Curve intersection based on cubic hybrid clipping.

Abstract

This study presents a novel approach to computing all intersections between two Bézier curves using cubic hybrid clipping. Each intersection is represented by two strip intervals that contain an intersection. In each step, one curve is bounded by two fat lines, and the other is bounded by two cubic Bézier curves, clipping away the domain that does not contain the intersections. By selecting the moving control points of the cubic hybrid curves, better cubic polynomial bounds are obtained to make the proposed method more efficient. It was proved that the two strip intervals have second- and fourth-order convergence rates for transversal intersections. Experimental results show that the new algorithm is the most efficient among all existing curve/curve intersection approaches.