We propose a method to approximate a polygonal object by a deformable smooth surface, namely the t-skin defined by Edelsbrunner for all 0 < t < 1. We guarantee that they are homeomorphic and their Hausdorff distance is at most ε > 0. Such construction makes 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.
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