Proximity queries for modeling and manufacturing

Collision detection and distance calculation are two examples of proximity queries between modelled objects. They are interesting both in their own right, and as useful tools to solve other problems (e.g., robot path planning). They also form useful abstractions away from the underlying representation of a geometric model. This paper considers the solution and use of such problems in geometric modeling and robotics, gives examples from our own work, and discusses the possible future of the technology.