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关于Bézier方法的数学基础

常庚哲,吴骏恒,   

  1. 中国科技大学,北京航空学院,
  • 出版日期:1980-01-14 发布日期:1980-01-14

常庚哲,吴骏恒,. 关于Bézier方法的数学基础[J]. 计算数学, 1980, 2(1): 41-49.

ON MATHEMATICAL FOUNDATIONS OF BZIER'S METHOD

  1. Chang Gen-zhe (Chinaese University of Science and Technology)Wu Jun-heng (Beijing Institute of Aeronautics and Astronautics)
  • Online:1980-01-14 Published:1980-01-14
1.引言 1974年,在美国犹他(Utah)大学召开了第一次国际性的计算机辅助几何设计(简称CAGD)会议,并出版了会议论文集。会议的中心论题,是讨论Coons曲面、Bezier曲面和样条函数方法在CAGD中的应用。大多数与会者都提到了Coons和Bezier的开创性的工作,公认他们的方法在CAGD方面起了基本而重要的作用。事实上,Coons方法和Bezier方法在现代CAGD中是使用最广的两种方法,并驾齐驱而各有千秋。
Bezier’s method is one of the most famous methods in Computational Geometry. In his book——Numerical Control——Bezier gives excellent expositions of the mathema-tical foundations of his method. In this paper a new expression of the functions is obtained. Utilizing this formula, we have not only derived some properties concerning the functions, for instance, and functions increase strictly at[0,1] etc, but also simplified systemati-cally all the mathematical discussions about Bezier’s method. Finally we have proved the plotting theorem completely by matrix calculation.
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[1] P. Bezier, Mathematical and Practical Possibilities of UNISURF, CAGD文集, 1974, 127-152.
[2] P. Bezier, Numerical Control-Mathematics and Applications, John Wiley and Sons, London,1972.
[3] W.J. Gordon, R.F. Riesenfeld, Bernstein-Bezier Methods for Computer-Aided Design of Free Form Curves and Surfaces, J. of ACM, 21: 2(1974) , 293-310.
[4] W.J. Gordon, R.F. Riesenfeld, B-Spline Curves and Surfaces, CAGD文集, 1974, 95-126.
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