Shape tracing: An extension of sphere tracing for 3D non-convex collision in protein docking

This paper presents an algorithm, similar to implicit sphere tracing, that ray marches 3D non-convex shapes for efficient collision detection. Instead of finding points on the surface where individual rays strike, an entire shape is marched in unison by a lower bound of the boundary distance, calculated at the closest point between the two surfaces. Advancing one shape towards the other by this new bound allows us to identify a contact in few steps. This method supports arbitrary nonconvex shapes, and can be run in parallel. We apply this to protein-protein docking and show that we can identify around 80 docking poses per second featuring contact but no overlap, irrespective of proteins' specific geometry. This paves the way to future fast docking algorithms, building upon implicit surface representations to quickly find a well-distributed subset of close candidate solutions for further investigation.