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 point repeating the one before it adds a segment of no length, which is passed over, so the segments either side of it count as consecutive. A curve that touches itself without crossing, where two segments meet at a point that is an end of both, is reported, since for the purposes this test serves, touching and crossing are equally fatal. Touching means meeting: segments any distance apart, however small, do not touch, where a geom.Region counts curves within 1e-7 mm of one another as touching.

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.

Only segments whose bounding boxes overlap are tested, found by sweeping along x, so a profile of half a million points takes a few hundredths of a second.

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

Source Code: geom.selfintersects