Alternating Spatial‐Temporal Optimization for Continuous Collision Detection of Signed Distance Fields

Abstract

We present a fast, robust method for continuous collision detection (CCD) directly between pairs of complex signed distance fields (SDFs). By casting CCD as an alternating spatio‐temporal optimization and driving a small set of smartly sampled surface points along SDF tangent spaces, our approach avoids dense sampling or triangle meshes entirely. The result is real‐time SDF‐SDF time‐of‐impact queries—often within 1 ms on a single CPU core—even for highly detailed, non‐convex geometry undergoing fast spinning motion. This is, to our knowledge, the first practical CCD method operating directly on SDF pairs.