A Bidirectional Generating Algorithm for Rational Parametric Curves

Zhong Li
Shanghai Jiao Tong University and Zhejiang Sci-Tech University

Lizhuang Ma
Shanghai Jiao Tong University

This paper appears in issue Volume 11, Number 3.
An electronic version of this article is available.

Abstract

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.

Author Information

Zhong Li, Department of Computer Science and Engineering, Shanghai Jiao Tong University200030 Shanghai, China lizhongzju@hotmail.com

Lizhuang Ma, Department of Computer Science and Engineering, Shanghai Jiao Tong University200030 Shanghai, China ma-lz@cs.sjtu.edu.cn

Source Code

Source code in C, written using the Microsoft VC 6.0 development environment.

Source.zip

BibTeX Entry

@article{LiMa06,
  author = "Zhong Li and Lizhuang Ma",
  title = "A Bidirectional Generating Algorithm for Rational Parametric Curves",
  journal = "journal of graphics, gpu, and game tools",
  volume = "11",
  number = "3",
  pages = "17-26",
  year = "2006",
}