A Complete and Non-Overlapping Tracing Algorithm for Closed Loops Wu, Shin-Ting 1 UNICAMP - State University of Campinas Electrial and Computer Engineering Faculty Dept. Computer Engineering and Industrial Automation P.O.Box 6101 13083-970 - Campinas, SP, Brazil {ting}@dca.fee.unicamp.br Osmar Al´ essio UNINCOR - University Valley of Green River Institute of Mathematics {osmaralessio}@yahoo.com.br Sueli I. R. Costa UNICAMP - State University of Campinas Institute of Mathematics sueli@ime.unicamp.br 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 geo- metrical 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 incre- mentally 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. Key words: Rotation index, Regular closed plane curve, Surface–surface intersection, Marching-based algorithm, Geometric modeling. 1 Corresponding author Preprint submitted to Elsevier Science June 15, 2005