Optimal Bit Allocation in 3D Compression

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 of resolution used per vertex coordinate via quantization. Let A be a triangle mesh approximation for an original model O. Suppose that A has V vertices, each represented using B bits per coordinate. Given a file size F for A, what are the optimal values of B and V? Given a desired error level E, what are estimates of B and V, and how many total bits are needed? We develop answers to these questions by using a shape complexity measure K that allows us to express the optimal value of B for a general model in terms of V and K alone. We give formulas linking B, V, F, E and K, and we provide a simple algorithm for estimating the optimal B and V for an existing triangle mesh with a given file size F