 
Summary: Seed Polytopes for Incremental Approximation #
O. Aichholzer + F. Aurenhammer # T. Hackl + B. Kornberger + S. Plantinga § G. Rote ¶
A. Sturm ¶ G. Vegter §
Abstract
Approximating a given threedimensional 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 al
gorithms, 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
