Improving the Numerical Robustness of Sphere Swept Collision Detection

This paper discusses improvements to the numerical robustness of the algorithm described in Kasper Fauerby's "Improved Collision Detection and Response." The algorithm addresses a common collision detection query: a moving sphere or ellipsoid vs. a set of motionless triangles. In its current form, the algorithm allows the sphere to penetrate the triangles. The sphere also displays "jittering" behavior when colliding with certain geometry. Most of these problems are the product of insufficient attention to numerical robustness, the focus of this paper. Motivated by the importance of numerical robustness in collision detection code, this paper addresses these problems in detail and proposes efficient solutions to them.