Tracing along an intersection closed loop, when should one stop?

In this paper we present an algorithm for estimating the rotation index of a closed loop from the number of singular points on it. On the basis of this index we also devise a procedure that guarantees to have an arbitrary loop being traced only once. Combining this procedure with a higher-order stepping algorithm, a robust intersection technique is resulted.

[1]  Michael I. Jordan,et al.  Surface/surface intersection , 1987, Comput. Aided Geom. Des..

[2]  Yuan-Shin Lee,et al.  Detection of loops and singularities of surface intersections , 1998, Comput. Aided Des..

[3]  H. Piaggio.  Differential Geometry of Curves and Surfaces , 1952, Nature.

[4]  Xiuzi Ye,et al.  Differential geometry of intersection curves of two surfaces , 1999, Comput. Aided Geom. Des..

[5]  F. A. Seiler,et al.  Numerical Recipes in C: The Art of Scientific Computing , 1989 .

[6]  Gregor Müllenheim.  On determining start points for a surface/surface intersection algorithm , 1991, Comput. Aided Geom. Des..

[7]  Nicholas M. Patrikalakis,et al.  Topological and differential-equation methods for surface intersections , 1992, Comput. Aided Des..

[8]  D. Struik.  Lectures on classical differential geometry , 1951 .

[9]  Eric Klassen,et al.  Exploiting topological and geometric properties for selective subdivision , 1985, SCG '85.

[10]  Sueli I. Rodrigues Costa,et al.  On estimating local geometric properties of intersection curves , 2000, Proceedings 13th Brazilian Symposium on Computer Graphics and Image Processing (Cat. No.PR00878).

[11]  Chandrajit L. Bajaj,et al.  Tracing surface intersections , 1988, Comput. Aided Geom. Des..

[12]  William H. Press,et al.  The Art of Scientific Computing Second Edition , 1998 .

[13]  Shin-Ting Wu,et al.  Marching along a regular surface/surface intersection with circular steps , 1999, Comput. Aided Geom. Des..

[14]  Thomas W. Sederberg,et al.  Loop detection in surface patch intersections , 1988, Comput. Aided Geom. Des..

[15]  Ren C. Luo,et al.  Topological method for loop detection of surface intersection problems , 1995, Comput. Aided Des..

[16]  T. Sederberg,et al.  Improved test for closed loops in surface intersections , 1989 .

[17]  Robert E. Barnhill,et al.  A marching method for parametric surface/surface intersection , 1990, Comput. Aided Geom. Des..

[18]  M. Berger,et al.  Differential Geometry: Manifolds, Curves, and Surfaces , 1987 .

[19]  E. Bompiani.  Review: D. J. Struik, Lectures on classical differential geometry , 1951 .

[20]  Robert P. Markot,et al.  Procedural method for evaluating the intersection curves of two parametric surfaces , 1991, Comput. Aided Des..