Numerically Robust Continuous Collision Detection for Dynamic Explicit Surfaces

We present a new, provably robust method for continuous collision detection for moving triangle meshes. Our method augments the spatial coordinate system by one dimension, representing time. We can then apply numerically robust predicates from computational geometry to detect intersections in space-time. These predicates use only multiplication and addition, so we can determine the maximum numerical error accumulated in their computation. From this forward error analysis, we can identify and handle degenerate geometric configurations without resorting to user-tuned error tolerances.