Approximating polygonal objects with deformable smooth surfaces

Abstract

We propose a method to approximate a polygonal object with adeformable smooth surface, namely the t-skin defined byEdelsbrunner for all 0< t < 1. We guarantee that they arehomeomorphic and their Hausdorff distance is at most \epsilon>0.This construction makes it possible for fully automatic, smoothand robust deformation between two polygonal objects withdifferent topologies. En route to our results, we also give anapproximation of a polygonal object with a union of balls.