Paths — API

Source: src/ut_path.scad and src/frontend/. For how to choose and use these, see usage/paths.md; for the data format, ir.md.

Frontends

Each returns a path.


`ut_polyline(pts, r = 0, closed = false, frame = "transport", normal = undef, twist = 0)`	Waypoints with fillet radii. `closed = true` is refused.
`ut_turtle(cmds, start = [0,0,0], dir = [1,0,0], up = [0,0,1], frame = "transport", normal = undef, twist = 0)`	A list of `feed`, `bend` and `roll` commands.
`ut_curve(f, t = [0, 1], n = 100, dfdt = undef, frame = "transport", normal = undef, twist = 0)`	A function literal sampled at `n + 1` points.
`ut_spine(segs, closed = false, opts = [])`	A list of segments. Asserts contiguity and tangent continuity.


`ut_line(p0, p1)`	A straight. Zero length is an error.
`ut_arc(c, u, v, r, ang)`	An arc: `point(x) = c + r(cos(angx)u + sin(angx)*v)` for `x` in 0..1. `u`, `v` orthonormal, `r > 0`, `0 < ang <= 180`.
`ut_arc_from(c, from, to, axis)`	The arc about `c` from `from` to `to`, turning about `axis`.
`ut_sampled(pts, tans)`	A sampled chain: at least two 3D points, one tangent per point.

	returns
`ut_segs(path)`	the segment list
`ut_closed(path)`	`true` for a closed path
`ut_popts(path)`	the options stored in the path
`ut_length(path)`	developed length. Exact for lines and arcs; a chord sum for sampled segments.
`ut_at(path, s)`	`[position, unit tangent]` at arclength `s`, read from the segments, independent of `$fa`/`$fs`. Asserts `0 <= s <= ut_length(path)`.

Per segment:

	returns
`ut_seg_kind(s)`	`"L"`, `"A"` or `"P"`
`ut_seg_p0(s)`, `ut_seg_p1(s)`	start and end points
`ut_seg_t0(s)`, `ut_seg_t1(s)`	unit tangents at the start and end
`ut_seg_len(s)`	length


`ut_stations(path, opts = [])`	Compiles a path to a list of stations `[p, t, n, s]`. The only function that decides roll and resolution.

opts is a list of [key, value] pairs, taking precedence over the path’s own:

key	default
`"frame"`	`"transport"`	`"transport"`, `"fixed"`, or a list of one normal per station
`"normal"`	`[0,0,1]`	the reference for `"fixed"`, and the seed for `"transport"`
`"twist"`	`0`	degrees, distributed by arclength
`"symmetry"`	`0`	on a closed path, the section’s rotational symmetry order

	returns
`ut_st_p(st)`	position
`ut_st_t(st)`	unit tangent
`ut_st_n(st)`	unit roll normal, orthogonal to the tangent
`ut_st_s(st)`	arclength
`ut_st_mat(st)`	the 4×4 frame: columns `n`, `cross(t, n)`, `t`, and the position. No scale or shear.

A closed path’s station list does not repeat its first station at the end.