A cocktail algorithm for planar bzier curve intersections
Presented in this paper is a new intersection algorithm between planar Bzier 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 Bzier curve segments according to the shape characteristics of the curve. Then, the rational quadratic Bzier 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.
bzier curve intersections planar curve newton-raphson characterization