Optimizing the Separating Axis Theorem with Gauss Map Traversal

This article presents an optimized collision detection algorithm for convex polyhedra. Reframing the Separating Axis Theorem (SAT) as a sphere-based optimization problem, the author reveals that the minimum lies at the intersections of great circles on a Gauss map. A graph traversal algorithm avoids repeated support function calculations, requiring only one full evaluation initially. The algorithm then efficiently updates the support point by traversing the Gauss map, resulting in significant performance gains. Tests show a 5-10x speedup over traditional SAT.