O. Aichholzer, F. Aurenhammer, T. Hackl, B. Kornberger, S. Plantinga,
G. Rote, A. Sturm, and G. Vegter
Approximating a 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.
European Workshop on Computational Geometry EuroCG
'08, pages 13-16, Nancy, France, 2008.