Abstract: A method and apparatus that provides for off-line generation of, and run-time evaluation for, continuous LODs. The off-line multiresolution generation process is modified and constrained such that a progressive mesh representation for continuous LODs is created that allows properly designed run-time topological data structures to be overloaded to support both LOD construction and optimized rendering. More specifically, the offline generation process initially preprocesses the mesh to generate a triangle-fan covering composed of only complete cycles. The multiresolution generation process is then constrained to maintain this complete cycle covering for every interim mesh. For run-time evaluation, a topological adjacency representation is used that can serve dual uses. This supportive run-time representation is partitioned so as to allow efficient access by the renderer to the subset of the adjacency information that is the fan covering.