Compressing Volumes and Animations

For simplicity, we limit our discussion to simple meshes, which are homeomorphic to a triangulation of a sphere. Yet, most of the techniques presented here are applicable, or have been extended to, more general topologies, including meshes with borders, handles, non-manifold vertices and edges, non-triangular faces [Ross99, GBTS99, RoCa99, ToGo98, RSS01, KRS99, BPZ99, IsSn00, Lo&02]. Hence, we assume that the triangle mesh is a connected manifold surface with no boundary and no handle and that it has v vertices, e edges, and t triangles. We consider an edge to be a relatively open line segment that does not include its endpoints. Similarly, a face is the relative interior of a triangle, excluding its edges and vertices. The surface of the mesh is the union of its faces, edges, and vertices, which are assumed to be all pair-wise disjoint.