A cocktail algorithm for planar Bezier curve intersections

Abstract

Presented in this paper is a new intersection algorithm between planar Bezier curves. The algorithm, named the cocktail algorithm, mixes and matches the merits of existing intersection algorithms appropriately. In the proposed approach, curves are approximated by a number of rational quadratic Bezier curve segments according to the shape characteristics of the curve. Then, the rational quadratic Bezier curve approximations are intersected using the implicitization method to produce the seeds of the numerical process. Experimental results reveal that the performance of the cocktail algorithm is superior to others for the curves with degrees higher than cubic. For cubic curves, however, the cocktail algorithm is slightly slower than the implicitization method with a hard coded resultant, but faster than others. (C) 1999 Elsevier Science Ltd. All rights reserved.