Theoretically Based Robust Algorithms for Tracking Intersection Curves of Two Deforming Parametric Surfaces

Abstract. This paper presents the mathematical framework, and develops algorithms accordingly, to continuously and robustly track the intersection curves of two deforming parametric surfaces, with the deformation represented as generalized offset vector fields. The set of intersection curves of 2 deforming surfaces, over all time, is formulated as an implicit 2-manifold I in the augmented (by time domain) parametric space R5 . Hyper-planes corresponding to some fixed time instants may touch I at some isolated transition points, which delineate transition events, i.e., the topological changes to the intersection curves. These transition points are the 0-dimensional solution to a rational system of 5 constraints in 5 variables, and can be computed efficiently and robustly with a rational constraint solver using subdivision and hyper tangent bounding cones. The actual transition events are computed by contouring the local osculating paraboloids. Away from any transition points, the int...

• Type: Conference
• Year: 2006
• Where: GMP
• Authors: Xianming Chen, Richard F. Riesenfeld, Elaine Cohen, James N. Damon
• Keywords: GMP 2006, Intersection Curves, Transition Events, Transition Points