Fast and Accurate Spacio-temporal Intersection Detection with the GJK Algorithm

This paper discusses an extrusion technique to quickly and robustly tackle the four-dimensional problem of spacio-temporal intersection detection for rigid bodies with arbitrary motion. We combine the GJK algorithm with Brent’s method to determine non-collision or timeof-impact (TOI) for an object pair over a complete time interval. Experimental results show this method capable of supporting accurate rigid body simulation of large scale and highly dynamic environments at interactive frame rates on a common PC.