| 基于插值的Bernstein多项式复合及其曲线曲面应用 |
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| 引用本文： | 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[J].软件学报,2002,13(10):2014-2020. |
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| 作者姓名： | 冯结青 彭群生 |
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| 作者单位： | 浙江大学,CAD&CG国家重点实验室,浙江,杭州,310027 |
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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) |
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| 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.
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| 关 键 词： | Bernstein多项式 函数复合 多项式插值 符号计算 数值精度 |
| 收稿时间： | 2001/1/11 0:00:00 |
| 修稿时间： | 2001年1月11日 |
Bernstein Polynomial Composition Through Interpolation and Its Applications in Curves and Surfaces |
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| FENG Jie-qing and PENG Qun-sheng.Bernstein Polynomial Composition Through Interpolation and Its Applications in Curves and Surfaces[J].Journal of Software,2002,13(10):2014-2020. |
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| Authors: | FENG Jie-qing and PENG Qun-sheng |
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| 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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| Keywords: | Bernstein polynomial functional composition polynomial interpolation symbolic computation numerical accuracy |
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