An iterative algorithm for finding a nearest pair of points in two convex subsets of Rn

Efficient Computation of the Hausdorff Distance Between Polytopes by Exterior Random Covering

“…When d = 3 there exist some fast algorithms for projecting onto polyhedra [21,24,25] that can be used in (10). This expression needs to project all the vertices of both polytopes.…”

“…We call HERC to an algorithm for computing the Hausdorff distance between polyhedra, based on (10) and on the following techniques • Local Search Algorithm Based on Faces (LSABF) [24,25], for finding the projections which appear in (10). • Exterior Random Covering (ERC) for computing the maximum distance.…”

A local search algorithm for ray-convex polyhedron intersection

“…It also describes some global properties of the directions whose corresponding rays intersect the polyhedron. Proof (i) See [16]. (ii) Follows from (i) and the convexity of P.…”

“…Local search strategies provide a fast way of solving some geometric optimization problems [5,6,10,[15][16][17]. For solving the RCPI problem, we can determine a starting face and a way to go from a face to the next one, until arriving at a decision face.…”

“…If p is far enough from P (1) is fulfilled. Below we give the C-like pseudocode of an algorithm based on the above proposition, see [16].…”