Computing metric and topological properties of configuration-space obstacles

The author describes an algorithm that takes two polygons as input, and computes a representation of their corresponding configuration-space obstacle, including contact information. The algorithm´s output includes a full metric and topological description of the obstacle surface, as well as the set of polygon features that are in contact for each point of the surface. The representation is exact, up to the limits of floating-point arithmetic. The algorithm has been implemented and test-run on over 40 input pairs; run times varied between 12 and 135 s