package OCADml

of_list l

Construct a path from a list of points l (no-op).

of_seq s

Construct a path from a sequence of points s.

of_array a

Construct a path from an array of points a.

to_list t

Convert the path t to a list of points (no-op).

to_seq t

Convert the path t to a sequence of points.

to_array t

Convert the path t to a array of points.

length ?closed path

Calculate the length (total travel distance) of the path. If closed is true, include the distance between the endpoints (default = false).

cummulative_length ?closed path

Calculate the cummulative length (distance travelled by each point) along the path. If closed is true, include the distance between the endpoints (default = false).

to_continuous path

Return a continuous function from values over the range of 0. to 1. to positions along path (like a bezier function), treated as open (closed = false) by default.

resample ~freq path

Resample path with the given frequency (either a flat number of points, or a target point spacing). Note that the only points guaranteed to appear in the output are the start and end points of path. For upsampling that preserves input points, see subdivide.

subdivide ?closed ~freq path

Subdivides path with given frequency, including each of the original points in the output (unlike resample). This can be a flat number of points provided directly with `N (n, by), or as a multiple of number of points in path with `Refine (factor, by). The strategy for distribution of points for these count based methods is set with the second parameter by, which can be either `BySeg (same number of additional points per segment) and `ByLen (segments gain new points proportional to their length). Alternatively, a maximum `Spacing dist can be specified instead. The `Rough point sampling variants will favour sampling uniformity, at the expense of not adhering exactly to the requested point count.

cut ?closed ~distances path

Cut path at a list of increasing distances (`Absolute or `Relative) along it from the start. If closed is true, the segment between the end and beginning of path will be considered, and the first point will be the last of the second path returned. Negative `Abs distance will start from the end to find the split point. Raises Invalid_argument if distance is an endpoint, or further than the end of the path.

split ?closed ~distance path

Split path into two at the position distance (`Absolute or `Relative) along path from the start. Otherwise the behaviour is the same as cut.

noncollinear_triple ?eps path

Returns a pair of triples of non-collinear indices and the corresponding points from path (if the path is not completely collinear). Two well separated points are selected, and the third point is the furthest off the line drawn by the first two points.

is_collinear ?eps path

Returns true if all points in path are collinear (fall within eps distance of the same line).

prune_collinear path

Remove collinear points from path. If closed is true the last point can be pruned as collinear with the first. The first point is never pruned.

deduplicate_consecutive ?closed ?keep ?eq path

Remove consecutive duplicate points as determined by the (approximate) equality function eq (V.approx ~eps:1e-9 by default) from path. By default keep is `First, which includes the first point of each run of duplicates in the output. This can be instead be set to keep the `Last, or to `FirstAndEnds or `LastAndEnds, which follow their respective simpler rules with the caveat of preserving the endpoints (first and last points) of the path. The path is treated as open (closed = false) by default, if closed is true the last point of the path may be dropped (even if keep is `FirstAndEnds | `LastAndEnds).

deriv ?closed ?h path

Computes a numerical derivative of path, with h (default 1.) giving the step size of the sampling of path, so that the derivative can be scaled correctly. Setting closed to true will include computation of the derivative between the last and first point of the path (default false).

deriv_nonuniform ?closed ?h path

Computes a numerical derivative of path, with h giving the non-uniform step sizes of the sampling of path, so that the derivative can be scaled correctly. Setting closed to true will include computation of the derivative between the last and first point of the path (default false). As h provides scaling factors for each segment of the path, it must have a length of one less than path if it's unclosed, and the same length if closed is true.

tangents ?uniform ?closed path

Compute tangent unit vectors of path. Set closed to true to indicate that tangents should include between the end and beginning of the path (default = false). Sampling of path is assumed to be uniform unless the parameter is set to false, in which case the derivatives will be adjusted to correct for non-uniform sampling of points.

continuous_closest_point ?closed ?n_steps ?max_err f p

Find the closest position (from 0. to 1.) along the path function f to the point p.

• n_steps sets the granularity of search at each stage.
• max_err the maximum distance the solution can be from the target p

segment ?closed path

Break path into line segments. If closed is true, include a segment between the last and first points of path (default false).

reindex_polygon reference poly

Rotate the polygonal (closed / coplanar) path poly to optimize its pairwise point association with the reference polygon. Paths should have the same clockwise winding direction (not checked / corrected).

lerp a b u

Linearly interpolate between the paths a and b. Raises Invalid_argument if the paths are of unequal length.

nearby_idxs ?min_tree_size ?radius path p

Find the indices of points within radius (default = 1e-9) distance from the target point p in path. Match indices will be returned in arbitrary order (unsorted). When path is provided (eagerly on partial application), the length will be checked and a function to perform the search will be generated. If path is shorter than min_tree_size, it will be a simple direct search otherwise a BallTree3.t will be constructed. Thus, if you plan to search for more than one target point, take care to apply this function in two steps to avoid repeated length checks and closure/tree generations.

nearby_points ?min_tree_size ?radius path

Find the points within radius (default = 1e-9) distance from the target point p in path. Matched points will be returned in arbitrary order (unsorted). When path is provided (eagerly on partial application), the length will be checked and a function to perform the search will be generated. If path is shorter than min_tree_size, it will be a simple direct search otherwise a BallTree3.t will be constructed. Thus, if you plan to search for more than one target point, take care to apply this function in two steps to avoid repeated length checks and closure/tree generations.

closest_tangent ?closed ?offset ~line t

Find the tangent segment (and its index) on the curved path t closest to line after offset (default = V3.zero) is applied to the points of t (can be used to centre the path relative to line to help in choosing the desired tangent).

of_tups ps

Create a 3d path from a list of xyz coordinate triples.

of_path2 ?plane path

Lift a 2d path onto plane (default = Plane.xy).

to_path2 ?plane t

Project the 3d path t onto plane (default = Plane.xy).

to_plane ?no_check ?eps t

Compute the normalized cartesian equation of the plane that the path t resides on. If there are fewer than three points in t, or they are not coplanar within the tolerance eps (unless no_check = true), an Invalid_argument exception is raised.

project plane t

Project the 3d path t onto plane.

circle ?fn ?fa ?fs ?plane radius

Draw a circular path of radius r onto plane (default = Plane.xy).

square ?center ?plane dims

Draw a rectangular path with xy dims (e.g. width and height) onto plane (default = Plane.xy). If center is true then the path will be centred around the origin (default = false).

ellipse ?fn ?fa ?fs ?plane radii

Draw an ellipse with xy radii onto plane (default = Plane.xy). The greater of the two radii is used for fragment/resolution calculation.

star ?plane ~r1 ~r2 n

Draw an n pointed star with inner radius r1 and outer radius r2 onto plane (default = Plane.xy).

arc ?rev ?fn ?fa ?fs ?plane ?wedge ~centre ~radius ~start a

Draw an arc onto a 3d plane (default = Plane.xy). See Path2.arc.

arc_about_centre ?rev ?fn ?fa ?fs ?dir ?wedge ~centre p1 p2

Draw an arc between p1 and p2, about centre, on the 3d plane occupied by the three points. See Path2.arc_about_centre.

arc_through ?rev ?fn ?fa ?fs ?wedge p1 p2 p3

Draw an arc through the points p1, p2, and p3. See Path2.arc_through.

helix ?fn ?fa ?fs ?left ~n_turns ~pitch ?r2 r1

Draw a 3d helical path around a cylinder/cone with start radius r1 and end radius r2 (default = r1).

• n_turns sets the number of revolutions around the z-axis
• pitch describes the height of one complete turn
• left is used to set handedness (default = true)
• fn, fa, and fs parameters govern quality as they do in OpenSCAD

Configuration module with types and helpers for specifying path roundovers.

roundover ?fn ?fa ?fs ?overrun path_spec

Apply the roundover specifictions in path_spec on the bundled path/shape, with quality set by the fn, fa, and fs parameters. Collinear points are ignored (included in output without roundover applied).

When overrun is set to `Fail (as it is by default) this function will raise Failure if computed joint distances would lead to point insertion that causes the path to reverse/double back on itself. Alternatively:

• `Warn will print the detected overruns to stdout rather than raising Failure (useful for debuggin)
• `Fix will automatically reduce the corner joints involved in each overrun proportional to their lengths.
• `NoCheck skips overrun detection

normal t

Calculate the normal vector of the path t. An Invalid_argument exception is raised if there are fewer than three points in t.

centroid ?eps t

Compute the centroid of the path t. If t is collinear or self-intersecting (within eps tolerance), an Invalid_argument exception is raised.

area ?signed t

Calculate the area of the co-planar path (describing a polygon) t. If signed is true, the signed area is returned.

coplanar ?eps t

Returns true if all points in t are coplanar, within the tolerance eps. If there are fewer than 3 points, or the path is collinear, this returns false.

bbox t

Compute the 3d bounding box of the path t.

scaler ?ez scale

Create a lookup from relative position (0. to 1.) to scaling transformation matrix for interpolating from {x = 1.; y = 1.} at 0. to scale by 1.. If provided, the pair of handle points ez will be used to ease the scaling (see Easing.make).

twister ?ez angle

Create a lookup from relative position (0. to 1.) to rotation transformation matrix for interpolating from 0. (no rotation) at 0. to angle by 1.. If provided, the pair of handle points ez will be used to ease the scaling (see Easing.make).

to_transforms ?mode ?scale_ez ?twist_ez ?scale ?twist t

Generate list of transformations that can be applied to three-dimensional vectors (V3.t via Affine3.transform) or shapes, to move them along the path t (intended to be applied to the vector/shape from its original position each time). Note that the transforms are generated assuming the shape is centred on the origin, and for the purposes of alignment to the beginning of the path and scaling/twisting, laying flat on the XY plane.

When mode is `Auto | `Align _ | `NoAlign (default it `Auto), tangents are used to estimate appropriate rotations for each translation, using quaternion alignment from tangent to tangent, accumulating rotation along the way. In the case of `Auto, some effort is made to automatically apply an alignment rotation towards the first tangent of the path before each transformation such that the orientation of the shape being swept will be consistent and sensible, though some manual rotation of the shape before sweeping along the generated transforms may be necessary to get the desired result.

`Align v and `NoAlign follow the same quaternion accumulation strategy along the path t, however they differ from `Auto in their handling of pre-alignment transformations. With `Align v, the vector v will be used to align the assumed shape normal of (v3 0. 0. 1.) to, while `NoAlign will skip the alignment step entirely (likely desirable if the intention is to sweep a shape not laying on the XY plane).

Setting mode = `Euler will use euler rotations instead, which can have results more in line with expectations in some scenarios (helical-like paths for example, though Mesh.helix_extrude may be a better fit in that case), but fail in others. For instance, `Euler can generate an abrupt when the path tangent is exactly vertical.

If provided, scale and twist, specify scaling and rotation to be applied along the path increasing up to the provided value by the end. Scaling/twisting proceeds linearly by default, unless the corresponding _ez parameters are provided to describe the desired eased transition (see scaler and twister).

helical_transforms ?fn ?fs ?fa ?scale_ez ?twist_ez ?scale ?twist ?left ~n_turns ~pitch ?r2 r1

Affine transformations following a helical path. This can be thought of like a special case of to_transforms, but using a path generated with helix, and with rotational calculations taking into account the helical trajectory.

prune_transforms ?min_dist ~shape transforms

Filter transforms into (idx, m) pairs for which the polygon computed by applying m to the corresponding shape (result of shape idx, allowing for scaling operations etc) is at least min_dist (default 0.05) above the plane of the previous polygon. This can be useful for avoiding self-intersections in the output of Mesh.sweep. Note that all polygons returned by shape must be planar, else Failure will be raised.

distance_match a b

If the closed polygonal paths a and b have incommensurate lengths, points on the smaller path are duplicated and the larger path is shifted (list rotated) in such a way that the total length of the edges between the associated vertices (same index/position) is minimized. The replacement paths, now having the same lengths, are returned as a pair (with the same order). This algorithm generally produces a good result when both a and b are discrete profiles with a small number of vertices.

This is computationally intensive ( O(N³) ), if the profiles are already known to be lined up, with their zeroth indices corresponding, then aligned_distance_match provides a ( O(N²) ) solution.

aligned_distance_match a b

Like distance_match, but the paths a and b are assumed to already be "lined up", with the zeroth indices in each corresponding to one another.

tangent_match a b

If the closed polygonal paths a and b have incommensurate lengths, points on the larger (ideally convex, curved) path are grouped by association of their tangents with the edges of the smaller (ideally discrete) polygonal path. The points of the smaller path are then duplicated to associate with their corresponding spans of tangents on the curve, and the larger path is rotated to line up the indices. The profiles, now having the same length are returned as a pair in the order that they were applied returned.

This algorithm generally produces good results when connecting a discrete polygon to a convex finely sampled curve. It may fail if the curved profile is non-convex, or doesn't have enough points to distinguish all of the tangent points from each other.