Generation of configuration space obstacles: the case of a moving sphere

Algebraic algorithms are presented for generating the boundary of configuration space obstacles arising from the motion of a sphere among obstacles. The boundaries of the obstacles are given by patches of algebraic surfaces. Algorithms are given for both implicit and parametric surface patches. Both convex and nonconvex obstacles are considered. In the case of convex obstacles, the topology of convolution faces is the same as the adjacency graph of faces, edges, and vertices of the obstacle. Further, there are no redundancies in the convolution faces. Redundancies on the convolution can occur in the case of nonconvex obstacles. It is possible to detect these redundancies from the the intersections and self-intersections of convolution faces. Simple solids are also considered