Curve intersection using hybrid clipping

Abstract

This paper presents a novel approach, called hybrid clipping, for computing all intersections between two polynomial Bézier curves within a given parametric domain in the plane. Like Bézier clipping, we compute a ‘fat line’ (a region along a line) to bound one of the curves. Then we compute a ‘fat curve’ around the optimal low degree approximation curve to the other curve. By clipping the fat curve with the fat line, we obtain a new reduced subdomain enclosing the intersection. The clipping process proceeds iteratively and then a sequence of subdomains that is guaranteed to converge to the corresponding intersection will be obtained. We have proved that the hybrid clipping technique has at least a quadratic convergence rate. Experimental results have been presented to show the performance of the proposed approach with comparison with Bézier clipping.