Simplifying polygonal models using successive mappings

We present the use of mapping functions to automatically generate levels of detail with known error bounds for polygonal models. We develop a piece-wise linear mapping function for each simplification operation and use this function to measure deviation of the new surface from both the previous level of detail and from the original surface. In addition, we use the mapping function to compute appropriate texture coordinates if the original map has texture coordinates at its vertices. Our overall algorithm uses edge collapse operations. We present rigorous procedures for the generation of local planar projections as well as for the selection of a new vertex position for the edge collapse operation. As compared to earlier methods, our algorithm is able to compute tight error bounds on surface deviation and produce an entire continuum of levels of detail with mappings between them. We demonstrate the effectiveness of our algorithm on several models: a Ford Bronco consisting of over 300 parts and 70, 000 triangles, a textured lion model consisting of 49 parts and 86, 000 triangles, and a textured, wrinkled torus consisting of 79, 000 triangles.