Collision detection and response are important for interactive graphics applications such as vehicle simulators and virtual reality. Unfortunately, previous collision detection algorithms are too slow for interactive use. The paper presents a new algorithm for rigid or articulated objects that meets performance goals through a form of time critical computing. The algorithm supports progressive refinement, detecting collisions between successively tighter approximations to object surfaces as the application allows it more processing time. The algorithm uses simple four dimensional geometry to approximate motion, and hierarchies of spheres to approximate three dimensional surfaces at multiple resolutions. In a sample application, the algorithm allows interactive performance that is not possible with a good previous algorithm. In particular, the new algorithm provides acceptable accuracy while maintaining a steady and high frame rate, which in some cases improves on the previous algorithm's rate by more than two orders of magnitude.
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