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DOI:
Journal of Software:2002.13(10):2014-2020

基于插值的Bernstein多项式复合及其曲线曲面应用
冯结青,彭群生
(浙江大学,CAD&CG国家重点实验室,浙江,杭州,310027)
Bernstein Polynomial Composition Through Interpolation and Its Applications in Curves and Surfaces
FENG Jie-qing,PENG Qun-sheng
()
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Received:January 11, 2001    Revised:January 11, 2001
> 中文摘要: 在曲线曲面造型中,Bernstein多项式复合被广泛用于许多几何操作,因而具有重要的理论和实际意义.基于多项式插值和符号计算的思想,研究了Bernstein多项式函数复合问题, 并将其应用于曲线曲面的情形.与两种已有方法相比,新方法具有速度快、易于编程实现、占用存储空间少的特点,但数值精度低于基于广义de Casteljau算法的多项式复合结果.
Abstract:In curve and surface modeling, Bernstein polynomial compositions are widely used for various geometric operations. So it is important to investigate them both in theory and practice. The problems are investigated by using polynomial interpolation and symbolic computation, and the proposed method is applied for curve and surface cases. Compared with two existing methods, the proposed method has the advantages on computational cost, coding efficiency, storage cost. However its numerical accuracy is lower than the method based on the generalized de Casteljau algorithm.
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基金项目:国家自然科学基金资助项目(69903008);国家创新研究群体科学基金资助项目( 60021201) 国家自然科学基金资助项目(69903008);国家创新研究群体科学基金资助项目( 60021201)
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冯结青,彭群生.基于插值的Bernstein多项式复合及其曲线曲面应用.软件学报,2002,13(10):2014-2020

FENG Jie-qing,PENG Qun-sheng.Bernstein Polynomial Composition Through Interpolation and Its Applications in Curves and Surfaces.Journal of Software,2002,13(10):2014-2020