O. Aichholzer, F. Aurenhammer, T. Hackl, B. Kornberger, S. Plantinga,
G. Rote, A. Sturm, and G. Vegter
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.
