To use 3D models on the Internet or in other bandwidth-limited applications, it is often necessary to compress their triangle mesh representations. We consider the problem of balancing two forms of lossy mesh compression: reduction of the number of vertices by simplification, and reduction of the number of bits per vertex coordinate. Let A(V , B) be a triangle mesh approximation for an original model O. Suppose that A(V , B) has V vertices, each represented using B bits per coordinate. Given a limit F on the file size for A (V , B) , what are the optimal values of B and V that minimize the approximation error? Given a desired error bound E, what are optimal B and V , and how many total bits are needed? We develop answers to these questions by using a shape complexity measure K, which, for any given object approximates the product EV. We give formulae linking B, V , F, E and K, and we explore a simple algorithm for estimating K and the optimal B and V for piecewise spherical approximations of arbitrary triangle meshes.
King and Rossignac REF have further balanced the reduction of the number of vertices and the reduction of bits per vertex coordinate using a shape complexity measure.
Optimal Bit Allocation in Compressed 3D Models
Computational Geometry: Theory and Applications
Mathematics Computer Science