Marching along a regular surface surface intersection with circular steps

This paper presents a simple and elegant algorithm to estimate adaptively the stepping direction and size for tracing a branch of the intersection curve between two regular surfaces without any nonlinear equation system solver (Kriezis and Patrikalakis, 1991; Abdel-Malek and Yeh, 1996; Grandine and Klein, 1997). The step is neither along the tangent vector at the current point (Barnhill, 1987) nor along a parabola in a vicinity of the current point (Stoyanov, 1992); it is along a circle at the current point. Although no curvature analysis or power series expansions about each point of the intersection curve were used in its construction, we demonstrate that our circle tends to the exact osculating circle, when the distance between two subsequent sampling points tends to zero. Through numerical examples, we also show that the performance of our algorithm by handling singular points, bifurcations, and points on the closely spaced branches, is equivalent to the ones based on embedding schemes (Abdel-Malek and Yeh, 1996; Grandine and Klein, 1997). (C) 1999 Elsevier Science B.V. All rights reserved.