Approximation by skin surfaces

Authors:
Nico Kruithof;Gert Vegter
Affiliations:
University of Groningen, The Netherlands;University of Groningen, The Netherlands
Venue:
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Year:
2003

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Abstract

We present a method to approximate a simple, regular C2 surface W in IR3 by a (tangent continuous) skin surface S. The input of our algorithm is a set of approximate W-maximal balls, where the boundary of the union of these balls is homeomorphic to W. By generating hyperboloid and spherical patches over the intersection curves of the balls the algorithm determines a one-parameter family of skin-surfaces, where a parameter controls the size of the patches. The skin surface S is homeomorphic to W, and the approximate W-maximal balls in the input set are also S-maximal. The Hausdorff distance between the regions enclosed by the input surface W and the approximating skin surface S depends linearly on a parameter related to the sampling density of the approximate W-maximal balls.