Local Optimization for Robust Signed Distance Field Collision

Abstract

Signed distance fields (SDFs) are a popular shape representation for collision detection. This is due to their query efficiency, and the ability to provide robust inside/outside information. Although it is straightforward to test points for interpenetration with an SDF, it is not clear how to extend this to continuous surfaces, such as triangle meshes. In this paper, we propose a per-element local optimization to find the closest points between the SDF isosurface and mesh elements. This allows us to generate accurate contact points between sharp point-face pairs, and handle smoothly varying edge-edge contact. We compare three numerical methods for solving the local optimization problem: projected gradient descent, Frank-Wolfe, and golden-section search. Finally, we demonstrate the applicability of our method to a wide range of scenarios including collision of simulated cloth, rigid bodies, and deformable solids.