Fast Penetration Volume for Rigid Bodies

Handling collisions among a large number of bodies can be a performance bottleneck in video games and many other real-time applications. We present a new framework for detecting and resolving collisions using the penetration volume as an interpenetration measure. Given two non-convex polyhedral bodies, a new sampling paradigm locates their near-contact configurations in advance, and stores associated contact information in a compact database. At runtime, we retrieve a given configuration's nearest neighbors. By taking advantage of the penetration volume's continuity, cheap geometric methods can use the neighbors to estimate contact information as well as a translational gradient. This results in an extremely fast, geometry-independent, and trivially parallelizable computation, which constitutes the first global volume-based collision resolution. When processing multiple collisions simultaneously on a 4-core processor, the average running cost is as low as 5 microseconds. Furthermore, no additional proximity or contact-regions queries are required. These results are orders of magnitude faster than previous penetration volume approaches.

The work was supervised by Prof. Dani Lischinski of the Hebrew University.