**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.