Approximating Polygonal Objects by Deformable Smooth Surfaces

We propose a method to approximate a polygonal object by a deformable smooth surface, namely the t-skin defined by Edelsbrunner [5] for all 0 < t < 1. We guarantee that they are homeomorphic and their Hausdorff distance is at most > 0. This construction make it possible for fully automatic, smooth and robust deformation between two polygonal objects with different topologies. En route to our results, we also give an approximation of a polygonal object with a union of balls, which is a straightforward modification of our earlier work [4].