AHD: The alternate hierarchical decomposition of nonconvex polytopes (generalization of a convex polytope based spatial data model)

Robust convex decomposition, RCD, of polytopes is the convex decomposition of nonconvex polytopes using algorithms whose implementation is based on arbitrary precision arithmetic. Decomposing nonconvex polytopes using RCD can make the data representation model consistent enabling generalization with level of detail. Our approach, alternate hierarchical decomposition, AHD, for the decomposition of nonconvex polytopes with arbitrary genus, is a recursive approach whose implementation is robust, efficient and scalable to any dimension. Our approach decomposes the given nonconvex polytope with arbitrary genus into a set of component convex hulls, which are represented hierarchically in a tree structure, convex hull tree, CHT.