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Seed Polytopes for Incremental Approximation

Approximating a given three-dimensional object in order to simplify its handling is a classical topic in computational geometry and related fields. A typical approach is based on incremental approximation algorithms, which start with a small and topologically correct polytope representation (the seed polytope) of a given sample point cloud or input mesh. In addition, a correspondence between the faces of the polytope and the respective regions of the object boundary is needed to guarantee correctness. We construct such a polytope by first computing a simplified though still homotopy equivalent medial axis transform of the input object. Then, we inflate this medial axis to a polytope of small size. Since our approximation maintains topology, the simplified medial axis transform is also useful for skin surfaces and envelope surfaces.