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Generation, and manipulation of triangular meshes (points and faces).

This data type and its constructors/transformers are based on the the vnf structure module of the BOSL2 OpenSCAD library, but with the constraint that all faces are triangular on construction.

`val empty : t`

An empty `t`

, with no points.

`make ~points ~faces`

Create a mesh `t`

from a list of `V3.t`

`points`

, and a list of `faces`

described by indices into `points`

.

`val size : t -> int`

`type endcaps = [ `

`| `Loop`

(*Last/top row wrapped to the first/bottom

*)`| `Both`

(*Both bottom and top rows are closed with flat faces

*)`| `None`

(*Neither top or bottom rows are closed with a face

*)`| `Top`

(*A face is generated to close the top row with itself

*)`| `Bot`

(*A face is generated to close the bottom row with itself

*)

` ]`

Describes desired row wrapping behaviour in `of_rows`

, which creates a mesh from rows of points.

Quadrilateral face triangulation strategy.

`prune_rows ?min_dist rows`

Filter `rows`

such that each row polygon is at least `min_dist`

(default `0.05`

) above the plane of the previous polygon, indicating the dropped indices. This can be useful for avoiding self-intersections in the output of `of_rows`

. Note that all polygons in `rows`

must be planar, else `Failure`

will be raised.

```
val of_rows :
?rev:bool ->
?endcaps:endcaps ->
?col_wrap:bool ->
?style:style ->
V3.t list list ->
t
```

`of_rows ?rev ?endcaps ?col_wrap ?style rows`

Create a triangular mesh `t`

from a list of layers (counter_clockwise loops of 3d points). `endcaps`

defaults to ``Both`

, which specifies that faces should be generated to close off the bottom and top layers of the generated shape. If it is instead set to ``Loop`

, the open faces of the first and last layers will be closed with one another. For more advanced usages, one or both of the endcaps can be left open, so the resulting meshes can be closed off by some other means.

`col_wrap`

sets whether faces should be generated to loop between the ends of each row.- If
`rev`

is`true`

, faces winding direction will be reversed (default =`false`

) `style`

governs how the quadrilaterals formed by the rows and columns of points are divided into triangles:``Default`

is an arbitrary systematic subdivision in the same direction``Alt`

is the uniform subdivision in the other (alternate direction)``MinEdge`

picks the shorter edge to subdivide the quadrilateral, so the division may not be uniform across the shape``Quincunx`

adds a vertex in the middle of each quadrilateral and creates four triangles``Convex`

and``Concave`

choose the locally convex/concave subdivision

- If
`rows`

is empty, a`empty`

is returned. Throws`Invalid_argument`

if`rows`

contains only one row, or if it is not rectangular (any row differs in length).

`of_ragged ?looped ?reverse rows`

Create a triangular mesh from a list of rows, where each row can differ in length relative to its neighbours by up to 2. Since the rows can be ragged, no (columnar) wrapping is done, thus they are best described as rows, rather than layers as with `of_rows`

which produces a mesh of a closed shape. Instead, this function is useful for the generation of triangular patches that can be joined with one another to create a complete mesh. Setting `looped`

to true will generate faces between the last and first rows, so long as their lengths differ by no more than 2. Face winding order is reversed if `reverse`

is `true`

. Throws `Invalid_argument`

if a row length delta of greater than 2 is encountered.

`of_path3 ?rev layer`

Create a mesh from a single path (a closed loop of `V3.t`

, should be coplanar though it is not confirmed), returning a `t`

with a single face including all of the points. Face winding order is reversed if `rev`

is `true`

. This can be useful for producing a flat patch mesh to be combined with other meshes to produce a complete shape.

`of_poly2 ?rev poly`

Create a mesh from a 2d polygon. If `poly`

does not have any holes, then this is equivalent to `of_path2`

. If there are holes, polyhole partitioning is performed to determine a set of faces that can close the points.

The earcutting algorithm used to partition the polygon into faces is a port of RonaldoCMP's work found here.

`of_poly3 ?rev poly`

Create a mesh from a 3d polygon. If `poly`

does not have any holes, then this is equivalent to `of_path3`

. If there are holes, polyhole partitioning is performed to determine a set of faces that can close the points.

The earcutting algorithm used to partition the polygon into faces is a port of RonaldoCMP's work found here.

`of_polygons polys`

Create a triangular mesh from a list of polygonal point faces.

`hull points`

Create a convex hull mesh that encloses `points`

. If the points are coplanar, a 2-dimensional hull is found, resulting in an unclosed single face mesh (as with `of_path3`

). Unused points are not discarded.

Functions for generating meshes which cover over a sequence of closed polygonal `Path3.t`

profiles. Ported from the skin module of the BOSL2 OpenSCAD library.

Path resampling vertex mapping strategies.

Each of these variants specify that profiles of incommensurate length should simply resampled with `Path3.subdivide`

with the provided point distribution frequency strategy (`[`ByLen | `BySeg]`

). In the case of ``Direct _`

, the profiles are assumed to be "lined up", with the points at their zeroth indices corresponding to eachother. The ``Reindex _`

strategy will rotate the second profile of a pair via `Path3.reindex_polygon`

following resampling to minimize the distance between the zeroth indices of the two paths.

`type duplicator = [ `

`| `Distance`

(*Minimize the length of the edges between associated vertices. Best results when connecting discrete polygon profiles with low point counts.

*)`| `FastDistance`

(*Like

*)``Distance`

, but profiles are assumed to already be lined up, with their zeroth indices corresponding to one another.`| `Tangent`

(*Split finely sampled (convex) curve into groups of points, and map each group to point on the smaller discrete polygon. Can fail if the larger curved path is non-convex, or does not have enough points.

*)

` ]`

Point duplicating vertex mapping strategies.

Each of these variants specify profiles of incommensurate length should be matched up by computing vertex mappings between the profiles, and duplicating vertices on the smaller/shorter profile until the point counts are equalized. See the conspicuously named vertex matching functions `Path3.distance_match`

, `Path3.aligned_distance_match`

, and `Path3.tangent_match`

for more details (also available in the `Path2`

module).

Vertex count matching strategy specification type.

```
val slice_profiles :
?looped:bool ->
slices:[< `Flat of int | `Mix of int list ] ->
Path3.t list ->
Path3.t list
```

`slice_profiles ?looped ~slices profiles`

Linearly transition between each neighbouring pair of closed paths in `profiles`

to produce new interpolated list of profiles. The number of `slices`

inserted between can either be the same between each pair (``Flat n`

), or specified separately with ``Mix ns`

. If `looped`

is `true`

, then slices will also be inserted between the last and initial profiles (default is `false`

). Lists of profiles such as these can be used to produce meshes with `of_rows`

(as `skin`

does).

Raises `Invalid_argument`

if the length of ``Mix ns`

does not correspond to the number of transitions, or if `profiles`

has fewer than two elements.

```
val skin :
?style:style ->
?endcaps:endcaps ->
?refine:int ->
?mapping:[ `Flat of mapping | `Mix of mapping list ] ->
slices:[< `Flat of int | `Mix of int list ] ->
Path3.t list ->
t
```

`skin ?style ?endcaps ?refine ?mapping ~slices profiles`

Produce a mesh that skins over two or more 3d `profiles`

-- closed, ideally coplanar (though some slight variation can be ok) paths. This works by linearly interpolating between neighbouring profiles with `slices`

steps, and passing the profiles along to `of_rows`

, which generates faces to enclose the shape. For this to be well defined, each row must have the same length, thus `mapping`

can be used to specify the strategy used to map/associate the vertices between them and reconcile the point counts and improve alignment for their connecting edges (see `resampler`

and `duplicator`

configuration variants). By default this is ``Direct`

, which simply applies resampling without altering the vertex associations established by the start indices of each profile.

`refine`

can be specified to apply additional upsampling which may help to improve the smoothness of the resulting mesh. Uses`Path3.subdivide`

with the sampling frequency indicated for`resampler`

mapped transitions, and``BySeg`

for`duplicator`

s.`slices`

and`mapping`

can be provided as``Flat _`

to be applied to all transitions, or as``Mix l`

, where`l`

is a list with length equal to the number of profile transitions (`length profiles - 1`

, or`length profiles`

if`endcaps`

is``Loop`

)**NOTE:**mixing mapping strategies can be fickle, and some combinations may not work depending on the profiles. This may improve as kinks are worked out, but maybe not

```
val skin_between :
?style:style ->
?endcaps:[ `Both | `None | `Top | `Bot ] ->
?refine:int ->
?mapping:mapping ->
slices:int ->
Path3.t ->
Path3.t ->
t
```

`skin_between ?style ?endcaps ?refine ?mapping ~slices a b`

Create a mesh that *skins* over a linear interpolation/morph between 3d profiles `a`

and `b`

over `slices`

steps. See `skin`

for more details.

```
val skline :
?style:style ->
?endcaps:endcaps ->
?refine:int ->
?sampling:[ `Flat of [ `ByLen | `BySeg ] | `Mix of [ `ByLen | `BySeg ] list ] ->
?fn:int ->
?size:
[ `Abs of float list
| `Rel of float list
| `Flat of [ `Abs of float | `Rel of float ]
| `Mix of [ `Abs of float | `Rel of float ] list ] ->
?tangents:[ `NonUniform | `Uniform | `Tangents of V3.t list ] ->
Path3.t list ->
t
```

`skline ?style ?endcaps ?refine ?sampling ?fn ?size ?tangents profiles`

Create a mesh bound by bezier splines passing through the paths formed by the points of `profiles`

-- closed, ideally coplanar (though some slight variation can be ok) paths. Unlike this functions linear counterpart `skin`

, only direct mapping (vertex associations are already handled by the user, as determined by the start index of each profile) is available, though `?sampling`

is provided to give control over whether points are added by segment or by length when resampling (default ``ByLen`

).

`fn`

sets the number of segments to be sampled from the splines (default`64`

)`refine`

can be specified to apply additional upsampling which may help to improve the smoothness of the resulting mesh. Uses`Path3.subdivide`

with the sampling frequency indicated by`sampling`

.- see
`Bezier3.of_path`

for notes on`?size`

and`?tangents`

Sweeps, extrusions and morphs from 2d to 3d. Each of which can be given rounded over end caps via their optional `?caps`

parameters with specifications contsructed by the `Cap`

module. and the optional `?caps`

. Roundovers are based on the implementations found in the BOSL2 library's `offset_sweep`

functions from the rounding module.

`module Cap : sig ... end`

Configuration module for declaring how extrusions from 2d to 3d via `sweep`

should be capped off.

```
val sweep :
?style:style ->
?check_valid:[ `Quality of int | `No ] ->
?merge:bool ->
?winding:[ `CCW | `CW | `NoCheck ] ->
?caps:Cap.t ->
transforms:Affine3.t list ->
Poly2.t ->
t
```

`sweep ?check_valid ?style ?winding ?merge ?fn ?fs ?fa ?caps ~transforms poly`

Sweep a 2d polygon into a 3d mesh by applying a sequence of `transforms`

to the original shape. The `winding`

parameter can be used to set automatic enforcement of polygon winding direction, which will impact the winding of the generated faces of the mesh. What is done with the endcaps can be specified with `caps`

. By default the ends of the extrusion are sealed with flat faces, but they can instead be looped to eachother, left empty, or rounded over. If `style`

is provided, it will be passed along to `of_rows`

, which handles converting the swept shapes into a mesh.

If `merge`

is `true`

(as is default), `merge_points`

is applied to the resulting mesh, as duplicate points are introduced when end caps are joined to the outer and inner meshes. If the duplicate points aren't a problem for you (they aren't *necessarily*), this can be turned off to save some compute.

`check_valid`

determines whether validity checks are performed during offset operations (see `Path2.offset`

), for cap roundovers (if specified). Additionally, unless `check_valid`

is ``No`

, polygon validation will be performed with final outer and inner paths of the caps before their mesh is generated.

```
val extrude :
?style:style ->
?check_valid:[ `Quality of int | `No ] ->
?merge:bool ->
?winding:[ `CCW | `CW | `NoCheck ] ->
?fa:float ->
?slices:int ->
?scale_ez:(V2.t * V2.t) ->
?twist_ez:(V2.t * V2.t) ->
?scale:V2.t ->
?twist:float ->
?center:bool ->
?caps:[ `Caps of Cap.caps ] ->
height:float ->
Poly2.t ->
t
```

`extrude ~height poly`

Vertically extrude a 2d polygon 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. Roundovers described by `caps`

are taken into account such that the final shape conforms to the specified `height`

. If `height`

is less than the combined height of `caps`

, there will simply be no "mid-section" (and the resulting height will not reflect the `height`

parameter).

`?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`(v2 1. 1.)`

, no scaling.- Scaling/twisting proceed linearly by default, though bezier easing can be specified by providing handle points to the
`scale_ez`

and`twist_ez`

parameter respectively. (see`Path3.scaler`

and`Path3.twister`

).

```
val revolve :
?style:style ->
?check_valid:[ `No | `Quality of int ] ->
?merge:bool ->
?winding:[ `CCW | `CW | `NoCheck ] ->
?fn:int ->
?fa:float ->
?fs:float ->
?skew:V2.t ->
?angle:float ->
Poly2.t ->
t
```

`revolve ?angle ?skew poly`

Revolve a 2d polygon (defined within the X+ half-plane) around the z-axis. An `angle`

between **0** and **2π** can be provided to specify an incomplete revolution, by default the result loops back onto itself.

`skew:{x; y}`

skews the revolved mesh in the`x`

z and`y`

z planes

```
val path_extrude :
?style:style ->
?check_valid:[ `Quality of int | `No ] ->
?merge:bool ->
?winding:[ `CCW | `CW | `NoCheck ] ->
?caps:Cap.t ->
?euler:bool ->
?scale_ez:(V2.t * V2.t) ->
?twist_ez:(V2.t * V2.t) ->
?scale:V2.t ->
?twist:float ->
path:Path3.t ->
Poly2.t ->
t
```

```
path_extrude ?check_valid ?style ?merge ?winding ?caps ?euler
?scale_ez ?twist_ez ?scale ?twist ~path poly
```

Extrude a 2d polygon along the given `path`

into a 3d mesh. This is a convenience function that composes transform generation using `Path3.to_transforms`

with `sweep`

.

```
val helix_extrude :
?style:style ->
?check_valid:[ `Quality of int | `No ] ->
?merge:bool ->
?fn:int ->
?fa:float ->
?fs:float ->
?scale_ez:(V2.t * V2.t) ->
?twist_ez:(V2.t * V2.t) ->
?scale:V2.t ->
?twist:float ->
?caps:[ `Caps of Cap.caps ] ->
?left:bool ->
n_turns:int ->
pitch:float ->
?r2:float ->
float ->
Poly2.t ->
t
```

```
helix_extrude ?check_valid ?style ?merge ?fn ?fs ?fa ?scale_ez ?twist_ez ?scale ?twist
?caps ?left ~n_turns ~pitch ?r2 r1 poly
```

Helical extrusion of a 2d polygon into a 3d mesh. This is a special case of `path_extrude`

, but following a path generated with `Path3.helix`

, and using transforms that take the helical rotation into account.

These functions serve as the morphing counterparts of the fixed polygon sweeping functions above. In contrast to the more general `skin`

which transitions between 3d `Path3.t`

profiles in sequence, these restrict the bounding shapes to 2d, and lift to 3d via the provided transforms, or path specifications. This separation of the morphing transition and spatial transformations allows for the easy addition of non-linear `Easing`

between the shapes via the `?ez`

parameters (default is linear transition along the spatial distance covered by the sweep beginning from its origin).

```
val morphing_sweep :
?style:style ->
?check_valid:[ `Quality of int | `No ] ->
?merge:bool ->
?winding:[ `CCW | `CW | `NoCheck ] ->
?caps:[ `Caps of Cap.caps ] ->
?outer_map:mapping ->
?hole_map:[ `Same | `Flat of mapping | `Mix of mapping list ] ->
?refine:int ->
?ez:(V2.t * V2.t) ->
transforms:Affine3.t list ->
Poly2.t ->
Poly2.t ->
t
```

`morphing_sweep ~transforms a b`

Morph between the polygons `a`

and `b`

while sweeping the hybrids along `transforms`

to create a mesh. The `outer_map`

, `hole_map`

, and `refine`

correspond to the the similarly named parameters of the more general `skin`

, while the optional `ez`

parameter allows the transition to be bezier eased via `Easing.make`

, rather than strictly linearly. See `sweep`

for details on the remaining common parameters.

```
val morph :
?style:style ->
?check_valid:[ `Quality of int | `No ] ->
?merge:bool ->
?winding:[ `CCW | `CW | `NoCheck ] ->
?fa:float ->
?slices:int ->
?scale_ez:(V2.t * V2.t) ->
?twist_ez:(V2.t * V2.t) ->
?scale:V2.t ->
?twist:float ->
?center:bool ->
?caps:[ `Caps of Cap.caps ] ->
?outer_map:mapping ->
?hole_map:[ `Flat of mapping | `Mix of mapping list | `Same ] ->
?refine:int ->
?ez:(V2.t * V2.t) ->
height:float ->
Poly2.t ->
Poly2.t ->
t
```

`morph ~height a b`

Vertically morph between the 2d polygons `a`

and `b`

. This function is to `morphing_sweep`

, as `extrude`

is to `sweep`

. See each of the former for details on their common parameters.

```
val path_morph :
?style:style ->
?check_valid:[ `Quality of int | `No ] ->
?merge:bool ->
?winding:[ `CCW | `CW | `NoCheck ] ->
?caps:[ `Caps of Cap.caps ] ->
?outer_map:mapping ->
?hole_map:[ `Flat of mapping | `Mix of mapping list | `Same ] ->
?refine:int ->
?ez:(V2.t * V2.t) ->
?euler:bool ->
?scale_ez:(V2.t * V2.t) ->
?twist_ez:(V2.t * V2.t) ->
?scale:V2.t ->
?twist:float ->
path:Path3.t ->
Poly2.t ->
Poly2.t ->
t
```

`path_morph ~path poly`

Morph between the 2d polygons `a`

and `b`

along the given `path`

. This is a convenience function that composes transform generation using `Path3.to_transforms`

with `morphing_sweep`

.

```
val helix_morph :
?style:style ->
?check_valid:[ `Quality of int | `No ] ->
?merge:bool ->
?fn:int ->
?fa:float ->
?fs:float ->
?scale_ez:(V2.t * V2.t) ->
?twist_ez:(V2.t * V2.t) ->
?scale:V2.t ->
?twist:float ->
?caps:[ `Caps of Cap.caps ] ->
?outer_map:mapping ->
?hole_map:[ `Flat of mapping | `Mix of mapping list | `Same ] ->
?refine:int ->
?ez:(V2.t * V2.t) ->
?left:bool ->
n_turns:int ->
pitch:float ->
?r2:float ->
float ->
Poly2.t ->
Poly2.t ->
t
```

`helix_morph ~n_turns ~pitch ?r2 r1 a b`

Morph between the 2d polygons `a`

and `b`

along a helical path. This is a special case of `path_morph`

, but following a path generated with `Path3.helix`

, and using transforms that take the helical rotation into account.

`module Prism : sig ... end`

Rounded prism configuration module.

```
val prism :
?debug:bool ->
?fn:int ->
?holes:Prism.holes ->
?outer:Prism.spec ->
Poly3.t ->
Poly3.t ->
t
```

`prism ?debug ?fn ?holes ?outer bottom top`

Create a prism with continuous curvature rounding from the given `bottom`

and `top`

polygons. The edges running between the corresponding paths must produce a valid polyhedron with coplanar side faces, thus the top should generally be the same shape as the bottom translated/transformed in such a way as to not violate this assumption (avoid z-rotation for one). Roundover specifications are provided with `outer`

and `holes`

(see `Prism.spec`

and `Prism.holes`

for details).

`debug`

can be set to`true`

to skip validity checks that would otherwise raise exceptions on failure, so a mesh can still be obtained for inspection.

```
val linear_prism :
?debug:bool ->
?fn:int ->
?holes:Prism.holes ->
?outer:Prism.spec ->
?center:bool ->
height:float ->
Poly2.t ->
t
```

`linear_prism ?debug ?fn ?holes ?outer ?center ~height bottom`

Create a prism with continuous curvature rounding by extruding the polygon `bottom`

linearaly upward to the given `height`

. If `center`

is `true`

, the resulting prism will be centred in z around the xy plane. See the more general case `prism`

for more details.

Ported from the PlotFunction library by Ryan Colyer.

```
val cartesian_plot :
min_x:float ->
x_steps:int ->
max_x:float ->
min_y:float ->
y_steps:int ->
max_y:float ->
(x:float -> y:float -> float) ->
t
```

`cartesian_plot ~min_x ~x_steps ~max_x ~min_y ~y_steps ~max_y f`

Create a mesh of the function `f`

(from x and y to z) over the ranges of x and y defined by the rest of the parameters.

```
val polar_plot :
?r_step:float ->
max_r:float ->
(r:float -> a:float -> float) ->
t
```

`polar_plot ?r_step ~max_r f`

Create a mesh of the function `f`

(from radius and angle to z) between the z-axis and the radius `max_r`

, with the minimum radial step `r_step`

.

```
val axial_plot :
?fn:int ->
min_z:float ->
z_steps:int ->
max_z:float ->
(z:float -> a:float -> float) ->
t
```

`axial_plot ?fn ~min_z ~z_step ~max_z f`

Create a mesh of the function `f`

(from z-height and angle to radius). `fn`

sets the number of angular steps around the z-axis.

`join ts`

Join a list of meshes. This is not a boolean operation, it is simply collecting the points from each and updating face indices accordingly. Intended for use when building a closed mesh from a set of partial meshes.

`merge_points ?eps t`

Eliminate duplicate points (less than `eps`

distance apart) from `t`

.

`drop_unused_points t`

Drop unreferenced points (not included in any face) from the mesh `t`

.

`of_polyhedron ?eps points faces`

Triangulate the faces of the polygonal mesh described by `points`

and `faces`

. Some degree of non-coplanarity in the input faces can be fine, though too much can cause triangulation to fail. If provided, `eps`

is used for duplicate point and collinearity checks.

`val volume : t -> float`

`volume t`

Calculate the volume of the mesh `t`

.

`val area : t -> float`

`area t`

Calculate the surface area of the mesh `t`

.

`val quaternion : ?about:V3.t -> Quaternion.t -> t -> t`

`val to_stl : ?ascii:bool -> ?rev:bool -> string -> t -> unit`

`to_stl ?ascii ?rev path t`

Write the mesh `t`

to disk at `path`

as an stl. Binary serialization is performed by default, but the `ascii`

format is also available.

- As OCADml meshes (
`t`

) are typically generated to follow the CCW inner face convention of OpenSCAD, this can result in normals pointing the opposite direction expected by other programs with which you may want to use the output`stl`

. Thus facets are reversed by default during serialization, however this can be avoided by setting`~rev:false`

.

`val of_stl : ?rev:bool -> ?eps:float -> string -> t`

`of_stl ?rev ?eps path`

Load a mesh from the stl file at `path`

(both binary and ascii encodings are supported).

`eps`

can be provided to control the precision of point de-duplication/merge operation performed after loading (default is`1e-6`

)- facets are reversed by default during deserialization to counter the default reversal performed by
`to_stl`

, however this can be avoided by setting`~rev:false`

.

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