Abstract: 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 "epsilon" from the original model and that all points of the original model are within a distance "epsilon" 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. The local algorithm provides a fast method for generating approximations to large input meshes (at least hundreds of thousands of triangles). The global algorithm provides the opportunity to avoid local "minima" and possibly achieve better simplifications as a result. Each approximation attempts to minimize the total number of polygons required to satisfy the above "epsilon" constraint. The key advantages of our approach are: General technique providing guaranteed error bounds for genus-preserving simplification Automation of both the simplification process and the selection of appropriate viewing distances Prevention of self-intersection Preservation of sharp features Allows variation of approximation distance across different portions of a model.