A complete and non-overlapping tracing algorithm for closed loops

Authors:
Wu Shin-Ting;Osmar Aléssio;Sueli I. R. Costa
Affiliations:
UNICAMP--State University of Campinas, Electrical and Computer Engineering Faculty, Department of Computer Engineering and Industrial Automation, Campinas, SP, Brazil;UNINCOR--University Valley of Green River, Institute of Mathematics, Brazil;UNICAMP--State University of Campinas, Institute of Mathematics, Brazil
Venue:
Computer Aided Geometric Design
Year:
2005

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Abstract

A procedure for tracing completely closed loops given implicitly by the intersection of two regular surfaces, without resorting to the parametric domain subdivisions or resulting in arc overlapping, is presented. Our primary hypothesis is that the rotation index, a global geometrical property, may be a useful complementary tool to the local differential geometrical properties for improving the efficiency of the well-known marching-based surface-surface intersection algorithms. To validate this hypothesis, we devised a novel approach for incrementally computing the rotation index of a closed plane curve given implicitly while the curve is traced. Moreover, we also proposed its integration in a marching procedure that employs adaptative circular steps.