Real-time Collision Detection between General SDFs

Signed Distance Fields (SDFs) have found widespread utility in collision detection applications due to their superior query efficiency and ability to represent continuous geometries. However, little attention has been paid to calculating the intersection of two arbitrary SDFs. In this paper, we propose a novel, accurate, and real-time approach for SDF-based collision detection between two solids, both represented as SDFs. Our primary strategy entails using interval calculations and the SDF gradient to guide the search for intersection points within the geometry. For arbitrary objects, we take inspiration from existing collision detection pipelines and segment the two SDFs into multiple parts with bounding volumes. Once potential collisions between two parts are identified, our method quickly computes comprehensive intersection information such as penetration depth, contact points, and contact normals. Our method is general in that it accepts both continuous and discrete SDF representations. Experiment results show that our method can detect collisions in high-precision models in real time, highlighting its potential for a wide range of applications in computer graphics and virtual reality.