A Bidirectional Generating Algorithm for Rational Parametric Curves

摘要

A generating algorithm for rational quadratic Bezier curves is provided. In the algorithm, we find the recurrence relation to get every pixel along the curve, using the bidirectional strategy for rendering and the forward and backward difference method for computing. The algorithm has a fast generating speed, and the curves keep a reasonable rendering accuracy. This algorithm can easily be generalized to render higher-degree rational Bezier curves and other rational parametric curves; it has broad applications. Source code is available online at the website listed at the end of this paper.