A Geometric Interpretation of the Boolean Gilbert-Johnson-Keerthi Algorithm

The Gilbert-Johnson-Keerthi (GJK) algorithm is an iterative improvement technique for finding the minimum distance between two convex objects. It can easily be extended to work with concave objects and return the pair of closest points. [4] The key operation of GJK is testing whether a Voronoi region of a simplex contains the origin or not. In this paper we show that, in the context where one is interested only in the Boolean value of whether two convex objects intersect, and not in the actual distance between them, the number of test cases in GJK can be significantly reduced. This results in a simpler and more efficient algorithm that can be used in many computational geometry applications.