Implant Sprays: Compression of Progressive Tetrahedral Mesh Connectivity

Abstract

Irregular tetrahedral meshes, which are popular in many engineering and scientific applications, often contain a large number of vertices. A mesh of V vertices and T tetrahedra requires 48-V bits or less to store the vertex coordinates, 4-T-log₂(V) bits to store the tetrahedra-vertex incidence relations, also called connectivity information, and k-V bits to store the k-bit value samples associated with the vertices. Given that T is 5 to 7 times larger than V and that V often exceeds 32², the storage space required for the connectivity is larger than 300-V bits and thus dominates the overall storage cost. Our "implants spray" compression approach introduced in this paper reduces this cost to about 30-V bits or less - a 10:1 compression ratio. Furthermore, implant spray supports the progressive refinement of a crude model through a series of vertex-splits operations.