ABSTRACT
One of the fundamental components of a haptic rendering algorithm is collision detection, to determine where and when virtual objects collide. Among collision detection methods, the continuous ones enable penetration-free simulations of contacting objects and allow for detailed haptic interaction. In this chapter, we provide a basic introduction to interval-based continuous collision detection methods for rigid and articulated bodies. We present time-parameterized equations for continuous collision detection between rigid primitives, as well as methods to efficiently solve these equations. We also describe continuous overlap tests between hierarchies of bounding volumes, which help achieve efficient collision detection for complex models. An appendix gathers some basic template data structures to allow the reader to easily start implementing the methods described in this chapter.
12.1 Why Continuous Collision Detection? Collision detection methods can roughly be split into two categories. Until recently, most collision detection methods that have been proposed are discrete: they sample the objects’ trajectories at discrete times and report interpenetrations.
