Seed Polytopes for Incremental Approximation
نویسندگان
چکیده
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.
منابع مشابه
ACS Algorithms for Complex Shapes with Certified Numerics and Topology Seed polytopes for incremental approximations of general surfaces in 3D
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 th...
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