We propose the idea of simplification envelopes for generating a hierarchy of level-of-detail approximations for a given polygonal model. Our approach guarantees that all points of an approximation are within a user-specifiable distance from the original model and that all points of the original model are within a distance from the approximation. Simplification envelopes provide a general framework within which a large collection of existing simplification algorithms can run. We demonstrate this technique in conjunction with two algorithms, one local, the other global.
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Cohen et al. (1996) studied this question.
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