Generation of Continuous Smooth Curves Resulting from Operations on Parametric Surface Patches

In recent years a number of techniques based on the subdivision principle have been suggested for detecting the curves resulting from the intersection of two parametrically defined surface patches. Silhouette curves of surfaces can also be detected using analogous techniques. Usually the output is a set of pixels or line segments which form the complete curve, though not necessarily in an ordered manner. This paper presents data structures for maintaining the result of subdivision, and algorithms for tracing the curves in a continuous fashion. Using a few iterations of the Newton-Raphson technique the curve points may be refined to any required precision. For each point on the curve the nonlinear equations are chosen by looking at the local topological nature of the curve so as to guarantee convergence of the Newton-Raphson technique in one or two iterations