Getting contours of two overlapped regions bounded by cubic bezier curves and straight lines

摘要

We present an algorithm for getting the contour(s) of two overlapped regions which are bounded by cubic Bezier curve and straight line segments. It was used in font design to solve the problem of converting the stroke-contour-based description of Chinese character into outlined description. The algorithm involves locating intersections and forming contour boundary. The interesection calculation of curve/curve is based on Bezier clipping method(1). The approach of forming contour is a generalization of Weiler-Atherton algorithm(cf.(2)). The efficiency of the algorithm depends on the efficiency of intersection calculation, mainly related to the number of intersections, how they are spaced and how the edges are positioned. As our experience, in general the algorithm is efficient. Especially, when applied in Chinese font design, the effect is satisfied. Though it is originally used in font design, the algorithm can also be looked as a Bezier curved region clipping method and used in other areas of computer graphics.