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

TL;DR

This paper presents a simplified and more efficient version of the GJK algorithm for determining whether two convex objects intersect, focusing solely on the Boolean intersection test rather than computing the exact distance.

Contribution

The paper introduces a geometric interpretation that reduces the number of tests in GJK when only intersection information is needed, improving efficiency.

Findings

Significantly fewer test cases are needed for intersection detection.

The simplified algorithm is more computationally efficient.

Applicable to various computational geometry applications.

Abstract

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.