This repository is the MATLAB version of BeBOT (https://github.com/caslabuiowa/BeBOT).
BeBOT/MinDistBernstein2PolygonFast.m and BeBOT/MinDistBernstein2BernsteinFast.m compute the minimum distance between a Bernstein polynomial and a convex polytope (or point), and between two Bernstein polynomials. They are drop-in alternatives to MinDistBernstein2Polygon and MinDistBernstein2Bernstein: a best-first branch and bound in which the GJK distance between convex hulls of the Bernstein coefficients gives a lower bound, points on the curve give an upper bound, and pieces are subdivided with the de Casteljau algorithm until the result is certified within the tolerance epsilon (default 1e-6).
[dist, t, pt, info] = MinDistBernstein2PolygonFast(cpts, poly, epsilon);
[dist, t1, t2, info] = MinDistBernstein2BernsteinFast(cpts1, cpts2, epsilon);cpts are the Bernstein coefficients (one column per coefficient, time interval normalized to [0,1]) and poly the vertices of the polytope (one column per vertex). Helpers: gjk_lite.m (GJK distance with witness weights), split_bern.m (de Casteljau subdivision), eval_bern.m (evaluation). On the examples of Fig. 1 in the BeBOT book chapter, they are about 3–6x faster than the original functions in MATLAB R2024b.