Progressive Mesh Decomposition in the Operational Rate-Distortion Sense Using Global Error

Given a semi-regular mesh whose subdivision onne tivity is obtained with the 4-8 s heme, we propose an algorithm to de ompose the mesh into a ontrol mesh and a series of embedded detail meshes. Hen e, the output representation is adaptive and progressive. We use a tree-driven, ne to oarse approa h to simplify the mesh using vertex de imation. Previous approa hes use lo al error and greedy strategies to simplify meshes. Our method uses global error and a generalized vertex de imation te hnique borrowed from optimal tree pruning algorithms used in ompression. Although global error is used, our algorithm has ost (n logn). We show that a dire t approa h using the same error riterion has at least ost (n). We have a rate-distortion framework: ea h approximation satis es a onstraint in rate (e.g. number of triangles) while minimizing the distortion (e.g. distan e in l2 norm with the input mesh). The algorithm aims at the optimal approximations in the rate-distortion sense. We analyze the optimality of the algorithm and give several proofs for its properties. Our algorithm an be applied to meshes obtained with other subdivision s hemes (e.g. Loop, Catmull-Clark,...) and has also appli ations in ompression and nite element analysis.