Convex polyhedral chains: a representation for geometric data

A representation scheme for general polyhedra in arbitrary dimensions is presented. Each polyhedron is represented as a convex chain, i.e. an algebraic sum of convex polyhedra (cells). Each cell in turn is represented as the intersection of halfspaces and encoded in a vector. The notion of vertices is abandoned completely. It is shown how this approach allows the decomposition of set operations (such as intersection) on polyhedra into two independent steps. The first step consists of a collection of vector operations; the second step is a garbage collection where vectors that represent empty cells are eliminated. No special treatment of singular intersection cases is needed. This approach to set operations is significantly different from algorithms that have been proposed previously.