TF = geom.selfintersects (P) returns true when any two non-adjacent segments of the curve P intersect, and false otherwise. P is an $N$-by-2 matrix of points.

TF = geom.selfintersects (P, CLOSED) treats the curve as closed when CLOSED is true, adding the segment from the last point back to the first. CLOSED defaults to false.

[TF, IDX] = geom.selfintersects (…) additionally returns the offending segment pairs as an $M$-by-2 matrix of segment indices, one row per crossing pair, empty when there is none. Segment $k$ runs from point $k$ to point $k+1$.

Segments that merely share an end point are not crossings, so consecutive segments are never reported, nor are the first and last segments of a closed curve. A curve that touches itself without crossing — two segments meeting at a point that is an end of both — is reported, since for the purposes this test serves, touching and crossing are equally fatal.

This is the global companion to the local criterion in geom.curveoffset. An offset curve can satisfy the curvature condition at every point and still pinch closed somewhere along its length; only a test like this one sees that.

The test is exhaustive over segment pairs, so its cost grows as the square of the number of points. On a profile of a few thousand points that is a fraction of a second, but it is not something to call inside a loop over candidate designs.

See also: geom.curveoffset, geom.curvature, geom.signedarea

Source Code: geom.selfintersects