Utilities — API

Source: src/ut_core.scad, src/ut_math.scad, src/ut_view.scad.

Constants

OpenSCAD’s use does not export variables, so every constant is a function.

	value
`ut_eps()`	`1e-9`, the tolerance for “zero”
`ut_min_wall()`	`1.2`, the wall in mm below which `CHECK-3` and `NET-4` warn
`ut_up()`	`[0, 0, 1]`
`ut_back()`	`[0, 1, 0]`

Options and assertions


`ut_opt(opts, key, dflt = undef)`	The value of the first `[key, value]` pair in `opts` with that key, else `dflt`.
`ut_req(cond, msg)`	Asserts `cond` with `msg` and returns `true`, so it can prefix an expression.

Vectors and angles

All angles are in degrees.

	returns
`ut_unit(v)`	`v` normalised
`ut_turn(a, b)`	the angle between two 3D vectors, by `atan2`, never `acos`
`ut_rotv(v, ang, k)`	`v` rotated by `ang` about the unit axis `k`
`ut_ortho(t, n)`	`n` made orthogonal to `t` and normalised
`ut_ref_fallback(t, ref = undef)`	`ref` (default up) projected orthogonal to `t`; falls back to back, then +X, when `t` is parallel to it

Circles, polygons and meshes

	returns
`ut_fragments(r, ang = 360)`	the number of facets OpenSCAD’s `$fn`/`$fa`/`$fs` rule gives a radius `r` over `ang` degrees; at least 2
`ut_ring(r, n, a0 = 0)`	`n` points on a circle of radius `r`, counter-clockwise from angle `a0`
`ut_inradius(loop)`	the radius of the largest origin-centred circle inside a 2D loop, measured to its edges
`ut_sphere_inradius(r)`	the distance from the centre to the nearest face of the `sphere(r)` OpenSCAD emits at the current resolution: `r*cos(180/n)^2`, exact for 8 or more facets and low below that
`ut_area2d(poly)`	signed area; positive for counter-clockwise
`ut_volume(pts, faces)`	the volume of a closed mesh, by the divergence theorem

A polygon’s inscribed circle is smaller than the circle its vertices lie on by cos(180/n), and a faceted sphere loses that factor twice. Use ut_inradius and ut_sphere_inradius for anything that must fit inside.

Viewing


`ut_cutaway(normal = [0,1,0], at = 0, on = true, size = 1000)`	Module. Removes the part of its children on the `normal` side of the plane at distance `at` along `normal`. `on = false` passes the children through. `size` is the edge of the cutting cube.

It forces a CSG difference, so do not leave it on around geometry you export. The difference is evaluated with render(), which costs a CGAL evaluation in preview. That is deliberate: the cutter is large enough to contain the camera, and OpenSCAD does not subtract a solid the viewer is inside when it previews.