Projection-homeomorphic surfaces

Authors:
F. Chazal;A. Lieutier;J. Rossignac
Affiliations:
Mathematics Institute of Burgundy, Dijon - France;Dassault Systèmes and LMC/IMAG, Grenoble, France;IRIS, GVU Georgia Tech. Atlanta, Georgia
Venue:
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Year:
2005

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Abstract

Consider two (n - 1)-dimensional manifolds, S and S' in Rn. We say that they are projection-homeomorphic when the closest projection of each one onto the other is a homeomorphism. We give tight conditions under which S and S' are projection-homeomorphic. These conditions involve the local feature size for S and for S' and the Hausdorff distance between them. Our results hold for arbitrary n.