OCaml DSL for 3D solid modelling in OpenSCAD
Module Scad_ml . Scad
type two_d =
| TwoD
type three_d =
| ThreeD
type scad

The scad type is kept abstract, as the available constructor functions provide much less cumbersome means of building up models.

type 'space t

This GADT allows scads to be tagged as 2D or 3D, restricting usage of functions that should only apply to one or the other, and preventing mixing during boolean operations.

type d2 = two_d t

Two-dimensional shape

type d3 = three_d t

Three-dimensional shape

A note on special facet parameters

The optional parameters ?fa, ?fs, and ?fn correspond to the OpenSCAD "special parameters" governing the number of facets used to generate arcs ($fa, $fs, and $fn respectively). Where present, they govern the following:

  • ?fa is the minimum angle for a fragment. Note that this should be given in radians here (as opposed to degrees in the OpenSCAD language).
  • ?fs is the minimum size/length of a fragment. Even if ?fa is given, and very small, this parameter will limit how small the generated fragments can be.
  • ?fn will set the absolute number of fragments to be used (causing the previous two parameters to be ignored.

3d shape primitives

val cube : ?center:bool -> (float * float * float) -> d3

cube ?center dimensions

Creates a cube in the first octant, with the given xyz dimensions. When center is true, the cube is centered on the origin.

val sphere : ?fa:float -> ?fs:float -> ?fn:int -> float -> d3

sphere ?fa ?fs ?fn radius

Creates a sphere with given radius at the origin of the coordinate system.

val cylinder : ?center:bool -> ?fa:float -> ?fs:float -> ?fn:int -> float -> float -> d3

cylinder ?center ?fa ?fs ?fn radius height

Creates a cylinder centered about the z axis. When center is true, it will also be centered vertically, otherwise the base will sit upon the XY plane.

val cone : ?center:bool -> ?fa:float -> ?fs:float -> ?fn:int -> height:float -> float -> float -> d3

cone ?center ?fa ?fs ?fn ~height r1 r2

Creates a cone (using the cylinder primitive) with bottom radius r1 and top radius r2.

val polyhedron : ?convexity:int -> Vec3.t list -> int list list -> d3

polyhedron points faces

A polyhedron is the most general 3D primitive solid. It can be used to create any regular or irregular shape including those with concave as well as convex features. Curved surfaces are approximated by a series of flat

The Vec3.t list of coordinate points represents the vertices of the shape. How these points define the surface of the generated shape is specified by the faces (0-based) index lists. Each element of faces should define a face in the same order (from the perspective of viewing the drawn shape from the outside, OpenSCAD prefers clockwise ordering) face using the points at the indices in points. These may be defined in any order, as long as enough are provided to fully enclose the shape.

The optional ?convexity parameter specifies the maximum number of faces a ray intersecting the object might penetrate. This parameter is needed only for correct display of the object in OpenCSG preview mode. It has no effect on the polyhedron rendering. For display problems, setting it to 10 should work fine for most cases.

If you are having trouble, please see the debugging polyhedra section of the OpenSCAD user manual.

2d shape primitives

val square : ?center:bool -> (float * float) -> d2

square ?center dimensions

Creates a square or rectangle in the first quadrant, with given xyz dimensions. When ?center is true the square is centered on the origin.

val circle : ?fa:float -> ?fs:float -> ?fn:int -> float -> d2

circle ?fa ?fs ?fn radius

Creates a circle with given radius at the origin.

val polygon : ?convexity:int -> ?paths:int list list -> (float * float) list -> d2

polygon ?convexity ?paths points

Creates a multiple sided shape from a list of xy points. If ?paths is not specified, then all points will be used in the order that they appear. A single path list specifies the order to traverse the points to draw the outline of the polygon. Any additional lists of indices will describe secondary shapes to be subtracted from the first. In this way, holes can be placed in the shape without a subsequent boolean difference operation.

For information on the ?convexity, please see the documentation for polyhedron.

val text : ?size:float -> ?font:string -> ?halign:Text.h_align -> ?valign:Text.v_align -> ?spacing:float -> ?direction:Text.direction -> ?language:string -> ?script:string -> ?fn:int -> string -> d2

text ?size ?font ?halign ?valign ?spacing ?direction ?language ?script ?fn str

Creates 2D geometric text object with contents str, using a named font installed on the local system or provided as a separate font file.

  • ?size specifies the ascent (height above baseline). Default is 10.
  • ?font is the name of the font that should be used. This is not the name of the font file, but the logical font name (internally handled by the fontconfig library).
  • ?halign and ?valign set the horizontal and vertical alignments of the text. Defaults are Left and Baseline respectively.
  • ?spacing gives a factor by which to increase/decrease the character spacing. A value of 1.0 would result in normal spacing.
  • ?direction sets the text flow. Default is LeftToRight.
  • ?language sets the language of the text. Default is "en".
  • ?script sets the script of the text. Default is "latin".


These functions can be applied freely to both 2d and 3d shapes.

val translate : Vec3.t -> 's t -> 's t

translate p t

Moves t along the vector p.

val rotate : Vec3.t -> 's t -> 's t

rotate r t

Performs an Euler rotation (x -> y -> z) on t with the angles r (in radians).

val rotate_about_pt : Vec3.t -> Vec3.t -> 's t -> 's t

rotate_about_pt r p t

Translates t along the vector p, rotating the resulting shape by r, and finally, moving back along the vector p. Functionally, rotating about the point in space arrived at by the initial translation along the vector p.

val vector_rotate : Vec3.t -> float -> 's t -> 's t

vector_rotate ax r t

Rotates t about the arbitrary axis ax by the angle r.

val vector_rotate_about_pt : Vec3.t -> float -> Vec3.t -> 's t -> 's t

vector_rotate_about_pt ax r p t

Translates t along the vector p, rotating the resulting shape around ax by angle r, and finally, moving back along the vector p. Functionally, rotating about the point in space arrived at by the initial translation along the vector p.

val multmatrix : MultMatrix.t -> 's t -> 's t

multmatrix mat t

Multiplies the geometry t with the given 4x3 affine transformation matrix. You can find a detailed explanation of how these are formed and interpreted here.

val mirror : (float * float * float) -> 's t -> 's t

mirror ax t

Mirrors t on a plane through the origin, defined by the normal vector ax.

val quaternion : Quaternion.t -> 's t -> 's t

quaternion q t

Applys the quaternion rotation q to t.

val quaternion_about_pt : Quaternion.t -> Vec3.t -> 's t -> 's t

quaternion_about_pt q p t

Translates t along the vector p, rotating the resulting shape with the quaternion q, and finally, moving back along the vector p. Functionally, rotating about the point in space arrived at by the initial translation along the vector p.

val scale : (float * float * float) -> 's t -> 's t

scale factors t

Scales t by the given factors in xyz.

val resize : (float * float * float) -> 's t -> 's t

resize dimensions t

Adjusts the size of t to match the given dimensions.

val offset : ?chamfer:bool -> [ `Delta of float | `Radius of float ] -> d2 -> d2

offset ?chamfer offset t

Generates a new 2D interior or exterior outline from an existing outline t.

  • `Delta d will create a new outline whose sides are a fixed distance d (+ve out, -ve in) from the original outline.
  • `Radius r creates a new outline as if a circle of some radius r is rotated around the exterior (r > 0) or interior (r < 0) original outline.
  • ?chamfer determines whether edges should be chamfered off when using `Delta offsets.

Helpful diagrams of what each of these offset styles and chamfering look like can be found here.

val color : ?alpha:float -> Color.t -> 's t -> 's t

color ?alpha color t

Displays t with the specified color and ?alpha value. This is only used for the F5 preview as CGAL and STL (F6, render) do not currently support color. Defaults to opaque (alpha = 1.0).

Boolean Combination

Perform boolean operations between shapes of the same dimension (non-mixing of 2d and 3d shapes is enforced by the the GADT t. Notethatthe polymorphicversionsof{!union, minkowski, hull, and intersection, throw exceptions when the input list is empty. If empty list inputs are expected, then use the appropriate _2d or _3d variant.

val union : 's t list -> 's t

union ts

Creates the union/sum (logical or) ts. Throws an exception if ts is empty, use union_2d or union_3d if you would like empty unions to pass silently.

Note: It is mandatory for all unions, explicit or implicit, that external faces to be merged not be coincident. Failure to follow this rule results in a design with undefined behavior, and can result in a render which is not manifold (with zero volume portions, or portions inside out), which typically leads to a warning and sometimes removal of a portion of the design from the rendered output. (This can also result in flickering effects during the preview.) This requirement is not a bug, but an intrinsic property of floating point comparisons and the fundamental inability to exactly represent irrational numbers such as those resulting from most rotations.

The solution to this is to use a small value called an epsilon when merging adjacent faces to guarantee that they overlap, like so:

let scad =
  let eps = 0.01 in
  union [ cube (1., 1., 1.)
        ; translate (1. -. eps, 0., 0.) (cube (2. +. eps, 2., 2.))
val union_2d : d2 list -> d2
val union_3d : d3 list -> d3
val minkowski : 's t list -> 's t

minkowski ts

Displays the minkowski sum of ts. Throws an exception if ts is empty, use minkowski_2d or minkowski_3d if you would like empty minkowski sums to pass silently.

val minkowski_2d : d2 list -> d2
val minkowski_3d : d3 list -> d3
val hull : 's t list -> 's t

hull ts

Displays the convex hull of ts. Throws an exception if ts is empty, use hull_2d or hull_3d if you would like empty hulls to pass silently.

val hull_2d : d2 list -> d2
val hull_3d : d3 list -> d3
val difference : 's t -> 's t list -> 's t

difference t sub

Subracts the shapes of sub from t (logical and not).

Note: It is mandatory that surfaces that are to be removed by a difference operation have an overlap, and that the negative piece being removed extends fully outside of the volume it is removing that surface from. Failure to follow this rule can cause preview artifacts and can result in non-manifold render warnings or the removal of pieces from the render output. See the description above in union for why this is required and an example of how to do this by this using a small epsilon value.

val intersection : 's t list -> 's t

intersection ts

Creates an in intersection of ts. This keeps the overlapping portion (logical and). Only the area which is common or shared by all shapes are retained. Throws an exception if ts is empty, use intersection_2d or intersection_3d if you would like empty intersections to pass silently.

val intersection_2d : d2 list -> d2
val intersection_3d : d3 list -> d3

3d to 2d

val projection : ?cut:bool -> d3 -> d2

projection ?cut t

Project a 3D model t to the XY plane, resulting in an infinitely thin 2D shape, which can then be extruded back into 3D, or rendered and exported as a .dxf. If ?cut is true, only points with z=0 (a slice of t where it intersects with the XY plane) are considered. When ?cut is false (the default when not specified), then points above and below the XY plane will be considered in forming the projection.

2d to 3d extrusions

val linear_extrude : ?height:float -> ?center:bool -> ?convexity:int -> ?twist:int -> ?slices:int -> ?scale:(float * float) -> ?fn:int -> d2 -> d3

linear_extrude ?height ?center ?convexity ?twist ?slices ?scale ?fn t

Takes a 2D object t, and extrudes it upwards from the XY plane to ?height. If ?center is true, the resulting 3D object is centered around the XY plane, rather than resting on top of it.

  • ?twist rotates the shape by the specified angle as it is extruded upwards
  • ?slices specifies the number of intermediate points along the Z axis of the extrusion. By default this increases with the value of ?twist, though manual refinement my improve results.
  • ?scale expands or contracts the shape in X and Y as it is extruded upward. Default is (1., 1.), no scaling.
  • ?convexity: see polyhedron documentation.
val rotate_extrude : ?angle:float -> ?convexity:int -> ?fa:float -> ?fs:float -> ?fn:int -> d2 -> d3

rotate_extrude ?angle ?convexity ?fa ?fs ?fn t

Spins a 2D shape t around the Z-axis in an arc of ?angle (default = 2π) to form a solid which has rotational symmetry. Since t is actually 2D (and does not really exist in Z), it is more like it is spun around the Y-axis to form the solid, which is then placed so that its axis of rotation lies along the Z-axis. For this reason, t must lie completely on either the right (recommended) or the left side of the Y-axis. Further explaination and examples can be found here.

val import_2d : ?dxf_layer:string -> ?convexity:int -> string -> d2

import_2d ?dxf_layer ?convexity file

Imports a file for use in the current OpenSCAD model. The file extension is used to determine which type. If file is a .dxf, ?dxf_layer can be used to indicate a specific layer for import. Throws exception if the extension does not match (case insensitive) one of the following 3D formats:

  • DXF
  • SVG Note: Requires version 2019.05 of OpenSCAD
val import_3d : ?convexity:int -> string -> d3

import_3d ?convexity file

Imports file for use in the current OpenSCAD model. The file extension is used to determine which type. Throws exception if the extension does not match (case insensitive) one of the following 3D formats:

  • STL (both ASCII and Binary)
  • OFF
  • AMF Note: Requires version 2019.05 of OpenSCAD
  • 3MF Note: Requires version 2019.05 of OpenSCAD
val render : ?convexity:int -> 'a t -> 'a t

render ?convexity t

Forces OpenSCAD to render and cache the mesh produced by the given t. This can help to speed up previewing (F5) when the cached shape is used many times. Note that this does however remove any colouration applied previously with color, or resulting from boolean operations such as difference. Output rendering (F6) performance is unaffected.

val to_string : 's t -> string

to_string t

Convert the scad t to a string in the OpenSCAD language.

val write : out_channel -> 's t -> unit

write oc t

Write the scad t to the given out_channel (typically a file), as an OpenSCAD script (using to_string).

module Infix : sig ... end