Conditions for use of a non-selfintersection conjecture

Authors:
L. -E. Andersson;N. F. Stewart;M. Zidani
Affiliations:
Department of Mathematics, University of Linköping, Linköping, SE-581 83, Sweden;Département IRO, Université de Montréal, CP 6128, Succ. CentreVille, H3C 3J7, Canada;Département IRO, Université de Montréal, CP 6128, Succ. CentreVille, H3C 3J7, Canada
Venue:
Computer Aided Geometric Design
Year:
2006

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Abstract

Volino and Thalmann have published a conjecture proposing sufficient conditions for non-selfintersection of surfaces. Such conditions may be used in solid modeling, computer graphics, and other application areas, as a basis for collision-detection algorithms. In this paper we clarify certain of the hypotheses of the proposed theorem, and give a proof. A brief summary of possible pitfalls related to using the conditions, when the hypotheses of the formal theorem given here are not satisfied, is also given. We also give examples, and show that the theorem can be extended to domains that are not simply connected.