() Func – Find point on given line, segment or ray that is closest to a given point.
• point_line_distance() Func – Find shortest distance from point to a line, segment or ray.
• point_plane_distance() Func – Determine distance between a point and plane.
• ruler() Mod – Creates a ruler. ^[Geom]
• segment_distance() Func – Find smallest distance between two line semgnets.

Distributors

• arc_copies() Func/Mod – Distributes duplicates of children along an arc. ^{[MatList] [Trans]}
• grid_copies() Func/Mod – Places copies of children in an [X,Y] grid. ^{[MatList] [Trans]}
• line_copies() Func/Mod – Places copies of children along an arbitrary line. ^{[MatList] [Trans]}
• mirror_copy() Func/Mod – Makes a copy of children mirrored across a given plane. ^{[MatList] [Trans]}
• move_copies() Func/Mod – Translates copies of all children. ^{[MatList] [Trans]}
• path_copies() Func/Mod – Uniformly distributes copies of children along a path. ^{[MatList] [Trans]}
• rot_copies() Func/Mod – Rotates copies of children. ^{[MatList] [Trans]}
• sphere_copies() Func/Mod – Distributes copies of children over the surface of a sphere. ^{[MatList] [Trans]}
• xcopies() Func/Mod – Places copies of children along the X axis. ^{[MatList] [Trans]}
• xflip_copy() Func/Mod – Makes a copy of children mirrored across the X axis. ^{[MatList] [Trans]}
• xrot_copies() Func/Mod – Rotates copies of children around the X axis. ^{[MatList] [Trans]}
• ycopies() Func/Mod – Places copies of children along the Y axis. ^{[MatList] [Trans]}
• yflip_copy() Func/Mod – Makes a copy of children mirrored across the Y axis. ^{[MatList] [Trans]}
• yrot_copies() Func/Mod – Rotates copies of children around the Y axis. ^{[MatList] [Trans]}
• zcopies() Func/Mod – Places copies of children along the Z axis. ^{[MatList] [Trans]}
• zflip_copy() Func/Mod – Makes a copy of children mirrored across the Z axis. ^{[MatList] [Trans]}
• zrot_copies() Func/Mod – Rotates copies of children around the Z axis. ^{[MatList] [Trans]}

Drawing Tools

• dashed_stroke() Func/Mod – Draws a dashed line along a path or region boundry. ^{[Geom] [PathList]}
• helix() Func – Creates a 2d spiral or 3d helical path. ^[Path]
• stroke() Mod – Draws a line along a path or region boundry. ^[Geom]

Error Checking

• assert_approx() Mod – Assert that a value is approximately what was expected.
• assert_equal() Mod – Assert that a value is expected.
• deprecate() Mod – Display a console note that a module is deprecated and suggest a replacement.
• no_children() Mod – Assert that the calling module does not support children.
• no_function() Func – Assert that the argument exists only as a module and not as a function.
• no_module() Mod – Assert that the argument exists only as a function and not as a module.
• req_children() Mod – Assert that the calling module requires children.
• shape_compare() Mod – Compares two child shapes. ^[Geom]

Extrusion

• associate_vertices() Func – Create vertex association to control how skin() links vertices. ^[PathList]
• cylindrical_extrude() Mod – Extrudes 2D children outwards around a cylinder. ^[Geom]
• cylindrical_heightfield() Func/Mod – Generates a cylindrical 3d surface from a 2D grid of values. ^{[Geom] [VNF]}
• extrude_from_to() Mod – Extrudes 2D children between two points in 3D space. ^[Geom]
• linear_sweep() Func/Mod – Create a linear extrusion from a path, with optional texturing. ^{[VNF] [Geom]}
• path_extrude() Mod – Extrudes 2D children along a 3D path. ^[Geom]
• path_extrude2d() Mod – Extrudes 2D children along a 2D path. ^[Geom]
• path_sweep() Func/Mod – Sweep a 2d polygon path along a 2d or 3d path. ^{[VNF] [Geom]}
• path_sweep2d() Func/Mod – Sweep a 2d polygon path along a 2d path allowing self-intersection. ^{[VNF] [Geom]}
• rotate_sweep() Func/Mod – Create a surface of revolution from a path with optional texturing. ^{[VNF] [Geom]}
• skin() Func/Mod – Connect a sequence of arbitrary polygons into a 3D object. ^{[VNF] [Geom]}
• spiral_sweep() Func/Mod – Sweep a path along a helix. ^{[VNF] [Geom]}
• sweep() Func/Mod – Construct a 3d object from arbitrary transformations of a 2d polygon path. ^{[VNF] [Geom]}
• sweep_attach() Mod – Attach children to sides of a path_sweep parent object ^[Geom]
• texture() Func – Produce a standard texture.

Extrusions

• jittered_poly() Mod – Creates a polygon with extra points for smoother twisted extrusions. ^[Geom]

FDM Optimized

• corrugated_wall() Mod – Makes a corrugated rectangular wall. ^[Geom]
• cubetruss() Mod – Creates a multi-cube straight cubetruss shape. ^[Geom]
• cubetruss_clip() Mod – Creates a clip for the end of a cubetruss to snap-lock it to another cubetruss. ^[Geom]
• cubetruss_corner() Mod – Creates a multi-cube corner cubetruss shape. ^[Geom]
• cubetruss_dist() Func – Returns the length of a cubetruss truss.
• cubetruss_foot() Mod – Creates a foot that can connect two cubetrusses. ^[Geom]
• cubetruss_joiner() Mod – Creates a joiner that can connect two cubetrusses end-to-end. ^[Geom]
• cubetruss_segment() Mod – Creates a single cubetruss cube. ^[Geom]
• cubetruss_support() Mod – Creates a cubetruss support structure shape. ^[Geom]
• cubetruss_uclip() Mod – Creates a joiner that can connect two cubetrusses end-to-end. ^[Geom]
• hex_panel() Mod – Create a hexagon braced panel of any shape ^[Geom]
• mask2d_teardrop() Func/Mod – Creates a 2D teardrop shape with specified max angle from vertical. ^{[Geom] [Path]}
• narrowing_strut() Mod – Makes a strut like an extruded baseball home plate. ^[Geom]
• onion() Func/Mod – Creates an attachable onion-like shape. ^{[Geom] [VNF]}
• sparse_cuboid() Mod – Makes an open cross-braced cuboid ^[Geom]
• sparse_wall() Mod – Makes an open cross-braced rectangular wall. ^[Geom]
• sparse_wall2d() Mod – Makes an open cross-braced rectangular wall. ^[Geom]
• teardrop() Func/Mod – Creates a teardrop shape. ^{[Geom] [VNF]}
• teardrop_corner_mask() Mod – Creates a shape to round a 90° corner but limit the angle of overhang. ^[Geom]
• teardrop_edge_mask() Mod – Creates a shape to round a 90° edge but limit the angle of overhang. ^[Geom]
• thinning_triangle() Mod – Makes a triangular wall with a thin middle. ^[Geom]
• thinning_wall() Mod – Makes a rectangular wall with a thin middle. ^[Geom]

Filters

• filter() Func – Returns just the list items which the given function returns true for.
• find_all() Func – Returns the indices of all items in a list that a given function returns true for.

Function Literals

• accumulate() Func – Applies a 2-arg function cumulatively to the items of a list, returning a list of every result.
• binsearch() Func – Does a binary search of a sorted list to find the index of a given value.
• f_1arg() Func – Creates a factory for a 2-arg function literal, where you can optionally pre-fill the arg.
• f_2arg() Func – Creates a factory for a 2-arg function literal, where you can optionally pre-fill the args.
• f_2arg_simple() Func – Creates a factory for a 2-arg function literal, where you can optionally pre-fill the args.
• f_3arg() Func – Creates a factory for a 3-arg function literal, where you can optionally pre-fill the args.
• f_abs() Func – Returns a function to calculate the absolute value of a given number.
• f_acos() Func – Returns a function to calculate the arccosine of a value.
• f_add() Func – Returns a function to add a and b.
• f_and() Func – Returns a function to check if both a and b are true.
• f_approx() Func – Returns a function to compare if a is approximately equal to b.
• f_asin() Func – Returns a function to calculate the arcsine of a value.
• f_atan() Func – Returns a function to calculate the arctangent of a value.
• f_atan2() Func – Returns a function to calculate the arctangent of y and x
• f_ceil() Func – Returns a function to calculate the integer ceiling of a given number.
• f_chr() Func – Returns a function to get a string character from its ordinal number.
• f_cmp() Func – Returns a function to compare values.
• f_cos() Func – Returns a function to calculate the cosine of a value.
• f_cross() Func – Returns a function to calculate the norm of a given vector.
• f_div() Func – Returns a function to divide a by b.
• f_eq() Func – Returns a function to compare if a is exactly equal to b.
• f_even() Func – Returns a function to check if a is an even number.
• f_exp() Func – Returns a function to calculate the natural exponent of a given number.
• f_floor() Func – Returns a function to calculate the integer floor of a given number.
• f_gt() Func – Returns a function to compare if a is greater than b.
• f_gte() Func – Returns a function to compare if a is greater than or equal to b.
• f_is_bool() Func – Returns a function to determine if a value is a boolean.
• f_is_def() Func – Returns a function to determine if a value is not undef.
• f_is_finite() Func – Returns a function to determine if a value is a number type that is finite.
• f_is_function() Func – Returns a function to determine if a value is a function literal.
• f_is_int() Func – Returns a function to determine if a value is an integer number.
• f_is_list() Func – Returns a function to determine if a value is a list.
• f_is_nan() Func – Returns a function to determine if a value is a number type that is Not a Number (NaN).
• f_is_num() Func – Returns a function to determine if a value is a number.
• f_is_patch() Func – Returns a function to determine if a value is a Bezier Patch structure.
• f_is_path() Func – Returns a function to determine if a value is a Path (a list of points).
• f_is_range() Func – Returns a function to determine if a value is a range.
• f_is_region() Func – Returns a function to determine if a value is a Region (a list of Paths).
• f_is_string() Func – Returns a function to determine if a value is a string.
• f_is_undef() Func – Returns a function to determine if a value is undef.
• f_is_vector() Func – Returns a function to determine if a value is a list of numbers.
• f_is_vnf() Func – Returns a function to determine if a value is a VNF structure.
• f_len() Func – Returns a function to calculate the length of a string or list.
• f_ln() Func – Returns a function to calculate the natural logarithm of a given number.
• f_log() Func – Returns a function to calculate the base 10 logarithm of a given number.
• f_lt() Func – Returns a function to compare if a is less than b.
• f_lte() Func – Returns a function to compare if a is less than or equal to b.
• f_max() Func – Returns a function to calculate the maximum value of a list.
• f_max2() Func – Returns a function to calculate the maximum of two values.
• f_max3() Func – Returns a function to calculate the maximum of three values.
• f_min() Func – Returns a function to calculate the minimum value of a list.
• f_min2() Func – Returns a function to calculate the minimum of two values.
• f_min3() Func – Returns a function to calculate the minimum of three values.
• f_mod() Func – Returns a function to calculate the modulo of a divided by b.
• f_mul() Func – Returns a function to multiply a by b.
• f_nand() Func – Returns a function to check if a and b are not both true.
• f_napprox() Func – Returns a function to compare if a is not approximately equal to b.
• f_neg() Func – Returns a function to calculate -a
• f_neq() Func – Returns a function to compare if a is not exactly equal to b.
• f_nor() Func – Returns a function to check if neither a nor b are true.
• f_norm() Func – Returns a function to calculate the norm of a given vector.
• f_not() Func – Returns a function to check if a is not true.
• f_odd() Func – Returns a function to check if a is an odd number.
• f_or() Func – Returns a function to check if either a or b is true.
• f_ord() Func – Returns a function to get the ordinal number of a string character.
• f_pow() Func – Returns a function to calculate a to the power of b.
• f_round() Func – Returns a function to calculate the integer rounding of a given number.
• f_sign() Func – Returns a function to calculate the sign of a given number.
• f_sin() Func – Returns a function to calculate the sine of a value.
• f_sqr() Func – Returns a function to calculate the square of a given number.
• f_sqrt() Func – Returns a function to calculate the square root of a given number.
• f_str() Func – Returns a function to get the string representation of an arbitrary value.
• f_str2() Func – Returns a function to concatenate the string representations of two arbitrary values.
• f_str3() Func – Returns a function to concatenate the string representations of three arbitrary values.
• f_sub() Func – Returns a function to subtract a from b.
• f_tan() Func – Returns a function to calculate the tangent of a value.
• f_xor() Func – Returns a function to check if either a or b, but not both, are true.
• filter() Func – Returns just the list items which the given function returns true for.
• find_all() Func – Returns the indices of all items in a list that a given function returns true for.
• find_first() Func – Returns the index of the first item in a list, after start, that a given function returns true for.
• for_n() Func – Iteratively calls a work function n times, returning the final result.
• hashmap() Func – Creates a hashmap manipulation function.
• is_func() Func – Returns true if the argument is a function literal.
• ival() Func – Generates a function with signature (i,x) that calls func(i)
• map() Func – Applies a function to each item in a list.
• reduce() Func – Applies a 2-arg function cumulatively to the items of a list, returning the final result.
• simple_hash() Func – Returns an integer hash of a given value.
• while() Func – While a cond function returns true, iteratively calls a work function, returning the final result.
• xval() Func – Generates a function with signature (i,x) that calls func(x)

Gears

• auto_profile_shift() Func – Returns the recommended profile shift for a gear.
• bevel_gear() Func/Mod – Creates a straight, zerol, or spiral bevel gear. ^{[Geom] [VNF]}
• bevel_pitch_angle() Func – Returns the pitch cone angle for a bevel gear.
• circular_pitch() Func – Returns tooth density expressed as "circular pitch".
• crown_gear() Func/Mod – Creates a crown gear that can mesh with a spur gear. ^{[Geom] [VNF]}
• diametral_pitch() Func – Returns tooth density expressed as "diametral pitch".
• enveloping_worm() Func/Mod – Creates a double-enveloping worm that will mate with a worm gear. ^{[Geom] [VNF]}
• gear_dist() Func – Returns the distance between two gear centers for spur gears or parallel axis helical gears.
• gear_dist_skew() Func – Returns the distance between two helical gear centers with skew axes.
• module_value() Func – Returns tooth density expressed as "module"
• outer_radius() Func – Returns the outer radius for a gear.
• pitch_radius() Func – Returns the pitch radius for a gear.
• rack() Func/Mod – Creates a straight or helical gear rack. ^{[Geom] [VNF]}
• rack2d() Func/Mod – Creates a 2D gear rack. ^{[Geom] [Path]}
• ring_gear() Mod – Creates a 3D ring gear. ^[Geom]
• ring_gear2d() Mod – Creates a 2D ring gear. ^[Geom]
• spur_gear() Func/Mod – Creates a spur gear, helical gear, or internal ring gear. ^{[Geom] [VNF]}
• spur_gear2d() Func/Mod – Creates a 2D spur gear or internal ring gear. ^{[Geom] [Region]}
• worm() Func/Mod – Creates a worm that will mate with a worm gear. ^{[Geom] [VNF]}
• worm_dist() Func – Returns the distance between a worm and a worm gear
• worm_gear() Func/Mod – Creates a worm gear that will mate with a worm. ^{[Geom] [VNF]}
• worm_gear_thickness() Func – Returns the thickness for a worm gear.

Geometry

• adj_ang_to_hyp() Func – Returns the hypotenuse length from the length of the adjacent and the angle.
• adj_ang_to_opp() Func – Returns the opposite side length from the length of the adjacent side and the angle.
• hyp_adj_to_ang() Func – Returns the angle from the lengths of the hypotenuse and the adjacent side.
• hyp_adj_to_opp() Func – Returns the opposite side length from the lengths of the hypotenuse and the adjacent side.
• adj_opp_to_ang() Func – Returns the angle from the lengths of the adjacent and opposite sides.
• adj_opp_to_hyp() Func – Returns the hypotenuse length from the lengths of the adjacent and opposite sides.
• align_polygon() Func – Find best alignment of a 2d polygon to a reference 2d polygon over a set of transformations.
• adj_ang_to_hyp() Func – Returns the hypotenuse length from the length of the adjacent and the angle.
• adj_ang_to_opp() Func – Returns the opposite side length from the length of the adjacent side and the angle.
• hyp_ang_to_adj() Func – Returns the adjacent side length from the length of the hypotenuse and the angle.
• hyp_ang_to_opp() Func – Returns the opposite side length from the length of the hypotenuse and the angle.
• opp_ang_to_adj() Func – Returns the adjacent side length from the length of the opposite side and the angle.
• opp_ang_to_hyp() Func – Returns the hypotenuse length from the length of the opposite side and the angle.
• are_points_on_plane() Func – Determine if all of the listed points are on a plane.
• are_polygons_equal() Func – Check if two polygons (not necessarily in the same point order) are equal.
• bezier_line_intersection() Func – Calculates where a bezier curve intersects a line.
• ccw_polygon() Func – Return counter-clockwise version of a polygon.
• centroid() Func – Compute centroid of a 2d or 3d polygon or a VNF.
• circle_2tangents() Func – Given two 2d or 3d rays, find a circle tangent to both.
• circle_3points() Func – Find a circle passing through three 2d or 3d points.
• circle_circle_intersection() Func – Find the intersection points of two 2d circles.
• circle_circle_tangents() Func – Find tangents to a pair of circles in 2d.
• circle_line_intersection() Func – Find the intersection points between a 2d circle and a line, ray or segment.
• circle_point_tangents() Func – Given a circle and point, find tangents to circle passing through the point.
• clockwise_polygon() Func – Return clockwise version of a polygon.
• closest_point() Func – Finds the closest point in a list of points.
• convex_collision() Func – Check whether the convex hulls of two point lists intersect.
• convex_distance() Func – Compute distance between convex hull of two point lists.
• furthest_point() Func – Finds the furthest point in a list of points.
• hull() Func – Convex hull of a list of 2d or 3d points. ^[Ext]
• hull2d_path() Func – Convex hull of a list of 2d points.
• hull3d_faces() Func – Convex hull of a list of 3d points.
• hull_points() Mod – Convex hull of a list of 2d or 3d points.
• hyp_adj_to_ang() Func – Returns the angle from the lengths of the hypotenuse and the adjacent side.
• hyp_adj_to_opp() Func – Returns the opposite side length from the lengths of the hypotenuse and the adjacent side.
• hyp_ang_to_adj() Func – Returns the adjacent side length from the length of the hypotenuse and the angle.
• hyp_ang_to_opp() Func – Returns the opposite side length from the length of the hypotenuse and the angle.
• hyp_opp_to_adj() Func – Returns the adjacent side length from the lengths of the hypotenuse and the opposite side.
• hyp_opp_to_ang() Func – Returns the angle from the lengths of the hypotenuse and the opposite side.
• is_collinear() Func – Determine if points are collinear.
• is_coplanar() Func – Check if 3d points are coplanar and not collinear.
• is_point_on_line() Func – Determine if a point is on a line, ray or segment.
• is_polygon_clockwise() Func – Determine if a 2d polygon winds clockwise.
• is_polygon_convex() Func – Check if a polygon is convex.
• law_of_cosines() Func – Applies the Law of Cosines for an arbitrary triangle.
• law_of_sines() Func – Applies the Law of Sines for an arbitrary triangle.
• line_closest_point() Func – Find point on given line, segment or ray that is closest to a given point.
• line_from_points() Func – Given a list of collinear points, return the line they define.
• line_intersection() Func – Compute intersection of two lines, segments or rays.
• line_normal() Func – Return normal vector to given line.
• adj_opp_to_ang() Func – Returns the angle from the lengths of the adjacent and opposite sides.
• adj_opp_to_hyp() Func – Returns the hypotenuse length from the lengths of the adjacent and opposite sides.
• opp_ang_to_adj() Func – Returns the adjacent side length from the length of the opposite side and the angle.
• opp_ang_to_hyp() Func – Returns the hypotenuse length from the length of the opposite side and the angle.
• hyp_opp_to_adj() Func – Returns the adjacent side length from the lengths of the hypotenuse and the opposite side.
• hyp_opp_to_ang() Func – Returns the angle from the lengths of the hypotenuse and the opposite side.
• plane3pt() Func – Return a plane from 3 points.
• plane3pt_indexed() Func – Given list of 3d points and 3 indices, return the plane they define.
• plane_closest_point() Func – Returns the orthogonal projection of points onto a plane.
• plane_from_normal() Func – Return plane defined by normal vector and a point.
• plane_from_points() Func – Return plane defined by a set of coplanar 3d points, with arbitrary normal direction.
• plane_from_polygon() Func – Given a 3d planar polygon, returns directed plane.
• plane_intersection() Func – Returns the intersection of two or three planes.
• plane_line_angle() Func – Returns the angle between a plane and a 3d line.
• plane_line_intersection() Func – Returns the intersection of a plane and 3d line, segment or ray.
• plane_normal() Func – Returns the normal vector to a plane.
• plane_offset() Func – Returns the signed offset of the plane from the origin.
• point_in_polygon() Func – Checks if a 2d point is inside or on the boundary of a 2d polygon.
• point_line_distance() Func – Find shortest distance from point to a line, segment or ray.
• point_plane_distance() Func – Determine distance between a point and plane.
• pointlist_bounds() Func – Returns the min and max bounding coordinates for the given list of points.
• polygon_area() Func – Calculate area of a 2d or 3d polygon.
• polygon_line_intersection() Func – Find intersection between 2d or 3d polygon and a line, segment or ray.
• polygon_normal() Func – Return normal to a polygon.
• polygon_triangulate() Func – Divide a polygon into triangles.
• quadratic_roots() Func – Computes roots for the quadratic equation.
• reindex_polygon() Func – Adjust point indexing of polygon to minimize pointwise distance to a reference polygon.
• reverse_polygon() Func – Reverse winding direction of polygon.
• segment_distance() Func – Find smallest distance between two line semgnets.
• segs() Func – Returns the number of sides for a circle given $fn, $fa, and $fs.
• sphere_line_intersection() Func – Find intersection between a sphere and line, ray or segment.

Hashing

• hashmap() Func – Creates a hashmap manipulation function.
• simple_hash() Func – Returns an integer hash of a given value.

Heightfield

• cylindrical_heightfield() Func/Mod – Generates a cylindrical 3d surface from a 2D grid of values. ^{[Geom] [VNF]}
• heightfield() Func/Mod – Generates a 3D surface from a 2D grid of values. ^{[Geom] [VNF]}

Hinges

• apply_folding_hinges_and_snaps() Mod – Adds snap shapes and removes living hinges from a child shape. ^[Geom]
• knuckle_hinge() Mod – Creates a knuckle-hinge shape. ^[Geom]
• living_hinge_mask() Mod – Creates a mask to make a folding "living" hinge. ^[Geom]
• snap_lock() Mod – Creates a snap-lock shape. ^[Geom]
• snap_socket() Mod – Creates a snap-lock socket shape. ^[Geom]

Hulling

• conv_hull() Mod – Performs a hull operation on the children using tags to determine what happens.
• hull() Func – Convex hull of a list of 2d or 3d points. ^[Ext]
• hull2d_path() Func – Convex hull of a list of 2d points.
• hull3d_faces() Func – Convex hull of a list of 3d points.
• hull_points() Mod – Convex hull of a list of 2d or 3d points.

Indexing

• count() Func – Creates a list of incrementing numbers.

Interpolation

• lerp() Func – Linearly interpolates between two values.
• lerpn() Func – Returns exactly n values, linearly interpolated between a and b.
• rot_resample() Func – Resample a list of rotation operators. ^[MatList]

Intersection

• bezier_line_intersection() Func – Calculates where a bezier curve intersects a line.
• circle_line_intersection() Func – Find the intersection points between a 2d circle and a line, ray or segment.
• convex_collision() Func – Check whether the convex hulls of two point lists intersect.
• plane_intersection() Func – Returns the intersection of two or three planes.
• plane_line_intersection() Func – Returns the intersection of a plane and 3d line, segment or ray.
• polygon_line_intersection() Func – Find intersection between 2d or 3d polygon and a line, segment or ray.
• sphere_line_intersection() Func – Find intersection between a sphere and line, ray or segment.

Iteration

• combinations() Func – Returns a list of all combinations of the list entries.
• for_n() Func – Iteratively calls a work function n times, returning the final result.
• idx() Func – Returns a range useful for iterating over a list.
• loop_done() Func – Returns true if the argument indicates the current C-style loop is finishing.
• loop_while() Func – Returns true if both arguments indicate the current C-style loop should continue.
• looping() Func – Returns true if the argument indicates the current C-style loop should continue.
• pair() Func – Returns a list of overlapping consecutive pairs in a list.
• permutations() Func – Returns a list of all permutations of the list entries.
• triplet() Func – Returns a list of overlapping consecutive triplets in a list.
• while() Func – While a cond function returns true, iteratively calls a work function, returning the final result.

Joiners

• dovetail() Mod – Creates a possibly tapered dovetail shape. ^[Geom]
• half_joiner() Func/Mod – Creates a half-joiner shape to mate with a half_joiner2() shape.. ^{[Geom] [VNF]}
• half_joiner2() Func/Mod – Creates a half_joiner2 shape to mate with a half_joiner() shape.. ^{[Geom] [VNF]}
• half_joiner_clear() Func/Mod – Creates a mask to clear space for a half_joiner(). ^{[Geom] [VNF]}
• joiner() Mod – Creates a joiner shape that can mate with another rotated joiner shape. ^[Geom]
• joiner_clear() Mod – Creates a mask to clear space for a joiner() shape. ^[Geom]
• rabbit_clip() Mod – Creates a rabbit-eared clip that can snap into a slot. ^[Geom]
• snap_pin() Mod – Creates a snap-pin that can slot into a snap_pin_socket() to join two parts. ^[Geom]
• snap_pin_socket() Mod – Creates a snap-pin socket for a snap_pin() to slot into. ^[Geom]

Knurling

• cylindrical_heightfield() Func/Mod – Generates a cylindrical 3d surface from a 2D grid of values. ^{[Geom] [VNF]}

Linear Algebra

• back_substitute() Func – Solve an upper triangular system, Rx=b.
• cholesky() Func – Compute the Cholesky factorization of a matrix.
• det2() Func – Compute determinant of 2x2 matrix.
• det3() Func – Compute determinant of 3x3 matrix.
• det4() Func – Compute determinant of 4x4 matrix.
• determinant() Func – compute determinant of an arbitrary square matrix.
• linear_solve() Func – Solve Ax=b or, for overdetermined case, solve the least square problem.
• linear_solve3() Func – Fast solution to Ax=b where A is 3x3.
• matrix_inverse() Func – General matrix inverse.
• matrix_trace() Func – Compute the trace of a square matrix.
• norm_fro() Func – Compute Frobenius norm of a matrix
• null_space() Func – Return basis for the null space of A.
• outer_product() Func – Compute the outer product of two vectors.
• qr_factor() Func – Compute QR factorization of a matrix.
• rot_inverse() Func – Invert 2d or 3d rotation transformations.
• transpose() Func – Transpose a matrix

Lines

• circle_line_intersection() Func – Find the intersection points between a 2d circle and a line, ray or segment.
• LINE Const – A constant for specifying an unbounded line in various geometry.scad functions. [false,false]
• line_closest_point() Func – Find point on given line, segment or ray that is closest to a given point.
• line_from_points() Func – Given a list of collinear points, return the line they define.
• line_intersection() Func – Compute intersection of two lines, segments or rays.
• line_normal() Func – Return normal vector to given line.
• plane_line_angle() Func – Returns the angle between a plane and a 3d line.
• plane_line_intersection() Func – Returns the intersection of a plane and 3d line, segment or ray.
• point_line_distance() Func – Find shortest distance from point to a line, segment or ray.
• polygon_line_intersection() Func – Find intersection between 2d or 3d polygon and a line, segment or ray.
• RAY Const – A constant for specifying a ray line in various geometry.scad functions. [true,false]
• SEGMENT Const – A constant for specifying a line segment in various geometry.scad functions. [true,true]
• sphere_line_intersection() Func – Find intersection between a sphere and line, ray or segment.

List Handling

• all_equal() Func – Returns true if all items in a list are approximately equal to each other.
• all_negative() Func – Returns true if the value(s) given are less than zero.
• all_nonnegative() Func – Returns true if the value(s) given are greater than or equal to zero.
• all_nonpositive() Func – Returns true if the value(s) given are less than or equal to zero.
• all_nonzero() Func – Returns true if the value(s) given are not aproximately zero.
• all_positive() Func – Returns true if the value(s) given are greater than zero.
• all_zero() Func – Returns true if the value(s) given are aproximately zero.
• are_ends_equal() Func – Returns true if the first and last items in a list are approximately equal.
• bselect() Func – Select list items using boolean index list.
• column() Func – Extract a column from a matrix.
• combinations() Func – Returns a list of all combinations of the list entries.
• compare_lists() Func – Compares two lists of values, possibly of different type.
• compare_vals() Func – Compares two values, possibly of different type.
• deduplicate() Func – Returns a list with all consecutive duplicate values removed.
• deduplicate_indexed() Func – Takes a list of indices into a list of values, and returns a list of indices whose values are not consecutively the same.
• find_approx() Func – Finds the indexes of the item(s) in the given list that are aproximately the given value.
• flatten() Func – Flattens a list of sublists into a single list.
• force_list() Func – Coerces non-list values into a list.
• force_region() Func – Given a polygon returns a region. ^[Region]
• full_flatten() Func – Recursively flattens nested sublists into a single list of non-list values.
• group_data() Func – Groups list data by integer group numbers.
• group_sort() Func – Returns a sorted list of groups of values.
• idx() Func – Returns a range useful for iterating over a list.
• in_list() Func – Returns true if a value is in a list.
• is_decreasing() Func – Returns true if exery item in a list is less than the previous item.
• is_homogeneous() Func – Returns true if all members of a list are of the same type.
• is_homogeneous() Func – Returns true if all members of a list are of the same type.
• is_increasing() Func – Returns true if every item in a list is greater than the previous item.
• is_region() Func – Returns true if the input appears to be a region.
• is_region_simple() Func – Returns true if the input is a region with no corner contact.
• is_valid_region() Func – Returns true if the input is a valid region.
• last() Func – Returns the last item of a list.
• list() Func – Expands a range into a full list.
• list_bset() Func – Returns a list where values are spread to locations indicated by a boolean index list.
• list_head() Func – Returns the elements at the beginning of a list.
• list_insert() Func – Inserts values into the middle of a list.
• list_pad() Func – Extend list to specified length.
• list_remove() Func – Removes items by index from a list.
• list_remove_values() Func – Removes items by value from a list.
• list_rotate() Func – Rotates the ordering of a list.
• list_set() Func – Sets the value of specific list items.
• list_shape() Func – Returns the dimensions of an array.
• list_smallest() Func – Returns the k smallest values in the list, in arbitrary order.
• list_tail() Func – Returns the elements at the end of a list.
• list_to_matrix() Func – Groups items in a list into sublists.
• list_unwrap() Func – Removes the last item of a list if its first and last values are equal.
• list_wrap() Func – Returns a list whose last value is the same as the first.
• make_region() Func – Converts lists of intersecting polygons into valid regions. ^[Region]
• max_index() Func – Returns the index of the minimal value in the given list.
• max_length() Func – Given a list of sublists, returns the length of the longest sublist.
• min_index() Func – Returns the index of the minimal value in the given list.
• min_length() Func – Given a list of sublists, returns the length of the shortest sublist.
• pair() Func – Returns a list of overlapping consecutive pairs in a list.
• permutations() Func – Returns a list of all permutations of the list entries.
• rainbow() Mod – Iterates through a list, displaying children in different colors. ^[Trans]
• region() Mod – Creates the 2D polygons described by the given region or list of polygons. ^[Geom]
• region_parts() Func – Splits a region into a list of connected regions. ^[RegList]
• repeat() Func – Returns a list of repeated copies of a value.
• repeat_entries() Func – Repeats list entries (as uniformly as possible) to make list of specified length.
• reverse() Func – Reverses the elements of a list.
• select() Func – Returns one or more items from a list, with wrapping.
• set_difference() Func – Returns a list of unique items that are in list A, but not in list B.
• set_intersection() Func – Returns a list of unique items that are in both given lists.
• set_union() Func – Merges two lists, returning a list of unique items.
• shuffle() Func – Randomizes the order of a list.
• slice() Func – Returns part of a list without wrapping.
• sort() Func – Returns a sorted list.
• sortidx() Func – Returns a list of sorted indices into a list.
• split_region_at_region_crossings() Func – Splits regions where polygons touch and at intersections.
• triplet() Func – Returns a list of overlapping consecutive triplets in a list.
• unique() Func – Returns a sorted list with all duplicates removed.
• unique_count() Func – Returns a sorted list of unique items with counts.

Lists

• vnf_from_polygons() Func – Returns a VNF from a list of 3D polygons. ^[VNF]
• vnf_from_region() Func – Returns a 3D VNF given a 2D region. ^[VNF]
• vnf_join() Func – Returns a single VNF structure from a list of VNF structures. ^[VNF]
• vnf_tri_array() Func – Returns a VNF from an array of points. The array need not be rectangular. ^[VNF]
• vnf_vertex_array() Func – Returns a VNF structure from a rectangular vertex list. ^[VNF]

Logic

• f_and() Func – Returns a function to check if both a and b are true.
• f_nand() Func – Returns a function to check if a and b are not both true.
• f_nor() Func – Returns a function to check if neither a nor b are true.
• f_not() Func – Returns a function to check if a is not true.
• f_or() Func – Returns a function to check if either a or b is true.
• f_xor() Func – Returns a function to check if either a or b, but not both, are true.

Looping

• accumulate() Func – Applies a 2-arg function cumulatively to the items of a list, returning a list of every result.
• filter() Func – Returns just the list items which the given function returns true for.
• find_all() Func – Returns the indices of all items in a list that a given function returns true for.
• for_n() Func – Iteratively calls a work function n times, returning the final result.
• map() Func – Applies a function to each item in a list.
• reduce() Func – Applies a 2-arg function cumulatively to the items of a list, returning the final result.
• while() Func – While a cond function returns true, iteratively calls a work function, returning the final result.

Masking

• back_half() Func/Mod – Masks the front half of an object along the X-Z plane, leaving the back half. ^{[Geom] [VNF] [Path] [Region]}
• bottom_half() Func/Mod – Masks the top half of an object along the X-Y plane, leaving the bottom half. ^{[Geom] [VNF] [Path] [Region]}
• chamfer_corner_mask() Mod – Creates a shape to chamfer a 90° corner. ^[Geom]
• chamfer_cylinder_mask() Mod – Creates a shape to chamfer the end of a cylinder. ^[Geom]
• chamfer_edge_mask() Mod – Creates a shape to chamfer a 90° edge. ^[Geom]
• corner_mask() Mod – Attaches a 3d mask shape to the given corners of the parent. ^[Trans]
• corner_profile() Mod – Rotationally extrudes a 2d edge profile into corner mask on the given corners of the parent. ^[Geom]
• edge_mask() Mod – Attaches a 3D mask shape to the given edges of the parent. ^[Trans]
• edge_profile() Mod – Extrudes a 2d edge profile into a mask on the given edges of the parent. ^[Geom]
• edge_profile_asym() Mod – Extrudes an asymmetric 2D profile into a mask on the given edges and corners of the parent. ^[Geom]
• face_mask() Mod – Ataches a 3d mask shape to the given faces of the parent. ^[Trans]
• face_profile() Mod – Extrudes a 2D edge profile into a mask for all edges and corners of the given faces on the parent. ^[Geom]
• front_half() Func/Mod – Masks the back half of an object along the X-Z plane, leaving the front half. ^{[Geom] [VNF] [Path] [Region]}
• half_of() Func/Mod – Masks half of an object at a cut plane. ^{[Geom] [VNF] [Path] [Region]}
• left_half() Func/Mod – Masks the right half of an object along the Y-Z plane, leaving the left half. ^{[Geom] [VNF] [Path] [Region]}
• partition() Mod – Cuts an object in two with matched joining edges, then separates the parts. ^{[Geom] [VNF] [Path] [Region]}
• partition_cut_mask() Mod – Creates a mask to cut an object into two subparts that can be reassembled. ^[Geom]
• partition_mask() Mod – Creates a mask to remove half an object with the remaining half suitable for reassembly. ^[Geom]
• right_half() Func/Mod – Masks the left half of an object along the Y-Z plane, leaving the right half. ^{[Geom] [VNF] [Path] [Region]}
• rounding_corner_mask() Mod – Creates a shape to round 90° corners. ^[Geom]
• rounding_cylinder_mask() Mod – Creates a shape to round the end of a cylinder. ^[Geom]
• rounding_hole_mask() Mod – Creates a shape to round the edge of a round hole. ^[Geom]
• teardrop_corner_mask() Mod – Creates a shape to round a 90° corner but limit the angle of overhang. ^[Geom]
• teardrop_edge_mask() Mod – Creates a shape to round a 90° edge but limit the angle of overhang. ^[Geom]
• top_half() Func/Mod – Masks the bottom half of an object along the X-Y plane, leaving the top half. ^{[Geom] [VNF] [Path] [Region]}

Masks

• hex_drive_mask() Mod – Creates a mask for a hex drive recess. ^[Geom]
• phillips_depth() Func – Returns the depth a phillips recess needs to be for a given diameter.
• phillips_diam() Func – Returns the diameter of a phillips recess of a given depth.
• phillips_mask() Mod – Creates a mask for a Philips screw drive. ^[Geom]
• robertson_mask() Mod – Creates a mask for a Robertson/Square drive recess. ^[Geom]
• rounding_edge_mask() Mod – Creates a shape to round a 90° edge. ^[Geom]
• torx_depth() Func – Returns the typical depth of a torx drive recess.
• torx_diam() Func – Returns the diameter of a torx drive.
• torx_info() Func – Returns the dimensions of a torx drive.
• torx_mask() Mod – Creates a mask for a torx drive recess. ^[Geom]
• torx_mask2d() Mod – Creates the 2D cross section for a torx drive recess. ^[Geom]

Masks (2D)

• mask2d_chamfer() Func/Mod – Produces a 2D chamfer mask shape. ^{[Geom] [Path]}
• mask2d_cove() Func/Mod – Creates a 2D cove (quarter-round) mask shape. ^{[Geom] [Path]}
• mask2d_dovetail() Func/Mod – Creates a 2D dovetail mask shape. ^{[Geom] [Path]}
• mask2d_ogee() Func/Mod – Creates a 2D ogee mask shape. ^{[Geom] [Path]}
• mask2d_rabbet() Func/Mod – Creates a rabbet mask shape. ^{[Geom] [Path]}
• mask2d_roundover() Func/Mod – Creates a circular mask shape for rounding edges or beading. ^{[Geom] [Path]}
• mask2d_teardrop() Func/Mod – Creates a 2D teardrop shape with specified max angle from vertical. ^{[Geom] [Path]}

Math

• acosh() Func – Returns the hyperbolic arc-cosine of the given value.
• add_scalar() Func – Adds a scalar value to every item in a vector.
• asinh() Func – Returns the hyperbolic arc-sine of the given value.
• atanh() Func – Returns the hyperbolic arc-tangent of the given value.
• binomial() Func – Returns the binomial coefficients of the integer n.
• binomial_coefficient() Func – Returns the k-th binomial coefficient of the integer n.
• c_conj() Func – Returns the complex conjugate of the input.
• c_div() Func – Divides two complex numbers.
• c_ident() Func – Returns an n by n complex identity matrix.
• c_imag() Func – Returns the imaginary part of a complex number, vector or matrix..
• c_mul() Func – Multiplies two complex numbers.
• c_norm() Func – Returns the norm of a complex number or vector.
• c_real() Func – Returns the real part of a complex number, vector or matrix..
• complex() Func – Replaces scalars in a list or matrix with complex number 2-vectors.
• constrain() Func – Returns a value constrained between minval and maxval, inclusive.
• convolve() Func – Returns the convolution of p and q.
• cosh() Func – Returns the hyperbolic cosine of the given value.
• count() Func – Creates a list of incrementing numbers.
• cumprod() Func – Returns the running cumulative product of a list of values.
• cumsum() Func – Returns the running cumulative sum of a list of values.
• deltas() Func – Returns the deltas between a list of values.
• deriv() Func – Returns the first derivative estimate of a list of data.
• deriv2() Func – Returns the second derivative estimate of a list of data.
• deriv3() Func – Returns the third derivative estimate of a list of data.
• EPSILON Const – A tiny value to compare floating point values. 1e-9
• factorial() Func – Returns the factorial of the given integer.
• gcd() Func – Returns the Greatest Common Divisor/Factor of two integers.
• hypot() Func – Returns the hypotenuse length of a 2D or 3D triangle.
• INF Const – The floating point value for Infinite.
• is_vector() Func – Returns true if the given value is a vector.
• lcm() Func – Returns the Least Common Multiple of two or more integers.
• lerp() Func – Linearly interpolates between two values.
• lerpn() Func – Returns exactly n values, linearly interpolated between a and b.
• log2() Func – Returns the log base 2 of the given value.
• mean() Func – Returns the mean value of a list of values.
• median() Func – Returns the median value of a list of values.
• modang() Func – Returns an angle normalized to between -180º and 180º.
• NAN Const – The floating point value for Not a Number.
• PHI Const – The golden ratio φ (phi). Approximately 1.6180339887
• poly_add() Func – Returns the polynomial sum of adding two polynomials.
• poly_div() Func – Returns the polynomial quotient and remainder results of dividing two polynomials.
• poly_mult() Func – Compute product of two polynomials, returning a polynomial.
• poly_roots() Func – Returns all complex valued roots of the given real polynomial.
• polynomial() Func – Evaluate a polynomial at a real or complex value.
• posmod() Func – Returns the positive modulo of a value.
• product() Func – Returns the multiplicative product of a list of values.
• quadratic_roots() Func – Computes roots for the quadratic equation.
• quant() Func – Returns x quantized to the nearest integer multiple of y.
• quantdn() Func – Returns x quantized down to an integer multiple of y.
• quantup() Func – Returns x quantized uo to an integer multiple of y.
• real_roots() Func – Returns all real roots of the given real polynomial.
• root_find() Func – Finds a root of the given continuous function.
• sinh() Func – Returns the hyperbolic sine of the given value.
• sqr() Func – Returns the square of the given value.
• sum() Func – Returns the sum of a list of values.
• sum_of_sines() Func – Returns the sum of one or more sine waves at a given angle.
• tanh() Func – Returns the hyperbolic tangent of the given value.
• unit() Func – Returns the unit length of a given vector.
• v_abs() Func – Returns the absolute values of the given vector.
• v_ceil() Func – Returns the values of the given vector, rounded up.
• v_div() Func – Returns the element-wise division of two equal-length vectors.
• v_floor() Func – Returns the values of the given vector, rounded down.
• v_lookup() Func – Like lookup(), but it can interpolate between vector results.
• v_mul() Func – Returns the element-wise multiplication of two equal-length vectors.
• v_theta() Func – Returns the angle counter-clockwise from X+ on the XY plane.
• vector_angle() Func – Returns the minor angle between two vectors.
• vector_axis() Func – Returns the perpendicular axis between two vectors.
• vector_bisect() Func – Returns the vector that bisects two vectors.
• vector_perp() Func – Returns component of a vector perpendicular to a second vector

Math Operators

• f_abs() Func – Returns a function to calculate the absolute value of a given number.
• f_acos() Func – Returns a function to calculate the arccosine of a value.
• f_add() Func – Returns a function to add a and b.
• f_asin() Func – Returns a function to calculate the arcsine of a value.
• f_atan() Func – Returns a function to calculate the arctangent of a value.
• f_atan2() Func – Returns a function to calculate the arctangent of y and x
• f_ceil() Func – Returns a function to calculate the integer ceiling of a given number.
• f_cos() Func – Returns a function to calculate the cosine of a value.
• f_div() Func – Returns a function to divide a by b.
• f_even() Func – Returns a function to check if a is an even number.
• f_exp() Func – Returns a function to calculate the natural exponent of a given number.
• f_floor() Func – Returns a function to calculate the integer floor of a given number.
• f_ln() Func – Returns a function to calculate the natural logarithm of a given number.
• f_log() Func – Returns a function to calculate the base 10 logarithm of a given number.
• f_max() Func – Returns a function to calculate the maximum value of a list.
• f_max2() Func – Returns a function to calculate the maximum of two values.
• f_max3() Func – Returns a function to calculate the maximum of three values.
• f_min() Func – Returns a function to calculate the minimum value of a list.
• f_min2() Func – Returns a function to calculate the minimum of two values.
• f_min3() Func – Returns a function to calculate the minimum of three values.
• f_mod() Func – Returns a function to calculate the modulo of a divided by b.
• f_mul() Func – Returns a function to multiply a by b.
• f_neg() Func – Returns a function to calculate -a
• f_odd() Func – Returns a function to check if a is an odd number.
• f_pow() Func – Returns a function to calculate a to the power of b.
• f_round() Func – Returns a function to calculate the integer rounding of a given number.
• f_sign() Func – Returns a function to calculate the sign of a given number.
• f_sin() Func – Returns a function to calculate the sine of a value.
• f_sqr() Func – Returns a function to calculate the square of a given number.
• f_sqrt() Func – Returns a function to calculate the square root of a given number.
• f_str3() Func – Returns a function to concatenate the string representations of three arbitrary values.
• f_sub() Func – Returns a function to subtract a from b.
• f_tan() Func – Returns a function to calculate the tangent of a value.

Matrices

• apply() Func – Applies a transformation matrix to a point, list of points, array of points, or a VNF. ^{[Path] [VNF] [Mat]}
• back() Func/Mod – Translates children backwards (Y+). ^{[Trans] [Path] [VNF] [Mat]}
• back_substitute() Func – Solve an upper triangular system, Rx=b.
• block_matrix() Func – Make a new matrix from a block of matrices.
• cholesky() Func – Compute the Cholesky factorization of a matrix.
• column() Func – Extract a column from a matrix.
• det2() Func – Compute determinant of 2x2 matrix.
• det3() Func – Compute determinant of 3x3 matrix.
• det4() Func – Compute determinant of 4x4 matrix.
• determinant() Func – compute determinant of an arbitrary square matrix.
• diagonal_matrix() Func – Make a diagonal matrix.
• down() Func/Mod – Translates children downwards (Z-). ^{[Trans] [Path] [VNF] [Mat]}
• echo_matrix() Func/Mod – Print a matrix neatly to the console.
• flatten() Func – Flattens a list of sublists into a single list.
• frame_map() Func/Mod – Rotates and possibly skews children from one frame of reference to another. ^{[Trans] [Path] [VNF] [Mat]}
• full_flatten() Func – Recursively flattens nested sublists into a single list of non-list values.
• fwd() Func/Mod – Translates children forwards (Y-). ^{[Trans] [Path] [VNF] [Mat]}
• hstack() Func – Make a new matrix by stacking matrices horizontally.
• IDENT Const – A constant containing the 3D identity transformation matrix. ^[Mat]
• ident() Func – Return identity matrix.
• is_matrix() Func – Check if input is a numeric matrix, optionally of specified size
• is_matrix_symmetric() Func – Checks if matrix is symmetric
• is_rotation() Func – Check if a transformation matrix represents a rotation.
• left() Func/Mod – Translates children leftwards (X-). ^{[Trans] [Path] [VNF] [Mat]}
• linear_solve() Func – Solve Ax=b or, for overdetermined case, solve the least square problem.
• linear_solve3() Func – Fast solution to Ax=b where A is 3x3.
• list_shape() Func – Returns the dimensions of an array.
• list_to_matrix() Func – Groups items in a list into sublists.
• matrix_inverse() Func – General matrix inverse.
• matrix_trace() Func – Compute the trace of a square matrix.
• mirror() Func/Mod – Reflects children across an arbitrary plane. ^{[Trans] [Path] [VNF] [Mat] [Ext]}
• move() Func/Mod – Translates children in an arbitrary direction. ^{[Trans] [Path] [VNF] [Mat]}
• norm_fro() Func – Compute Frobenius norm of a matrix
• null_space() Func – Return basis for the null space of A.
• outer_product() Func – Compute the outer product of two vectors.
• qr_factor() Func – Compute QR factorization of a matrix.
• right() Func/Mod – Translates children rightwards (X+). ^{[Trans] [Path] [VNF] [Mat]}
• rot() Func/Mod – Rotates children in various ways. ^{[Trans] [Path] [VNF] [Mat]}
• rot_decode() Func – Extract axis and rotation angle from a rotation matrix.
• rot_inverse() Func – Invert 2d or 3d rotation transformations.
• rot_resample() Func – Resample a list of rotation operators. ^[MatList]
• scale() Func/Mod – Scales children arbitrarily. ^{[Trans] [Path] [VNF] [Mat] [Ext]}
• skew() Func/Mod – Skews (or shears) children along various axes. ^{[Trans] [Path] [VNF] [Mat]}
• submatrix() Func – Extract a submatrix from a matrix
• submatrix_set() Func – Takes a matrix as input and change values in a submatrix.
• tilt() Func/Mod – Tilts children towards a direction ^{[Trans] [Path] [VNF] [Mat]}
• move() Func/Mod – Translates children in an arbitrary direction. ^{[Trans] [Path] [VNF] [Mat]}
• transpose() Func – Transpose a matrix
• up() Func/Mod – Translates children upwards (Z+). ^{[Trans] [Path] [VNF] [Mat]}
• xflip() Func/Mod – Reflects children across the YZ plane. ^{[Trans] [Path] [VNF] [Mat]}
• right() Func/Mod – Translates children rightwards (X+). ^{[Trans] [Path] [VNF] [Mat]}
• xrot() Func/Mod – Rotates children around the X axis using the right-hand rule. ^{[Trans] [Path] [VNF] [Mat]}
• xscale() Func/Mod – Scales children along the X axis. ^{[Trans] [Path] [VNF] [Mat]}
• yflip() Func/Mod – Reflects children across the XZ plane. ^{[Trans] [Path] [VNF] [Mat]}
• back() Func/Mod – Translates children backwards (Y+). ^{[Trans] [Path] [VNF] [Mat]}
• yrot() Func/Mod – Rotates children around the Y axis using the right-hand rule. ^{[Trans] [Path] [VNF] [Mat]}
• yscale() Func/Mod – Scales children along the Y axis. ^{[Trans] [Path] [VNF] [Mat]}
• zflip() Func/Mod – Reflects children across the XY plane. ^{[Trans] [Path] [VNF] [Mat]}
• up() Func/Mod – Translates children upwards (Z+). ^{[Trans] [Path] [VNF] [Mat]}
• zrot() Func/Mod – Rotates children around the Z axis using the right-hand rule. ^{[Trans] [Path] [VNF] [Mat]}
• zscale() Func/Mod – Scales children along the Z axis. ^{[Trans] [Path] [VNF] [Mat]}

Mini-Language

• turtle() Func – Uses turtle graphics to generate a 2D path. ^[Path]
• turtle3d() Func – Extends turtle graphics to 3d. Generates a 3D path or returns a list of transforms. ^{[MatList] [Path]}

Mirroring

• mirror() Func/Mod – Reflects children across an arbitrary plane. ^{[Trans] [Path] [VNF] [Mat] [Ext]}
• xflip() Func/Mod – Reflects children across the YZ plane. ^{[Trans] [Path] [VNF] [Mat]}
• yflip() Func/Mod – Reflects children across the XZ plane. ^{[Trans] [Path] [VNF] [Mat]}
• zflip() Func/Mod – Reflects children across the XY plane. ^{[Trans] [Path] [VNF] [Mat]}

Miscellaneous

• bounding_box() Mod – Creates the smallest bounding box that contains all the children. ^[Geom]
• chain_hull() Mod – Performs the union of hull operations between consecutive pairs of children. ^[Geom]
• cylindrical_extrude() Mod – Extrudes 2D children outwards around a cylinder. ^[Geom]
• extrude_from_to() Mod – Extrudes 2D children between two points in 3D space. ^[Geom]
• minkowski_difference() Mod – Removes diff shapes from base shape surface. ^[Geom]
• offset3d() Mod – Expands or contracts the surface of a 3D object. ^[Geom]
• path_extrude() Mod – Extrudes 2D children along a 3D path. ^[Geom]
• path_extrude2d() Mod – Extrudes 2D children along a 2D path. ^[Geom]
• round3d() Mod – Rounds arbitrary 3d objects. ^[Geom]

Modifiers

• ghost() Mod – Sets % modifier for attachable children and their descendents. ^[Trans]
• ghost_this() Mod – Apply % modifier to children at a single level. ^[Trans]
• highlight() Mod – Sets # modifier for attachable children and their descendents. ^[Trans]
• highlight_this() Mod – Apply # modifier to children at a single level. ^[Trans]

Modular Hose

• modular_hose() Mod – Creates modular hose parts.
• modular_hose_radius() Func – Returns the waist radius of the given modular hose size.

Motors

• nema_motor_info() Func – Returns dimension info for a given NEMA motor size.
• nema_mount_mask() Mod – Creates a standard NEMA mount holes mask. ^[Geom]
• nema_stepper_motor() Mod – Creates a NEMA standard stepper motor model. ^[Geom]

NURBS

• debug_nurbs() Mod – Shows a NURBS curve and its control points, knots and weights ^[Geom]

NURBS Curves

• nurbs_curve() Func – Computes one more more points on a NURBS curve. ^[Path]

NURBS Patches

• is_nurbs_patch() Func – Returns true if the given item looks like a NURBS patch.
• nurbs_patch_points() Func – Computes specifies point(s) on a NURBS surface patch
• nurbs_vnf() Func – Generates a (possibly non-manifold) VNF for a single NURBS surface patch. ^[VNF]

Offsets

• bent_cutout_mask() Mod – Create a mask for making a round-edged cutout in a cylindrical shell. ^[Geom]
• convex_offset_extrude() Mod – Make a solid from geometry where offset changes along the object's length. ^[Geom]
• join_prism() Func/Mod – Join an arbitrary prism to a plane, sphere, cylinder or another arbitrary prism with a fillet. ^{[Geom] [VNF]}
• offset_sweep() Func/Mod – Make a solid from a polygon with offset that changes along its length. ^{[Geom] [VNF]}
• rounded_prism() Func/Mod – Make a rounded 3d object by connecting two polygons with the same vertex count. ^{[Geom] [VNF]}

Partitions

• back_half() Func/Mod – Masks the front half of an object along the X-Z plane, leaving the back half. ^{[Geom] [VNF] [Path] [Region]}
• bottom_half() Func/Mod – Masks the top half of an object along the X-Y plane, leaving the bottom half. ^{[Geom] [VNF] [Path] [Region]}
• front_half() Func/Mod – Masks the back half of an object along the X-Z plane, leaving the front half. ^{[Geom] [VNF] [Path] [Region]}
• half_of() Func/Mod – Masks half of an object at a cut plane. ^{[Geom] [VNF] [Path] [Region]}
• left_half() Func/Mod – Masks the right half of an object along the Y-Z plane, leaving the left half. ^{[Geom] [VNF] [Path] [Region]}
• partition() Mod – Cuts an object in two with matched joining edges, then separates the parts. ^{[Geom] [VNF] [Path] [Region]}
• partition_cut_mask() Mod – Creates a mask to cut an object into two subparts that can be reassembled. ^[Geom]
• partition_mask() Mod – Creates a mask to remove half an object with the remaining half suitable for reassembly. ^[Geom]
• right_half() Func/Mod – Masks the left half of an object along the Y-Z plane, leaving the right half. ^{[Geom] [VNF] [Path] [Region]}
• top_half() Func/Mod – Masks the bottom half of an object along the X-Y plane, leaving the top half. ^{[Geom] [VNF] [Path] [Region]}

Parts

• apply_folding_hinges_and_snaps() Mod – Adds snap shapes and removes living hinges from a child shape. ^[Geom]
• auto_profile_shift() Func – Returns the recommended profile shift for a gear.
• ball_bearing() Mod – Creates a standardized ball bearing assembly. ^[Geom]
• ball_bearing_info() Func – Returns size info for a standardized ball bearing assembly.
• bevel_gear() Func/Mod – Creates a straight, zerol, or spiral bevel gear. ^{[Geom] [VNF]}
• bevel_pitch_angle() Func – Returns the pitch cone angle for a bevel gear.
• circular_pitch() Func – Returns tooth density expressed as "circular pitch".
• crown_gear() Func/Mod – Creates a crown gear that can mesh with a spur gear. ^{[Geom] [VNF]}
• cubetruss() Mod – Creates a multi-cube straight cubetruss shape. ^[Geom]
• cubetruss_clip() Mod – Creates a clip for the end of a cubetruss to snap-lock it to another cubetruss. ^[Geom]
• cubetruss_corner() Mod – Creates a multi-cube corner cubetruss shape. ^[Geom]
• cubetruss_dist() Func – Returns the length of a cubetruss truss.
• cubetruss_foot() Mod – Creates a foot that can connect two cubetrusses. ^[Geom]
• cubetruss_joiner() Mod – Creates a joiner that can connect two cubetrusses end-to-end. ^[Geom]
• cubetruss_segment() Mod – Creates a single cubetruss cube. ^[Geom]
• cubetruss_support() Mod – Creates a cubetruss support structure shape. ^[Geom]
• cubetruss_uclip() Mod – Creates a joiner that can connect two cubetrusses end-to-end. ^[Geom]
• diametral_pitch() Func – Returns tooth density expressed as "diametral pitch".
• dovetail() Mod – Creates a possibly tapered dovetail shape. ^[Geom]
• enveloping_worm() Func/Mod – Creates a double-enveloping worm that will mate with a worm gear. ^{[Geom] [VNF]}
• gear_dist() Func – Returns the distance between two gear centers for spur gears or parallel axis helical gears.
• gear_dist_skew() Func – Returns the distance between two helical gear centers with skew axes.
• half_joiner() Func/Mod – Creates a half-joiner shape to mate with a half_joiner2() shape.. ^{[Geom] [VNF]}
• half_joiner2() Func/Mod – Creates a half_joiner2 shape to mate with a half_joiner() shape.. ^{[Geom] [VNF]}
• half_joiner_clear() Func/Mod – Creates a mask to clear space for a half_joiner(). ^{[Geom] [VNF]}
• joiner() Mod – Creates a joiner shape that can mate with another rotated joiner shape. ^[Geom]
• joiner_clear() Mod – Creates a mask to clear space for a joiner() shape. ^[Geom]
• knuckle_hinge() Mod – Creates a knuckle-hinge shape. ^[Geom]
• linear_bearing() Mod – Creates a generic linear bearing cartridge. ^[Geom]
• linear_bearing_housing() Mod – Creates a generic linear bearing mount clamp. ^[Geom]
• living_hinge_mask() Mod – Creates a mask to make a folding "living" hinge. ^[Geom]
• lmXuu_bearing() Mod – Creates a standardized LM*UU linear bearing cartridge. ^[Geom]
• lmXuu_housing() Mod – Creates a standardized LM*UU linear bearing mount clamp. ^[Geom]
• lmXuu_info() Func – Returns the sizes of a standard LM*UU linear bearing cartridge.
• manfrotto_rc2_plate() Mod – Creates a Manfrotto RC2 tripod quick release mount plate. ^[Geom]
• modular_hose() Mod – Creates modular hose parts.
• modular_hose_radius() Func – Returns the waist radius of the given modular hose size.
• module_value() Func – Returns tooth density expressed as "module"
• nema_motor_info() Func – Returns dimension info for a given NEMA motor size.
• nema_mount_mask() Mod – Creates a standard NEMA mount holes mask. ^[Geom]
• nema_stepper_motor() Mod – Creates a NEMA standard stepper motor model. ^[Geom]
• outer_radius() Func – Returns the outer radius for a gear.
• pitch_radius() Func – Returns the pitch radius for a gear.
• rabbit_clip() Mod – Creates a rabbit-eared clip that can snap into a slot. ^[Geom]
• rack() Func/Mod – Creates a straight or helical gear rack. ^{[Geom] [VNF]}
• rack2d() Func/Mod – Creates a 2D gear rack. ^{[Geom] [Path]}
• rail() Mod – Creates a V-groove rail. ^[Geom]
• regular_polyhedron() Mod – Creates a regular polyhedron with optional rounding. ^[Geom]
• regular_polyhedron_info() Func – Returns info used to create a regular polyhedron.
• ring_gear() Mod – Creates a 3D ring gear. ^[Geom]
• ring_gear2d() Mod – Creates a 2D ring gear. ^[Geom]
• slider() Mod – Creates a V-groove slider. ^[Geom]
• snap_lock() Mod – Creates a snap-lock shape. ^[Geom]
• snap_pin() Mod – Creates a snap-pin that can slot into a snap_pin_socket() to join two parts. ^[Geom]
• snap_pin_socket() Mod – Creates a snap-pin socket for a snap_pin() to slot into. ^[Geom]
• snap_socket() Mod – Creates a snap-lock socket shape. ^[Geom]
• spur_gear() Func/Mod – Creates a spur gear, helical gear, or internal ring gear. ^{[Geom] [VNF]}
• spur_gear2d() Func/Mod – Creates a 2D spur gear or internal ring gear. ^{[Geom] [Region]}
• worm() Func/Mod – Creates a worm that will mate with a worm gear. ^{[Geom] [VNF]}
• worm_dist() Func – Returns the distance between a worm and a worm gear
• worm_gear() Func/Mod – Creates a worm gear that will mate with a worm. ^{[Geom] [VNF]}
• worm_gear_thickness() Func – Returns the thickness for a worm gear.

Path Generators

• arc() Func/Mod – Draws a 2D pie-slice or returns 2D or 3D path forming an arc. ^{[Geom] [Path]}
• egg() Func/Mod – Creates an egg-shaped 2d object. ^{[Geom] [Path]}
• ellipse() Func/Mod – Creates the approximation of an ellipse or a circle. ^{[Geom] [Path]}
• glued_circles() Func/Mod – Creates a shape of two circles joined by a curved waist. ^{[Geom] [Path]}
• helix() Func – Creates a 2d spiral or 3d helical path. ^[Path]
• hexagon() Func/Mod – Creates a regular hexagon. ^{[Geom] [Path]}
• keyhole() Func/Mod – Creates a 2D keyhole shape. ^{[Geom] [Path]}
• mask2d_chamfer() Func/Mod – Produces a 2D chamfer mask shape. ^{[Geom] [Path]}
• mask2d_cove() Func/Mod – Creates a 2D cove (quarter-round) mask shape. ^{[Geom] [Path]}
• mask2d_dovetail() Func/Mod – Creates a 2D dovetail mask shape. ^{[Geom] [Path]}
• mask2d_ogee() Func/Mod – Creates a 2D ogee mask shape. ^{[Geom] [Path]}
• mask2d_rabbet() Func/Mod – Creates a rabbet mask shape. ^{[Geom] [Path]}
• mask2d_roundover() Func/Mod – Creates a circular mask shape for rounding edges or beading. ^{[Geom] [Path]}
• mask2d_teardrop() Func/Mod – Creates a 2D teardrop shape with specified max angle from vertical. ^{[Geom] [Path]}
• octagon() Func/Mod – Creates a regular octagon. ^{[Geom] [Path]}
• path_text() Mod – Creates 2d or 3d text placed along a path. ^[Geom]
• pentagon() Func/Mod – Creates a regular pentagon. ^{[Geom] [Path]}
• rect() Func/Mod – Creates a 2d rectangle with optional corner rounding. ^{[Geom] [Path]}
• regular_ngon() Func/Mod – Creates a regular N-sided polygon. ^{[Geom] [Path]}
• reuleaux_polygon() Func/Mod – Creates a constant-width shape that is not circular. ^{[Geom] [Path]}
• right_triangle() Func/Mod – Creates a right triangle. ^{[Geom] [Path]}
• ring() Func/Mod – Draws a 2D ring or partial ring or returns a region or path ^{[Geom] [Region] [Path]}
• squircle() Func/Mod – Creates a shape between a circle and a square, centered on the origin. ^{[Geom] [Path]}
• star() Func/Mod – Creates a star-shaped polygon or returns a star-shaped region. ^{[Geom] [Path]}
• supershape() Func/Mod – Creates a 2D Superformula shape. ^{[Geom] [Path]}
• teardrop2d() Func/Mod – Creates a 2D teardrop shape. ^{[Geom] [Path]}
• trapezoid() Func/Mod – Creates a trapezoid with parallel top and bottom sides. ^{[Geom] [Path]}

Path Generators (2D)

• circle() Func/Mod – Creates the approximation of a circle. ^{[Geom] [Path] [Ext]}
• path_text() Mod – Creates 2d or 3d text placed along a path. ^[Geom]
• square() Func/Mod – Creates a 2D square or rectangle. ^{[Geom] [Path] [Ext]}
• turtle() Func – Uses turtle graphics to generate a 2D path. ^[Path]

Path Generators (3D)

• turtle3d() Func – Extends turtle graphics to 3d. Generates a 3D path or returns a list of transforms. ^{[MatList] [Path]}

Path Subdivision

• path_cut() Func – Cuts a path into subpaths at various points. ^[PathList]
• path_cut_points() Func – Returns a list of cut points at a list of distances from the first point in a path.
• slice_profiles() Func – Linearly interpolates between path profiles. ^[PathList]
• split_path_at_self_crossings() Func – Split a 2D path wherever it crosses itself. ^[PathList]
• subdivide_and_slice() Func – Resample list of paths to have the same point count and interpolate additional paths. ^[PathList]
• subdivide_path() Func – Subdivides a path to produce a more finely sampled path. ^[Path]

Paths

• altaz_to_xyz() Func – Convert altitude/azimuth/range to 3D cartesian coordinates. ^[Path]
• associate_vertices() Func – Create vertex association to control how skin() links vertices. ^[PathList]
• catenary() Func – Returns a 2D Catenary chain or arch path. ^[Path]
• cylindrical_to_xyz() Func – Convert cylindrical coordinates to cartesian coordinates. ^[Path]
• dashed_stroke() Func/Mod – Draws a dashed line along a path or region boundry. ^{[Geom] [PathList]}
• force_path() Func – Checks that path is a region with one component. ^[Path]
• force_region() Func – Given a polygon returns a region. ^[Region]
• helix() Func – Creates a 2d spiral or 3d helical path. ^[Path]
• is_1region() Func – Returns true if path is a region with one component.
• is_path() Func – Returns True if 'list' is a path.
• is_path_simple() Func – Returns true if a path has no self intersections.
• is_region() Func – Returns true if the input appears to be a region.
• is_region_simple() Func – Returns true if the input is a region with no corner contact.
• is_valid_region() Func – Returns true if the input is a valid region.
• lift_plane() Func – Map a list of 2D points onto a plane in 3D. ^[Path]
• list_unwrap() Func – Removes the last item of a list if its first and last values are equal.
• list_wrap() Func – Returns a list whose last value is the same as the first.
• make_region() Func – Converts lists of intersecting polygons into valid regions. ^[Region]
• offset() Func – Takes a 2D path, polygon or region and returns a path offset by an amount. ^{[Path] [Region] [Ext]}
• offset_stroke() Func/Mod – Draws a line along a path with options to specify angles and roundings at the ends. ^{[Path] [Region]}
• partition() Mod – Cuts an object in two with matched joining edges, then separates the parts. ^{[Geom] [VNF] [Path] [Region]}
• partition_cut_mask() Mod – Creates a mask to cut an object into two subparts that can be reassembled. ^[Geom]
• partition_mask() Mod – Creates a mask to remove half an object with the remaining half suitable for reassembly. ^[Geom]
• path2d() Func – Convert a path to 2D. ^[Path]
• path3d() Func – Convert a path to 3D. ^[Path]
• path4d() Func – Convert a path to 4d. ^[Path]
• path_closest_point() Func – Returns the closest place on a path to a given point.
• path_curvature() Func – Returns the estimated numerical curvature of the path.
• path_cut() Func – Cuts a path into subpaths at various points. ^[PathList]
• path_cut_points() Func – Returns a list of cut points at a list of distances from the first point in a path.
• path_extrude() Mod – Extrudes 2D children along a 3D path. ^[Geom]
• path_join() Func – Join paths end to end with optional rounding. ^[Path]
• path_length() Func – Returns the path length.
• path_length_fractions() Func – Returns the fractional distance of each point along the length of a path.
• path_merge_collinear() Func – Removes unnecessary points from a path. ^[Path]
• path_normals() Func – Returns normal vectors for each point along a path.
• path_segment_lengths() Func – Returns a list of the lengths of segments in a path.
• path_sweep() Func/Mod – Sweep a 2d polygon path along a 2d or 3d path. ^{[VNF] [Geom]}
• path_sweep2d() Func/Mod – Sweep a 2d polygon path along a 2d path allowing self-intersection. ^{[VNF] [Geom]}
• path_tangents() Func – Returns tangent vectors for each point along a path.
• path_text() Mod – Creates 2d or 3d text placed along a path. ^[Geom]
• path_torsion() Func – Returns the estimated numerical torsion of the path.
• polar_to_xy() Func – Convert 2D polar coordinates to cartesian coordinates. ^[Path]
• polygon_parts() Func – Parses a self-intersecting polygon into a list of non-intersecting polygons. ^[PathList]
• project_plane() Func – Project a set of points onto a specified plane, returning 2D points. ^[Path]
• region() Mod – Creates the 2D polygons described by the given region or list of polygons. ^[Geom]
• resample_path() Func – Returns an equidistant set of points along a path. ^[Path]
• round_corners() Func – Round or chamfer the corners of a path (clipping them off). ^[Path]
• slice_profiles() Func – Linearly interpolates between path profiles. ^[PathList]
• smooth_path() Func – Create smoothed path that passes through all the points of a given path. ^[Path]
• spherical_to_xyz() Func – Convert spherical coordinates to 3D cartesian coordinates. ^[Path]
• split_path_at_self_crossings() Func – Split a 2D path wherever it crosses itself. ^[PathList]
• subdivide_and_slice() Func – Resample list of paths to have the same point count and interpolate additional paths. ^[PathList]
• subdivide_path() Func – Subdivides a path to produce a more finely sampled path. ^[Path]
• sweep() Func/Mod – Construct a 3d object from arbitrary transformations of a 2d polygon path. ^{[VNF] [Geom]}
• sweep_attach() Mod – Attach children to sides of a path_sweep parent object ^[Geom]
• xy_to_polar() Func – Convert 2D cartesian coordinates to polar coordinates (radius and angle)
• xyz_to_altaz() Func – Convert 3D cartesian coordinates to [altitude,azimuth,range].
• xyz_to_cylindrical() Func – Convert 3D cartesian coordinates to cylindrical coordinates.
• xyz_to_spherical() Func – Convert 3D cartesian coordinates to spherical coordinates.

Paths (2D)

• arc() Func/Mod – Draws a 2D pie-slice or returns 2D or 3D path forming an arc. ^{[Geom] [Path]}
• egg() Func/Mod – Creates an egg-shaped 2d object. ^{[Geom] [Path]}
• ellipse() Func/Mod – Creates the approximation of an ellipse or a circle. ^{[Geom] [Path]}
• glued_circles() Func/Mod – Creates a shape of two circles joined by a curved waist. ^{[Geom] [Path]}
• hexagon() Func/Mod – Creates a regular hexagon. ^{[Geom] [Path]}
• keyhole() Func/Mod – Creates a 2D keyhole shape. ^{[Geom] [Path]}
• mask2d_chamfer() Func/Mod – Produces a 2D chamfer mask shape. ^{[Geom] [Path]}
• mask2d_cove() Func/Mod – Creates a 2D cove (quarter-round) mask shape. ^{[Geom] [Path]}
• mask2d_dovetail() Func/Mod – Creates a 2D dovetail mask shape. ^{[Geom] [Path]}
• mask2d_ogee() Func/Mod – Creates a 2D ogee mask shape. ^{[Geom] [Path]}
• mask2d_rabbet() Func/Mod – Creates a rabbet mask shape. ^{[Geom] [Path]}
• mask2d_roundover() Func/Mod – Creates a circular mask shape for rounding edges or beading. ^{[Geom] [Path]}
• mask2d_teardrop() Func/Mod – Creates a 2D teardrop shape with specified max angle from vertical. ^{[Geom] [Path]}
• octagon() Func/Mod – Creates a regular octagon. ^{[Geom] [Path]}
• path_text() Mod – Creates 2d or 3d text placed along a path. ^[Geom]
• pentagon() Func/Mod – Creates a regular pentagon. ^{[Geom] [Path]}
• rect() Func/Mod – Creates a 2d rectangle with optional corner rounding. ^{[Geom] [Path]}
• regular_ngon() Func/Mod – Creates a regular N-sided polygon. ^{[Geom] [Path]}
• reuleaux_polygon() Func/Mod – Creates a constant-width shape that is not circular. ^{[Geom] [Path]}
• right_triangle() Func/Mod – Creates a right triangle. ^{[Geom] [Path]}
• ring() Func/Mod – Draws a 2D ring or partial ring or returns a region or path ^{[Geom] [Region] [Path]}
• squircle() Func/Mod – Creates a shape between a circle and a square, centered on the origin. ^{[Geom] [Path]}
• star() Func/Mod – Creates a star-shaped polygon or returns a star-shaped region. ^{[Geom] [Path]}
• stroke() Mod – Draws a line along a path or region boundry. ^[Geom]
• supershape() Func/Mod – Creates a 2D Superformula shape. ^{[Geom] [Path]}
• teardrop2d() Func/Mod – Creates a 2D teardrop shape. ^{[Geom] [Path]}
• trapezoid() Func/Mod – Creates a trapezoid with parallel top and bottom sides. ^{[Geom] [Path]}

Paths (3D)

• arc() Func/Mod – Draws a 2D pie-slice or returns 2D or 3D path forming an arc. ^{[Geom] [Path]}
• path_text() Mod – Creates 2d or 3d text placed along a path. ^[Geom]
• stroke() Mod – Draws a line along a path or region boundry. ^[Geom]

Planes

• are_points_on_plane() Func – Determine if all of the listed points are on a plane.
• plane3pt() Func – Return a plane from 3 points.
• plane3pt_indexed() Func – Given list of 3d points and 3 indices, return the plane they define.
• plane_closest_point() Func – Returns the orthogonal projection of points onto a plane.
• plane_from_normal() Func – Return plane defined by normal vector and a point.
• plane_from_points() Func – Return plane defined by a set of coplanar 3d points, with arbitrary normal direction.
• plane_from_polygon() Func – Given a 3d planar polygon, returns directed plane.
• plane_intersection() Func – Returns the intersection of two or three planes.
• plane_line_angle() Func – Returns the angle between a plane and a 3d line.
• plane_line_intersection() Func – Returns the intersection of a plane and 3d line, segment or ray.
• plane_normal() Func – Returns the normal vector to a plane.
• plane_offset() Func – Returns the signed offset of the plane from the origin.
• point_plane_distance() Func – Determine distance between a point and plane.

Points

• altaz_to_xyz() Func – Convert altitude/azimuth/range to 3D cartesian coordinates. ^[Path]
• are_points_on_plane() Func – Determine if all of the listed points are on a plane.
• closest_point() Func – Finds the closest point in a list of points.
• cylindrical_to_xyz() Func – Convert cylindrical coordinates to cartesian coordinates. ^[Path]
• furthest_point() Func – Finds the furthest point in a list of points.
• is_collinear() Func – Determine if points are collinear.
• is_point_on_line() Func – Determine if a point is on a line, ray or segment.
• lift_plane() Func – Map a list of 2D points onto a plane in 3D. ^[Path]
• line_from_points() Func – Given a list of collinear points, return the line they define.
• path2d() Func – Convert a path to 2D. ^[Path]
• path3d() Func – Convert a path to 3D. ^[Path]
• path4d() Func – Convert a path to 4d. ^[Path]
• plane_from_points() Func – Return plane defined by a set of coplanar 3d points, with arbitrary normal direction.
• point2d() Func – Convert a vector to 2D.
• point3d() Func – Convert a vector to 3D.
• point4d() Func – Convert a vector to 4d.
• point_in_region() Func – Tests if a point is inside, outside, or on the border of a region.
• point_line_distance() Func – Find shortest distance from point to a line, segment or ray.
• polar_to_xy() Func – Convert 2D polar coordinates to cartesian coordinates. ^[Path]
• project_plane() Func – Project a set of points onto a specified plane, returning 2D points. ^[Path]
• random_points() Func – Returns a list of random points.
• spherical_random_points() Func – Returns a list of random points on the surface of a sphere.
• spherical_to_xyz() Func – Convert spherical coordinates to 3D cartesian coordinates. ^[Path]
• vector_nearest() Func – Finds the k nearest points in a list to a given point.
• vector_search() Func – Finds points in a list that are close to a given point.
• vector_search_tree() Func – Makes a distance search tree for a list of points.
• xy_to_polar() Func – Convert 2D cartesian coordinates to polar coordinates (radius and angle)
• xyz_to_altaz() Func – Convert 3D cartesian coordinates to [altitude,azimuth,range].
• xyz_to_cylindrical() Func – Convert 3D cartesian coordinates to cylindrical coordinates.
• xyz_to_spherical() Func – Convert 3D cartesian coordinates to spherical coordinates.

Polygon

• random_polygon() Func – Returns the CCW path of a simple random polygon.

Polygons

• align_polygon() Func – Find best alignment of a 2d polygon to a reference 2d polygon over a set of transformations.
• are_polygons_equal() Func – Check if two polygons (not necessarily in the same point order) are equal.
• are_regions_equal() Func – Returns true if given regions are the same polygons.
• ccw_polygon() Func – Return counter-clockwise version of a polygon.
• centroid() Func – Compute centroid of a 2d or 3d polygon or a VNF.
• clockwise_polygon() Func – Return clockwise version of a polygon.
• difference() Func/Mod – Performs a Boolean difference operation. ^{[Geom] [Region]}
• exclusive_or() Func/Mod – Performs a Boolean exclusive-or operation. ^{[Geom] [Region]}
• force_region() Func – Given a polygon returns a region. ^[Region]
• hull_region() Func/Mod – Compute convex hull of region or 2d path ^{[Geom] [Path]}
• intersection() Func/Mod – Performs a Boolean intersection operation. ^{[Geom] [Region]}
• is_polygon_clockwise() Func – Determine if a 2d polygon winds clockwise.
• is_region() Func – Returns true if the input appears to be a region.
• is_region_simple() Func – Returns true if the input is a region with no corner contact.
• is_valid_region() Func – Returns true if the input is a valid region.
• make_region() Func – Converts lists of intersecting polygons into valid regions. ^[Region]
• offset() Func – Takes a 2D path, polygon or region and returns a path offset by an amount. ^{[Path] [Region] [Ext]}
• plane_from_polygon() Func – Given a 3d planar polygon, returns directed plane.
• point_in_polygon() Func – Checks if a 2d point is inside or on the boundary of a 2d polygon.
• polygon_area() Func – Calculate area of a 2d or 3d polygon.
• polygon_line_intersection() Func – Find intersection between 2d or 3d polygon and a line, segment or ray.
• polygon_normal() Func – Return normal to a polygon.
• polygon_parts() Func – Parses a self-intersecting polygon into a list of non-intersecting polygons. ^[PathList]
• region() Mod – Creates the 2D polygons described by the given region or list of polygons. ^[Geom]
• reindex_polygon() Func – Adjust point indexing of polygon to minimize pointwise distance to a reference polygon.
• reverse_polygon() Func – Reverse winding direction of polygon.
• split_region_at_region_crossings() Func – Splits regions where polygons touch and at intersections.
• union() Func/Mod – Performs a Boolean union operation. ^{[Geom] [Region]}

Polyhedra

• debug_vnf() Mod – A replacement for vnf_polyhedron() to help with debugging. ^[VNF]
• regular_polyhedron() Mod – Creates a regular polyhedron with optional rounding. ^[Geom]
• regular_polyhedron_info() Func – Returns info used to create a regular polyhedron.

Projection

• plane_closest_point() Func – Returns the orthogonal projection of points onto a plane.

Quantization

• quant() Func – Returns x quantized to the nearest integer multiple of y.
• quantdn() Func – Returns x quantized down to an integer multiple of y.
• quantup() Func – Returns x quantized uo to an integer multiple of y.

Random

• exponential_rands() Func – Returns a list of random numbers with an exponential distribution.
• gaussian_rands() Func – Returns a list of random numbers with a gaussian distribution.
• rand_int() Func – Returns a random integer.
• random_points() Func – Returns a list of random points.
• random_polygon() Func – Returns the CCW path of a simple random polygon.
• spherical_random_points() Func – Returns a list of random points on the surface of a sphere.

Reflection

• mirror() Func/Mod – Reflects children across an arbitrary plane. ^{[Trans] [Path] [VNF] [Mat] [Ext]}
• xflip() Func/Mod – Reflects children across the YZ plane. ^{[Trans] [Path] [VNF] [Mat]}
• yflip() Func/Mod – Reflects children across the XZ plane. ^{[Trans] [Path] [VNF] [Mat]}
• zflip() Func/Mod – Reflects children across the XY plane. ^{[Trans] [Path] [VNF] [Mat]}

Regions

• are_regions_equal() Func – Returns true if given regions are the same polygons.
• difference() Func/Mod – Performs a Boolean difference operation. ^{[Geom] [Region]}
• exclusive_or() Func/Mod – Performs a Boolean exclusive-or operation. ^{[Geom] [Region]}
• force_path() Func – Checks that path is a region with one component. ^[Path]
• force_region() Func – Given a polygon returns a region. ^[Region]
• hull_region() Func/Mod – Compute convex hull of region or 2d path ^{[Geom] [Path]}
• intersection() Func/Mod – Performs a Boolean intersection operation. ^{[Geom] [Region]}
• is_1region() Func – Returns true if path is a region with one component.
• is_region() Func – Returns true if the input appears to be a region.
• is_region_simple() Func – Returns true if the input is a region with no corner contact.
• is_valid_region() Func – Returns true if the input is a valid region.
• make_region() Func – Converts lists of intersecting polygons into valid regions. ^[Region]
• offset() Func – Takes a 2D path, polygon or region and returns a path offset by an amount. ^{[Path] [Region] [Ext]}
• path_merge_collinear() Func – Removes unnecessary points from a path. ^[Path]
• point_in_region() Func – Tests if a point is inside, outside, or on the border of a region.
• region() Mod – Creates the 2D polygons described by the given region or list of polygons. ^[Geom]
• region_area() Func – Computes the area of the specified valid region.
• region_parts() Func – Splits a region into a list of connected regions. ^[RegList]
• ring() Func/Mod – Draws a 2D ring or partial ring or returns a region or path ^{[Geom] [Region] [Path]}
• split_region_at_region_crossings() Func – Splits regions where polygons touch and at intersections.
• union() Func/Mod – Performs a Boolean union operation. ^{[Geom] [Region]}

Revolution

• rotate_sweep() Func/Mod – Create a surface of revolution from a path with optional texturing. ^{[VNF] [Geom]}

Rotation

• arc_copies() Func/Mod – Distributes duplicates of children along an arc. ^{[MatList] [Trans]}
• cylindrical_extrude() Mod – Extrudes 2D children outwards around a cylinder. ^[Geom]
• frame_map() Func/Mod – Rotates and possibly skews children from one frame of reference to another. ^{[Trans] [Path] [VNF] [Mat]}
• rot() Func/Mod – Rotates children in various ways. ^{[Trans] [Path] [VNF] [Mat]}
• rot_copies() Func/Mod – Rotates copies of children. ^{[MatList] [Trans]}
• rot_resample() Func – Resample a list of rotation operators. ^[MatList]
• sphere_copies() Func/Mod – Distributes copies of children over the surface of a sphere. ^{[MatList] [Trans]}
• tilt() Func/Mod – Tilts children towards a direction ^{[Trans] [Path] [VNF] [Mat]}
• xrot() Func/Mod – Rotates children around the X axis using the right-hand rule. ^{[Trans] [Path] [VNF] [Mat]}
• xrot_copies() Func/Mod – Rotates copies of children around the X axis. ^{[MatList] [Trans]}
• yrot() Func/Mod – Rotates children around the Y axis using the right-hand rule. ^{[Trans] [Path] [VNF] [Mat]}
• yrot_copies() Func/Mod – Rotates copies of children around the Y axis. ^{[MatList] [Trans]}
• zrot() Func/Mod – Rotates children around the Z axis using the right-hand rule. ^{[Trans] [Path] [VNF] [Mat]}
• zrot_copies() Func/Mod – Rotates copies of children around the Z axis. ^{[MatList] [Trans]}

Rounding

• bent_cutout_mask() Mod – Create a mask for making a round-edged cutout in a cylindrical shell. ^[Geom]
• convex_offset_extrude() Mod – Make a solid from geometry where offset changes along the object's length. ^[Geom]
• cyl() Func/Mod – Creates an attachable cylinder with roundovers and chamfering. ^{[Geom] [VNF]}
• join_prism() Func/Mod – Join an arbitrary prism to a plane, sphere, cylinder or another arbitrary prism with a fillet. ^{[Geom] [VNF]}
• offset_stroke() Func/Mod – Draws a line along a path with options to specify angles and roundings at the ends. ^{[Path] [Region]}
• offset_sweep() Func/Mod – Make a solid from a polygon with offset that changes along its length. ^{[Geom] [VNF]}
• path_join() Func – Join paths end to end with optional rounding. ^[Path]
• path_to_bezpath() Func – Generates a bezier path that passes through all points in a given linear path. ^[Path]
• regular_prism() Func/Mod – Creates a regular prism with roundovers and chamfering ^{[Geom] [VNF]}
• round2d() Mod – Rounds the corners of 2d objects. ^[Geom]
• round3d() Mod – Rounds arbitrary 3d objects. ^[Geom]
• round_corners() Func – Round or chamfer the corners of a path (clipping them off). ^[Path]
• rounded_prism() Func/Mod – Make a rounded 3d object by connecting two polygons with the same vertex count. ^{[Geom] [VNF]}
• rounding_corner_mask() Mod – Creates a shape to round 90° corners. ^[Geom]
• rounding_cylinder_mask() Mod – Creates a shape to round the end of a cylinder. ^[Geom]
• rounding_edge_mask() Mod – Creates a shape to round a 90° edge. ^[Geom]
• rounding_hole_mask() Mod – Creates a shape to round the edge of a round hole. ^[Geom]
• smooth_path() Func – Create smoothed path that passes through all the points of a given path. ^[Path]
• teardrop_corner_mask() Mod – Creates a shape to round a 90° corner but limit the angle of overhang. ^[Geom]
• teardrop_edge_mask() Mod – Creates a shape to round a 90° edge but limit the angle of overhang. ^[Geom]
• xcyl() Mod – creates a cylinder oriented along the X axis. ^[Geom]
• ycyl() Mod – Creates a cylinder oriented along the y axis. ^[Geom]
• zcyl() Mod – Creates a cylinder oriented along the Z axis. ^[Geom]

Scaling

• scale() Func/Mod – Scales children arbitrarily. ^{[Trans] [Path] [VNF] [Mat] [Ext]}
• xscale() Func/Mod – Scales children along the X axis. ^{[Trans] [Path] [VNF] [Mat]}
• yscale() Func/Mod – Scales children along the Y axis. ^{[Trans] [Path] [VNF] [Mat]}
• zscale() Func/Mod – Scales children along the Z axis. ^{[Trans] [Path] [VNF] [Mat]}

Screws

• acme_threaded_nut() Mod – Creates an ACME threaded nut. ^[Geom]
• acme_threaded_rod() Mod – Creates an ACME threaded rod. ^[Geom]
• ball_screw_rod() Mod – Creates a ball screw rod. ^[Geom]
• buttress_threaded_nut() Mod – Creates a buttress-threaded nut. ^[Geom]
• buttress_threaded_rod() Mod – Creates a buttress-threaded rod. ^[Geom]
• generic_threaded_nut() Mod – Creates a generic threaded nut. ^[Geom]
• generic_threaded_rod() Mod – Creates a generic threaded rod. ^[Geom]
• hex_drive_mask() Mod – Creates a mask for a hex drive recess. ^[Geom]
• npt_threaded_rod() Mod – Creates NPT pipe threading. ^[Geom]
• nut() Mod – Creates a standard nut. ^[Geom]
• nut_info() Func – Returns the dimensions and other info for the given nut.
• nut_trap_inline() Mod – Creates an inline nut trap mask. ^[Geom]
• nut_trap_side() Mod – Creates a side nut trap mask. ^[Geom]
• phillips_depth() Func – Returns the depth a phillips recess needs to be for a given diameter.
• phillips_diam() Func – Returns the diameter of a phillips recess of a given depth.
• phillips_mask() Mod – Creates a mask for a Philips screw drive. ^[Geom]
• robertson_mask() Mod – Creates a mask for a Robertson/Square drive recess. ^[Geom]
• screw() Mod – Creates a standard screw with optional tolerances. ^[Geom]
• screw_head() Mod – Creates a screw head. ^[Geom]
• screw_hole() Mod – Creates a screw hole. ^[Geom]
• screw_info() Func – Returns the dimensions and other info for the given screw.
• shoulder_screw() Mod – Creates a shoulder screw. ^[Geom]
• square_threaded_nut() Mod – Creates a square-threaded nut. ^[Geom]
• square_threaded_rod() Mod – Creates a square-threaded rod. ^[Geom]
• thread_helix() Mod – Creates a thread helix to add to a cylinder. ^[Geom]
• thread_specification() Func – Returns the thread geometry for a given screw.
• threaded_nut() Mod – Creates an UTS/ISO triangular threaded nut. ^[Geom]
• threaded_rod() Mod – Creates an UTS/ISO triangular threaded rod. ^[Geom]
• torx_depth() Func – Returns the typical depth of a torx drive recess.
• torx_diam() Func – Returns the diameter of a torx drive.
• torx_info() Func – Returns the dimensions of a torx drive.
• torx_mask() Mod – Creates a mask for a torx drive recess. ^[Geom]
• torx_mask2d() Mod – Creates the 2D cross section for a torx drive recess. ^[Geom]
• trapezoidal_threaded_nut() Mod – Creates a trapezoidal threaded nut. ^[Geom]
• trapezoidal_threaded_rod() Mod – Creates a trapezoidal threaded rod. ^[Geom]

Search

• vector_nearest() Func – Finds the k nearest points in a list to a given point.
• vector_search() Func – Finds points in a list that are close to a given point.
• vector_search_tree() Func – Makes a distance search tree for a list of points.

Searching

• binsearch() Func – Does a binary search of a sorted list to find the index of a given value.
• find_first() Func – Returns the index of the first item in a list, after start, that a given function returns true for.

Segments

• is_point_on_line() Func – Determine if a point is on a line, ray or segment.
• segment_distance() Func – Find smallest distance between two line semgnets.

Set Handling

• set_difference() Func – Returns a list of unique items that are in list A, but not in list B.
• set_intersection() Func – Returns a list of unique items that are in both given lists.
• set_union() Func – Merges two lists, returning a list of unique items.

Shapes

• regular_polyhedron() Mod – Creates a regular polyhedron with optional rounding. ^[Geom]
• regular_polyhedron_info() Func – Returns info used to create a regular polyhedron.

Shapes (2D)

• arc() Func/Mod – Draws a 2D pie-slice or returns 2D or 3D path forming an arc. ^{[Geom] [Path]}
• circle() Func/Mod – Creates the approximation of a circle. ^{[Geom] [Path] [Ext]}
• debug_polygon() Mod – Draws an annotated polygon. ^[Geom]
• debug_region() Mod – Draws an annotated region. ^[Geom]
• egg() Func/Mod – Creates an egg-shaped 2d object. ^{[Geom] [Path]}
• ellipse() Func/Mod – Creates the approximation of an ellipse or a circle. ^{[Geom] [Path]}
• glued_circles() Func/Mod – Creates a shape of two circles joined by a curved waist. ^{[Geom] [Path]}
• hexagon() Func/Mod – Creates a regular hexagon. ^{[Geom] [Path]}
• keyhole() Func/Mod – Creates a 2D keyhole shape. ^{[Geom] [Path]}
• mask2d_chamfer() Func/Mod – Produces a 2D chamfer mask shape. ^{[Geom] [Path]}
• mask2d_cove() Func/Mod – Creates a 2D cove (quarter-round) mask shape. ^{[Geom] [Path]}
• mask2d_dovetail() Func/Mod – Creates a 2D dovetail mask shape. ^{[Geom] [Path]}
• mask2d_ogee() Func/Mod – Creates a 2D ogee mask shape. ^{[Geom] [Path]}
• mask2d_rabbet() Func/Mod – Creates a rabbet mask shape. ^{[Geom] [Path]}
• mask2d_roundover() Func/Mod – Creates a circular mask shape for rounding edges or beading. ^{[Geom] [Path]}
• mask2d_teardrop() Func/Mod – Creates a 2D teardrop shape with specified max angle from vertical. ^{[Geom] [Path]}
• octagon() Func/Mod – Creates a regular octagon. ^{[Geom] [Path]}
• pentagon() Func/Mod – Creates a regular pentagon. ^{[Geom] [Path]}
• rect() Func/Mod – Creates a 2d rectangle with optional corner rounding. ^{[Geom] [Path]}
• regular_ngon() Func/Mod – Creates a regular N-sided polygon. ^{[Geom] [Path]}
• reuleaux_polygon() Func/Mod – Creates a constant-width shape that is not circular. ^{[Geom] [Path]}
• right_triangle() Func/Mod – Creates a right triangle. ^{[Geom] [Path]}
• ring() Func/Mod – Draws a 2D ring or partial ring or returns a region or path ^{[Geom] [Region] [Path]}
• square() Func/Mod – Creates a 2D square or rectangle. ^{[Geom] [Path] [Ext]}
• squircle() Func/Mod – Creates a shape between a circle and a square, centered on the origin. ^{[Geom] [Path]}
• star() Func/Mod – Creates a star-shaped polygon or returns a star-shaped region. ^{[Geom] [Path]}
• supershape() Func/Mod – Creates a 2D Superformula shape. ^{[Geom] [Path]}
• teardrop2d() Func/Mod – Creates a 2D teardrop shape. ^{[Geom] [Path]}
• trapezoid() Func/Mod – Creates a trapezoid with parallel top and bottom sides. ^{[Geom] [Path]}
• turtle() Func – Uses turtle graphics to generate a 2D path. ^[Path]

Shapes (3D)

• chamfer_corner_mask() Mod – Creates a shape to chamfer a 90° corner. ^[Geom]
• chamfer_edge_mask() Mod – Creates a shape to chamfer a 90° edge. ^[Geom]
• cube() Func/Mod – Creates a cube with anchors for attaching children. ^{[Geom] [VNF] [Ext]}
• cuboid() Mod – Creates a cube with chamfering and roundovers. ^[Geom]
• cylinder() Func/Mod – Creates an attachable cylinder. ^{[Geom] [VNF] [Ext]}
• fillet() Mod – Creates a smooth fillet between two faces. ^{[Geom] [VNF]}
• octahedron() Func/Mod – Creates an octahedron with axis-aligned points. ^{[Geom] [VNF]}
• onion() Func/Mod – Creates an attachable onion-like shape. ^{[Geom] [VNF]}
• pie_slice() Func/Mod – Creates a pie slice shape. ^{[Geom] [VNF]}
• prismoid() Func/Mod – Creates a rectangular prismoid shape with optional roundovers and chamfering. ^{[Geom] [VNF]}
• rect_tube() Mod – Creates a rectangular tube. ^[Geom]
• rounding_corner_mask() Mod – Creates a shape to round 90° corners. ^[Geom]
• rounding_edge_mask() Mod – Creates a shape to round a 90° edge. ^[Geom]
• sphere() Func/Mod – Creates an attachable spherical object. ^{[Geom] [VNF] [Ext]}
• spheroid() Func/Mod – Creates an attachable spherical object with controllable triangulation. ^{[Geom] [VNF]}
• teardrop() Func/Mod – Creates a teardrop shape. ^{[Geom] [VNF]}
• teardrop_corner_mask() Mod – Creates a shape to round a 90° corner but limit the angle of overhang. ^[Geom]
• teardrop_edge_mask() Mod – Creates a shape to round a 90° edge but limit the angle of overhang. ^[Geom]
• torus() Func/Mod – Creates an attachable torus. ^{[Geom] [VNF]}
• tube() Mod – Creates a cylindrical or conical tube. ^[Geom]
• turtle3d() Func – Extends turtle graphics to 3d. Generates a 3D path or returns a list of transforms. ^{[MatList] [Path]}
• wedge() Func/Mod – Creates a 3d triangular wedge. ^{[Geom] [VNF]}

Shapes2D

• difference() Func/Mod – Performs a Boolean difference operation. ^{[Geom] [Region]}
• exclusive_or() Func/Mod – Performs a Boolean exclusive-or operation. ^{[Geom] [Region]}
• hull_region() Func/Mod – Compute convex hull of region or 2d path ^{[Geom] [Path]}
• intersection() Func/Mod – Performs a Boolean intersection operation. ^{[Geom] [Region]}
• union() Func/Mod – Performs a Boolean union operation. ^{[Geom] [Region]}

Shapes3D

• difference() Func/Mod – Performs a Boolean difference operation. ^{[Geom] [Region]}
• exclusive_or() Func/Mod – Performs a Boolean exclusive-or operation. ^{[Geom] [Region]}
• intersection() Func/Mod – Performs a Boolean intersection operation. ^{[Geom] [Region]}
• union() Func/Mod – Performs a Boolean union operation. ^{[Geom] [Region]}

Shearing

• skew() Func/Mod – Skews (or shears) children along various axes. ^{[Trans] [Path] [VNF] [Mat]}

Shell

• shell2d() Mod – Creates a shell from 2D children. ^[Geom]

Skewing

• skew() Func/Mod – Skews (or shears) children along various axes. ^{[Trans] [Path] [VNF] [Mat]}

Skin

• skin() Func/Mod – Connect a sequence of arbitrary polygons into a 3D object. ^{[VNF] [Geom]}

Skinning

• associate_vertices() Func – Create vertex association to control how skin() links vertices. ^[PathList]

Sliders

• rail() Mod – Creates a V-groove rail. ^[Geom]
• slider() Mod – Creates a V-groove slider. ^[Geom]

Slop

• get_slop() Func – Returns the $slop value.

Spheres

• sphere_line_intersection() Func – Find intersection between a sphere and line, ray or segment.

Spiral

• spiral_sweep() Func/Mod – Sweep a path along a helix. ^{[VNF] [Geom]}

Statistics

• convolve() Func – Returns the convolution of p and q.
• cumprod() Func – Returns the running cumulative product of a list of values.
• cumsum() Func – Returns the running cumulative sum of a list of values.
• deltas() Func – Returns the deltas between a list of values.
• exponential_rands() Func – Returns a list of random numbers with an exponential distribution.
• gaussian_rands() Func – Returns a list of random numbers with a gaussian distribution.
• mean() Func – Returns the mean value of a list of values.
• median() Func – Returns the median value of a list of values.
• product() Func – Returns the multiplicative product of a list of values.
• sum_of_sines() Func – Returns the sum of one or more sine waves at a given angle.

String Operators

• f_chr() Func – Returns a function to get a string character from its ordinal number.
• f_len() Func – Returns a function to calculate the length of a string or list.
• f_ord() Func – Returns a function to get the ordinal number of a string character.
• f_str() Func – Returns a function to get the string representation of an arbitrary value.
• f_str2() Func – Returns a function to concatenate the string representations of two arbitrary values.

Strings

• downcase() Func – Lowercases all characters in a string.
• ends_with() Func – Returns true if the string ends with a given substring.
• format() Func – Formats multiple values into a string with a given format.
• format_fixed() Func – Formats a float into a string with a fixed number of decimal places.
• format_float() Func – Formats a float into a string with a given number of significant digits.
• format_int() Func – Formats an integer into a string, with possible leading zeros.
• is_digit() Func – Returns true if all characters in the string are decimal digits.
• is_hexdigit() Func – Returns true if all characters in the string are hexidecimal digits.
• is_letter() Func – Returns true if all characters in the string are letters.
• is_lower() Func – Returns true if all characters in the string are lowercase.
• is_upper() Func – Returns true if all characters in the string are uppercase.
• parse_float() Func – Parse a float from a string.
• parse_frac() Func – Parse a float from a fraction string.
• parse_int() Func – Parse an integer from a string.
• parse_num() Func – Parse a float from a decimal or fraction string.
• rand_str() Func – Create a randomized string.
• starts_with() Func – Returns true if the string starts with a given substring.
• str_find() Func – Finds a substring in a string.
• str_join() Func – Joints a list of strings into a single string.
• str_pad() Func – Pads a string to a given length.
• str_replace_char() Func – Replace given chars in a string with another substring.
• str_split() Func – Splits a longer string wherever a given substring occurs.
• str_strip() Func – Strips given leading and trailing characters from a string.
• substr() Func – Returns a substring from a string.
• substr_match() Func – Returns true if the string pattern matches the string str.
• suffix() Func – Returns the last few characters of a string.
• upcase() Func – Uppercases all characters in a string.

Sweep

• linear_sweep() Func/Mod – Create a linear extrusion from a path, with optional texturing. ^{[VNF] [Geom]}
• path_sweep() Func/Mod – Sweep a 2d polygon path along a 2d or 3d path. ^{[VNF] [Geom]}
• path_sweep2d() Func/Mod – Sweep a 2d polygon path along a 2d path allowing self-intersection. ^{[VNF] [Geom]}
• rotate_sweep() Func/Mod – Create a surface of revolution from a path with optional texturing. ^{[VNF] [Geom]}
• spiral_sweep() Func/Mod – Sweep a path along a helix. ^{[VNF] [Geom]}
• sweep() Func/Mod – Construct a 3d object from arbitrary transformations of a 2d polygon path. ^{[VNF] [Geom]}
• sweep_attach() Mod – Attach children to sides of a path_sweep parent object ^[Geom]

Tangents

• circle_2tangents() Func – Given two 2d or 3d rays, find a circle tangent to both.
• circle_circle_tangents() Func – Find tangents to a pair of circles in 2d.
• circle_point_tangents() Func – Given a circle and point, find tangents to circle passing through the point.

Test

• is_polygon_convex() Func – Check if a polygon is convex.

Testing

• is_consistent() Func – Returns true if the argument is a list with consistent structure and finite numerical data.
• same_shape() Func – Returns true if the argument lists are numeric and of the same shape.
• shape_compare() Mod – Compares two child shapes. ^[Geom]

Text

• path_text() Mod – Creates 2d or 3d text placed along a path. ^[Geom]
• text() Mod – Creates an attachable block of text. ^[Geom]
• text3d() Mod – Creates an attachable 3d text block. ^[Geom]

Textures

• cyl() Func/Mod – Creates an attachable cylinder with roundovers and chamfering. ^{[Geom] [VNF]}
• cylindrical_heightfield() Func/Mod – Generates a cylindrical 3d surface from a 2D grid of values. ^{[Geom] [VNF]}
• heightfield() Func/Mod – Generates a 3D surface from a 2D grid of values. ^{[Geom] [VNF]}
• linear_sweep() Func/Mod – Create a linear extrusion from a path, with optional texturing. ^{[VNF] [Geom]}
• regular_prism() Func/Mod – Creates a regular prism with roundovers and chamfering ^{[Geom] [VNF]}
• rotate_sweep() Func/Mod – Create a surface of revolution from a path with optional texturing. ^{[VNF] [Geom]}
• texture() Func – Produce a standard texture.
• xcyl() Mod – creates a cylinder oriented along the X axis. ^[Geom]
• ycyl() Mod – Creates a cylinder oriented along the y axis. ^[Geom]
• zcyl() Mod – Creates a cylinder oriented along the Z axis. ^[Geom]

Threading

• acme_threaded_nut() Mod – Creates an ACME threaded nut. ^[Geom]
• acme_threaded_rod() Mod – Creates an ACME threaded rod. ^[Geom]
• ball_screw_rod() Mod – Creates a ball screw rod. ^[Geom]
• bottle_adapter_cap_to_cap() Mod – Creates a generic adaptor between a cap and a cap. ^[Geom]
• bottle_adapter_neck_to_cap() Mod – Creates a generic adaptor between a neck and a cap. ^[Geom]
• bottle_adapter_neck_to_neck() Mod – Creates a generic adaptor between a neck and a neck. ^[Geom]
• buttress_threaded_nut() Mod – Creates a buttress-threaded nut. ^[Geom]
• buttress_threaded_rod() Mod – Creates a buttress-threaded rod. ^[Geom]
• generic_bottle_cap() Mod – Creates a generic cap for a bottle. ^[Geom]
• generic_bottle_neck() Mod – Creates a generic neck for a bottle. ^[Geom]
• generic_threaded_nut() Mod – Creates a generic threaded nut. ^[Geom]
• generic_threaded_rod() Mod – Creates a generic threaded rod. ^[Geom]
• npt_threaded_rod() Mod – Creates NPT pipe threading. ^[Geom]
• nut() Mod – Creates a standard nut. ^[Geom]
• nut_info() Func – Returns the dimensions and other info for the given nut.
• nut_trap_inline() Mod – Creates an inline nut trap mask. ^[Geom]
• nut_trap_side() Mod – Creates a side nut trap mask. ^[Geom]
• pco1810_cap() Mod – Creates a cap for a PCO1810 standard bottle. ^[Geom]
• pco1810_neck() Mod – Creates a neck for a PCO1810 standard bottle. ^[Geom]
• pco1881_cap() Mod – Creates a cap for a PCO1881 standard bottle. ^[Geom]
• pco1881_neck() Mod – Creates a neck for a PCO1881 standard bottle. ^[Geom]
• screw() Mod – Creates a standard screw with optional tolerances. ^[Geom]
• screw_head() Mod – Creates a screw head. ^[Geom]
• screw_hole() Mod – Creates a screw hole. ^[Geom]
• screw_info() Func – Returns the dimensions and other info for the given screw.
• shoulder_screw() Mod – Creates a shoulder screw. ^[Geom]
• sp_cap() Mod – Creates an SPI threaded bottle cap. ^[Geom]
• sp_diameter() Func – Returns the base diameter of an SPI bottle neck from the nominal diameter and type number.
• sp_neck() Mod – Creates an SPI threaded bottle neck. ^[Geom]
• square_threaded_nut() Mod – Creates a square-threaded nut. ^[Geom]
• square_threaded_rod() Mod – Creates a square-threaded rod. ^[Geom]
• thread_helix() Mod – Creates a thread helix to add to a cylinder. ^[Geom]
• thread_specification() Func – Returns the thread geometry for a given screw.
• threaded_nut() Mod – Creates an UTS/ISO triangular threaded nut. ^[Geom]
• threaded_rod() Mod – Creates an UTS/ISO triangular threaded rod. ^[Geom]
• trapezoidal_threaded_nut() Mod – Creates a trapezoidal threaded nut. ^[Geom]
• trapezoidal_threaded_rod() Mod – Creates a trapezoidal threaded rod. ^[Geom]

Transformations

• arc_copies() Func/Mod – Distributes duplicates of children along an arc. ^{[MatList] [Trans]}
• grid_copies() Func/Mod – Places copies of children in an [X,Y] grid. ^{[MatList] [Trans]}
• line_copies() Func/Mod – Places copies of children along an arbitrary line. ^{[MatList] [Trans]}
• mirror_copy() Func/Mod – Makes a copy of children mirrored across a given plane. ^{[MatList] [Trans]}
• move_copies() Func/Mod – Translates copies of all children. ^{[MatList] [Trans]}
• path_copies() Func/Mod – Uniformly distributes copies of children along a path. ^{[MatList] [Trans]}
• rot_copies() Func/Mod – Rotates copies of children. ^{[MatList] [Trans]}
• sphere_copies() Func/Mod – Distributes copies of children over the surface of a sphere. ^{[MatList] [Trans]}
• xcopies() Func/Mod – Places copies of children along the X axis. ^{[MatList] [Trans]}
• xflip_copy() Func/Mod – Makes a copy of children mirrored across the X axis. ^{[MatList] [Trans]}
• xrot_copies() Func/Mod – Rotates copies of children around the X axis. ^{[MatList] [Trans]}
• ycopies() Func/Mod – Places copies of children along the Y axis. ^{[MatList] [Trans]}
• yflip_copy() Func/Mod – Makes a copy of children mirrored across the Y axis. ^{[MatList] [Trans]}
• yrot_copies() Func/Mod – Rotates copies of children around the Y axis. ^{[MatList] [Trans]}
• zcopies() Func/Mod – Places copies of children along the Z axis. ^{[MatList] [Trans]}
• zflip_copy() Func/Mod – Makes a copy of children mirrored across the Z axis. ^{[MatList] [Trans]}
• zrot_copies() Func/Mod – Rotates copies of children around the Z axis. ^{[MatList] [Trans]}

Transforms

• apply() Func – Applies a transformation matrix to a point, list of points, array of points, or a VNF. ^{[Path] [VNF] [Mat]}
• back() Func/Mod – Translates children backwards (Y+). ^{[Trans] [Path] [VNF] [Mat]}
• down() Func/Mod – Translates children downwards (Z-). ^{[Trans] [Path] [VNF] [Mat]}
• frame_map() Func/Mod – Rotates and possibly skews children from one frame of reference to another. ^{[Trans] [Path] [VNF] [Mat]}
• fwd() Func/Mod – Translates children forwards (Y-). ^{[Trans] [Path] [VNF] [Mat]}
• IDENT Const – A constant containing the 3D identity transformation matrix. ^[Mat]
• ident() Func – Return identity matrix.
• is_rotation() Func – Check if a transformation matrix represents a rotation.
• left() Func/Mod – Translates children leftwards (X-). ^{[Trans] [Path] [VNF] [Mat]}
• mirror() Func/Mod – Reflects children across an arbitrary plane. ^{[Trans] [Path] [VNF] [Mat] [Ext]}
• move() Func/Mod – Translates children in an arbitrary direction. ^{[Trans] [Path] [VNF] [Mat]}
• parent() Func – Returns a description (transformation state and attachment geometry) of the parent
• restore() Mod – Restores transformation state and attachment geometry from a description ^[Trans]
• right() Func/Mod – Translates children rightwards (X+). ^{[Trans] [Path] [VNF] [Mat]}
• rot() Func/Mod – Rotates children in various ways. ^{[Trans] [Path] [VNF] [Mat]}
• rot_decode() Func – Extract axis and rotation angle from a rotation matrix.
• scale() Func/Mod – Scales children arbitrarily. ^{[Trans] [Path] [VNF] [Mat] [Ext]}
• skew() Func/Mod – Skews (or shears) children along various axes. ^{[Trans] [Path] [VNF] [Mat]}
• tilt() Func/Mod – Tilts children towards a direction ^{[Trans] [Path] [VNF] [Mat]}
• move() Func/Mod – Translates children in an arbitrary direction. ^{[Trans] [Path] [VNF] [Mat]}
• up() Func/Mod – Translates children upwards (Z+). ^{[Trans] [Path] [VNF] [Mat]}
• xflip() Func/Mod – Reflects children across the YZ plane. ^{[Trans] [Path] [VNF] [Mat]}
• right() Func/Mod – Translates children rightwards (X+). ^{[Trans] [Path] [VNF] [Mat]}
• xrot() Func/Mod – Rotates children around the X axis using the right-hand rule. ^{[Trans] [Path] [VNF] [Mat]}
• xscale() Func/Mod – Scales children along the X axis. ^{[Trans] [Path] [VNF] [Mat]}
• yflip() Func/Mod – Reflects children across the XZ plane. ^{[Trans] [Path] [VNF] [Mat]}
• back() Func/Mod – Translates children backwards (Y+). ^{[Trans] [Path] [VNF] [Mat]}
• yrot() Func/Mod – Rotates children around the Y axis using the right-hand rule. ^{[Trans] [Path] [VNF] [Mat]}
• yscale() Func/Mod – Scales children along the Y axis. ^{[Trans] [Path] [VNF] [Mat]}
• zflip() Func/Mod – Reflects children across the XY plane. ^{[Trans] [Path] [VNF] [Mat]}
• up() Func/Mod – Translates children upwards (Z+). ^{[Trans] [Path] [VNF] [Mat]}
• zrot() Func/Mod – Rotates children around the Z axis using the right-hand rule. ^{[Trans] [Path] [VNF] [Mat]}
• zscale() Func/Mod – Scales children along the Z axis. ^{[Trans] [Path] [VNF] [Mat]}

Translation

• back() Func/Mod – Translates children backwards (Y+). ^{[Trans] [Path] [VNF] [Mat]}
• down() Func/Mod – Translates children downwards (Z-). ^{[Trans] [Path] [VNF] [Mat]}
• fwd() Func/Mod – Translates children forwards (Y-). ^{[Trans] [Path] [VNF] [Mat]}
• grid_copies() Func/Mod – Places copies of children in an [X,Y] grid. ^{[MatList] [Trans]}
• left() Func/Mod – Translates children leftwards (X-). ^{[Trans] [Path] [VNF] [Mat]}
• line_copies() Func/Mod – Places copies of children along an arbitrary line. ^{[MatList] [Trans]}
• mirror_copy() Func/Mod – Makes a copy of children mirrored across a given plane. ^{[MatList] [Trans]}
• move() Func/Mod – Translates children in an arbitrary direction. ^{[Trans] [Path] [VNF] [Mat]}
• move_copies() Func/Mod – Translates copies of all children. ^{[MatList] [Trans]}
• right() Func/Mod – Translates children rightwards (X+). ^{[Trans] [Path] [VNF] [Mat]}
• move() Func/Mod – Translates children in an arbitrary direction. ^{[Trans] [Path] [VNF] [Mat]}
• up() Func/Mod – Translates children upwards (Z+). ^{[Trans] [Path] [VNF] [Mat]}
• xcopies() Func/Mod – Places copies of children along the X axis. ^{[MatList] [Trans]}
• xflip_copy() Func/Mod – Makes a copy of children mirrored across the X axis. ^{[MatList] [Trans]}
• right() Func/Mod – Translates children rightwards (X+). ^{[Trans] [Path] [VNF] [Mat]}
• ycopies() Func/Mod – Places copies of children along the Y axis. ^{[MatList] [Trans]}
• yflip_copy() Func/Mod – Makes a copy of children mirrored across the Y axis. ^{[MatList] [Trans]}
• back() Func/Mod – Translates children backwards (Y+). ^{[Trans] [Path] [VNF] [Mat]}
• zcopies() Func/Mod – Places copies of children along the Z axis. ^{[MatList] [Trans]}
• zflip_copy() Func/Mod – Makes a copy of children mirrored across the Z axis. ^{[MatList] [Trans]}
• up() Func/Mod – Translates children upwards (Z+). ^{[Trans] [Path] [VNF] [Mat]}

Triangles

• adj_ang_to_hyp() Func – Returns the hypotenuse length from the length of the adjacent and the angle.
• adj_ang_to_opp() Func – Returns the opposite side length from the length of the adjacent side and the angle.
• hyp_adj_to_ang() Func – Returns the angle from the lengths of the hypotenuse and the adjacent side.
• hyp_adj_to_opp() Func – Returns the opposite side length from the lengths of the hypotenuse and the adjacent side.
• adj_opp_to_ang() Func – Returns the angle from the lengths of the adjacent and opposite sides.
• adj_opp_to_hyp() Func – Returns the hypotenuse length from the lengths of the adjacent and opposite sides.
• adj_ang_to_hyp() Func – Returns the hypotenuse length from the length of the adjacent and the angle.
• adj_ang_to_opp() Func – Returns the opposite side length from the length of the adjacent side and the angle.
• hyp_ang_to_adj() Func – Returns the adjacent side length from the length of the hypotenuse and the angle.
• hyp_ang_to_opp() Func – Returns the opposite side length from the length of the hypotenuse and the angle.
• opp_ang_to_adj() Func – Returns the adjacent side length from the length of the opposite side and the angle.
• opp_ang_to_hyp() Func – Returns the hypotenuse length from the length of the opposite side and the angle.
• hyp_adj_to_ang() Func – Returns the angle from the lengths of the hypotenuse and the adjacent side.
• hyp_adj_to_opp() Func – Returns the opposite side length from the lengths of the hypotenuse and the adjacent side.
• hyp_ang_to_adj() Func – Returns the adjacent side length from the length of the hypotenuse and the angle.
• hyp_ang_to_opp() Func – Returns the opposite side length from the length of the hypotenuse and the angle.
• hyp_opp_to_adj() Func – Returns the adjacent side length from the lengths of the hypotenuse and the opposite side.
• hyp_opp_to_ang() Func – Returns the angle from the lengths of the hypotenuse and the opposite side.
• law_of_cosines() Func – Applies the Law of Cosines for an arbitrary triangle.
• law_of_sines() Func – Applies the Law of Sines for an arbitrary triangle.
• adj_opp_to_ang() Func – Returns the angle from the lengths of the adjacent and opposite sides.
• adj_opp_to_hyp() Func – Returns the hypotenuse length from the lengths of the adjacent and opposite sides.
• opp_ang_to_adj() Func – Returns the adjacent side length from the length of the opposite side and the angle.
• opp_ang_to_hyp() Func – Returns the hypotenuse length from the length of the opposite side and the angle.
• hyp_opp_to_adj() Func – Returns the adjacent side length from the lengths of the hypotenuse and the opposite side.
• hyp_opp_to_ang() Func – Returns the angle from the lengths of the hypotenuse and the opposite side.

Triangulation

• polygon_triangulate() Func – Divide a polygon into triangles.

Trigonometry

• acosh() Func – Returns the hyperbolic arc-cosine of the given value.
• adj_ang_to_hyp() Func – Returns the hypotenuse length from the length of the adjacent and the angle.
• adj_ang_to_opp() Func – Returns the opposite side length from the length of the adjacent side and the angle.
• hyp_adj_to_ang() Func – Returns the angle from the lengths of the hypotenuse and the adjacent side.
• hyp_adj_to_opp() Func – Returns the opposite side length from the lengths of the hypotenuse and the adjacent side.
• adj_opp_to_ang() Func – Returns the angle from the lengths of the adjacent and opposite sides.
• adj_opp_to_hyp() Func – Returns the hypotenuse length from the lengths of the adjacent and opposite sides.
• adj_ang_to_hyp() Func – Returns the hypotenuse length from the length of the adjacent and the angle.
• adj_ang_to_opp() Func – Returns the opposite side length from the length of the adjacent side and the angle.
• hyp_ang_to_adj() Func – Returns the adjacent side length from the length of the hypotenuse and the angle.
• hyp_ang_to_opp() Func – Returns the opposite side length from the length of the hypotenuse and the angle.
• opp_ang_to_adj() Func – Returns the adjacent side length from the length of the opposite side and the angle.
• opp_ang_to_hyp() Func – Returns the hypotenuse length from the length of the opposite side and the angle.
• asinh() Func – Returns the hyperbolic arc-sine of the given value.
• atanh() Func – Returns the hyperbolic arc-tangent of the given value.
• cosh() Func – Returns the hyperbolic cosine of the given value.
• hyp_adj_to_ang() Func – Returns the angle from the lengths of the hypotenuse and the adjacent side.
• hyp_adj_to_opp() Func – Returns the opposite side length from the lengths of the hypotenuse and the adjacent side.
• hyp_ang_to_adj() Func – Returns the adjacent side length from the length of the hypotenuse and the angle.
• hyp_ang_to_opp() Func – Returns the opposite side length from the length of the hypotenuse and the angle.
• hyp_opp_to_adj() Func – Returns the adjacent side length from the lengths of the hypotenuse and the opposite side.
• hyp_opp_to_ang() Func – Returns the angle from the lengths of the hypotenuse and the opposite side.
• law_of_cosines() Func – Applies the Law of Cosines for an arbitrary triangle.
• law_of_sines() Func – Applies the Law of Sines for an arbitrary triangle.
• adj_opp_to_ang() Func – Returns the angle from the lengths of the adjacent and opposite sides.
• adj_opp_to_hyp() Func – Returns the hypotenuse length from the lengths of the adjacent and opposite sides.
• opp_ang_to_adj() Func – Returns the adjacent side length from the length of the opposite side and the angle.
• opp_ang_to_hyp() Func – Returns the hypotenuse length from the length of the opposite side and the angle.
• hyp_opp_to_adj() Func – Returns the adjacent side length from the lengths of the hypotenuse and the opposite side.
• hyp_opp_to_ang() Func – Returns the angle from the lengths of the hypotenuse and the opposite side.
• sinh() Func – Returns the hyperbolic sine of the given value.
• tanh() Func – Returns the hyperbolic tangent of the given value.

Trusses

• cubetruss() Mod – Creates a multi-cube straight cubetruss shape. ^[Geom]
• cubetruss_clip() Mod – Creates a clip for the end of a cubetruss to snap-lock it to another cubetruss. ^[Geom]
• cubetruss_corner() Mod – Creates a multi-cube corner cubetruss shape. ^[Geom]
• cubetruss_dist() Func – Returns the length of a cubetruss truss.
• cubetruss_foot() Mod – Creates a foot that can connect two cubetrusses. ^[Geom]
• cubetruss_joiner() Mod – Creates a joiner that can connect two cubetrusses end-to-end. ^[Geom]
• cubetruss_segment() Mod – Creates a single cubetruss cube. ^[Geom]
• cubetruss_support() Mod – Creates a cubetruss support structure shape. ^[Geom]
• cubetruss_uclip() Mod – Creates a joiner that can connect two cubetrusses end-to-end. ^[Geom]

Type Checking

• all() Func – Returns true if all items in the argument list are true.
• all_integer() Func – Returns true if all of the numbers in the argument are integers.
• any() Func – Returns true if any item in the argument list is true.
• is_bezier_patch() Func – Returns true if the given item is a bezier patch.
• is_consistent() Func – Returns true if the argument is a list with consistent structure and finite numerical data.
• is_def() Func – Returns true if x is not undef.
• is_finite() Func – Returns true if the argument is a finite number.
• is_func() Func – Returns true if the argument is a function literal.
• is_homogeneous() Func – Returns true if all members of a list are of the same type.
• is_homogeneous() Func – Returns true if all members of a list are of the same type.
• is_int() Func – Returns true if the argument is an integer.
• is_int() Func – Returns true if the argument is an integer.
• is_nan() Func – Return true if the argument is "not a number".
• is_nurbs_patch() Func – Returns true if the given item looks like a NURBS patch.
• is_range() Func – Returns true if the argument is a range.
• is_str() Func – Returns true if the argument is a string.
• is_type() Func – Returns true if the type of 'x' is one of those in the list types.
• same_shape() Func – Returns true if the argument lists are numeric and of the same shape.
• typeof() Func – Returns a string representing the type of the value.
• valid_range() Func – Returns true if the argument is a valid range.

Type Conversion

• list() Func – Expands a range into a full list.

Type Queries

• f_is_bool() Func – Returns a function to determine if a value is a boolean.
• f_is_def() Func – Returns a function to determine if a value is not undef.
• f_is_finite() Func – Returns a function to determine if a value is a number type that is finite.
• f_is_function() Func – Returns a function to determine if a value is a function literal.
• f_is_int() Func – Returns a function to determine if a value is an integer number.
• f_is_list() Func – Returns a function to determine if a value is a list.
• f_is_nan() Func – Returns a function to determine if a value is a number type that is Not a Number (NaN).
• f_is_num() Func – Returns a function to determine if a value is a number.
• f_is_patch() Func – Returns a function to determine if a value is a Bezier Patch structure.
• f_is_path() Func – Returns a function to determine if a value is a Path (a list of points).
• f_is_range() Func – Returns a function to determine if a value is a range.
• f_is_region() Func – Returns a function to determine if a value is a Region (a list of Paths).
• f_is_string() Func – Returns a function to determine if a value is a string.
• f_is_undef() Func – Returns a function to determine if a value is undef.
• f_is_vector() Func – Returns a function to determine if a value is a list of numbers.
• f_is_vnf() Func – Returns a function to determine if a value is a VNF structure.

Undef Handling

• all_defined() Func – Returns true if all items in the given array are defined.
• any_defined() Func – Returns true if any item in the argument list is not undef.
• default() Func – Returns a default value if the argument is 'undef', else returns the argument.
• first_defined() Func – Returns the first value in the argument list that is not 'undef'.
• num_defined() Func – Returns the number of defined values in the the argument list.
• one_defined() Func – Returns the defined value in the argument list if only a single value is defined.
• u_add() Func – Returns the sum of 2 numbers if both are defined, otherwise returns undef.
• u_div() Func – Returns the quotient of 2 numbers if both are defined, otherwise returns undef.
• u_mul() Func – Returns the product of 2 numbers if both are defined, otherwise returns undef.
• u_sub() Func – Returns the difference of 2 numbers if both are defined, otherwise returns undef.

VNF Generators

• cube() Func/Mod – Creates a cube with anchors for attaching children. ^{[Geom] [VNF] [Ext]}
• cuboid() Mod – Creates a cube with chamfering and roundovers. ^[Geom]
• cylinder() Func/Mod – Creates an attachable cylinder. ^{[Geom] [VNF] [Ext]}
• octahedron() Func/Mod – Creates an octahedron with axis-aligned points. ^{[Geom] [VNF]}
• onion() Func/Mod – Creates an attachable onion-like shape. ^{[Geom] [VNF]}
• pie_slice() Func/Mod – Creates a pie slice shape. ^{[Geom] [VNF]}
• prismoid() Func/Mod – Creates a rectangular prismoid shape with optional roundovers and chamfering. ^{[Geom] [VNF]}
• rect_tube() Mod – Creates a rectangular tube. ^[Geom]
• sphere() Func/Mod – Creates an attachable spherical object. ^{[Geom] [VNF] [Ext]}
• spheroid() Func/Mod – Creates an attachable spherical object with controllable triangulation. ^{[Geom] [VNF]}
• teardrop() Func/Mod – Creates a teardrop shape. ^{[Geom] [VNF]}
• torus() Func/Mod – Creates an attachable torus. ^{[Geom] [VNF]}
• tube() Mod – Creates a cylindrical or conical tube. ^[Geom]
• vnf_from_polygons() Func – Returns a VNF from a list of 3D polygons. ^[VNF]
• vnf_from_region() Func – Returns a 3D VNF given a 2D region. ^[VNF]
• vnf_join() Func – Returns a single VNF structure from a list of VNF structures. ^[VNF]
• vnf_tri_array() Func – Returns a VNF from an array of points. The array need not be rectangular. ^[VNF]
• vnf_vertex_array() Func – Returns a VNF structure from a rectangular vertex list. ^[VNF]
• wedge() Func/Mod – Creates a 3d triangular wedge. ^{[Geom] [VNF]}

VNF Manipulation

• is_vnf() Func – Returns true given a VNF-like structure.
• is_vnf_list() Func – Returns true given a list of VNF-like structures.
• projection() Func – Returns projection or intersection of vnf with XY plane ^[VNF]
• vnf_area() Func – Returns the surface area of a VNF.
• vnf_bend() Func – Bends a VNF around an axis. ^[VNF]
• vnf_boundary() Func – Returns the boundary of a VNF as an list of paths ^[VNF]
• vnf_drop_unused_points() Func – Removes unreferenced vertices from a VNF. ^[VNF]
• vnf_faces() Func – Returns the list of faces from a VNF.
• vnf_halfspace() Func – Returns the intersection of the vnf with a half space. ^[VNF]
• vnf_merge_points() Func – Consolidates duplicate vertices of a VNF. ^[VNF]
• vnf_polyhedron() Mod – Returns a polyhedron from a VNF or list of VNFs. ^[Geom]
• vnf_quantize() Func – Quantizes the vertex coordinates of a VNF. ^[VNF]
• vnf_reverse_faces() Func – Reverses the faces of a VNF. ^[VNF]
• vnf_sheet() Func – Extends a VNF into a thin sheet by extruding normal to the VNF ^[VNF]
• vnf_slice() Func – Slice the faces of a VNF along an axis. ^[VNF]
• vnf_small_offset() Func – Computes an offset surface to a VNF for small offset distances ^[VNF]
• vnf_triangulate() Func – Triangulates the faces of a VNF. ^[VNF]
• vnf_unify_faces() Func – Remove triangulation from VNF, returning a copy with full faces ^[VNF]
• vnf_validate() Mod – Echos non-manifold VNF errors to the console. ^[VNF]
• vnf_vertices() Func – Returns the list of vertex points from a VNF.
• vnf_volume() Func – Returns the volume of a VNF.
• vnf_wireframe() Mod – Creates a wireframe model from a VNF. ^[VNF]

Vectors

• add_scalar() Func – Adds a scalar value to every item in a vector.
• BACK Const – The backwards (Y+) direction vector constant [0,1,0].
• BOTTOM Const – The down-wards (Z-) direction vector constant [0,0,-1].
• BOTTOM Const – The down-wards (Z-) direction vector constant [0,0,-1].
• CENTER Const – The center vector constant [0,0,0].
• CENTER Const – The center vector constant [0,0,0].
• CENTER Const – The center vector constant [0,0,0].
• BOTTOM Const – The down-wards (Z-) direction vector constant [0,0,-1].
• f_cross() Func – Returns a function to calculate the norm of a given vector.
• f_norm() Func – Returns a function to calculate the norm of a given vector.
• FRONT Const – The front-wards (Y-) direction vector constant [0,-1,0].
• FRONT Const – The front-wards (Y-) direction vector constant [0,-1,0].
• FRONT Const – The front-wards (Y-) direction vector constant [0,-1,0].
• is_vector() Func – Returns true if the given value is a vector.
• LEFT Const – The left-wards (X-) direction vector constant [-1,0,0].
• RIGHT Const – The right-wards (X+) direction vector constant [1,0,0].
• TOP Const – The top-wards (Z+) direction vector constant [0,0,1].
• unit() Func – Returns the unit length of a given vector.
• TOP Const – The top-wards (Z+) direction vector constant [0,0,1].
• v_abs() Func – Returns the absolute values of the given vector.
• v_ceil() Func – Returns the values of the given vector, rounded up.
• v_div() Func – Returns the element-wise division of two equal-length vectors.
• v_floor() Func – Returns the values of the given vector, rounded down.
• v_lookup() Func – Like lookup(), but it can interpolate between vector results.
• v_mul() Func – Returns the element-wise multiplication of two equal-length vectors.
• v_theta() Func – Returns the angle counter-clockwise from X+ on the XY plane.
• vector_angle() Func – Returns the minor angle between two vectors.
• vector_axis() Func – Returns the perpendicular axis between two vectors.
• vector_bisect() Func – Returns the vector that bisects two vectors.
• vector_perp() Func – Returns component of a vector perpendicular to a second vector

Versioning

• bosl_required() Mod – Asserts that the current version of the library is at least the given version.
• bosl_version() Func – Returns the BOSL2 version as a list.
• bosl_version_num() Func – Returns the BOSL2 version as a float.
• bosl_version_str() Func – Returns the BOSL2 version as a string.
• version_cmp() Func – Compares two versions.
• version_to_list() Func – Splits a version into a list of integer version parts.
• version_to_num() Func – Coerces a version into a standard version float.
• version_to_str() Func – Coerces a version into a standard version string.

Walls

• corrugated_wall() Mod – Makes a corrugated rectangular wall. ^[Geom]
• hex_panel() Mod – Create a hexagon braced panel of any shape ^[Geom]
• sparse_cuboid() Mod – Makes an open cross-braced cuboid ^[Geom]
• sparse_wall() Mod – Makes an open cross-braced rectangular wall. ^[Geom]
• sparse_wall2d() Mod – Makes an open cross-braced rectangular wall. ^[Geom]
• thinning_triangle() Mod – Makes a triangular wall with a thin middle. ^[Geom]
• thinning_wall() Mod – Makes a rectangular wall with a thin middle. ^[Geom]

Wiring

• wire_bundle() Mod – Creates a wire bundle for a given number of wires. ^[Geom]