Change of basis algorithms for surfaces in CAGD

Suresh Lodha; Ron Goldman

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Change of basis algorithms for surfaces in CAGD

机译：CAGD中曲面的基础算法的更改

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摘要

The computational complexity of general change of basis algorithms from one bivariate: polynomial basis of degree n to another bivariate polynomial basis of degree n using matrix multiplication is O(n~4). Applying blossoming and duality, we derive change of basis algorithms with computational complexity O(n~3) between two important classes of polynomial bases used for representing surfaces in CAGD: B-bases and L-bases. Change of basis algorithms for B-bases follow from their blossoming property; change of basis algorithms for L-bases follow from the duality between L-bases and B-bases. The Bezier and multinomial bases are special cases of both B-bases and L-bases, so these algorithms can be used to convert between the B6zier and multinomial forms. We also show that the bivariate Horner evaluation algorithm for the multinomial basis is dual to the bivariate de Boor evaluation algorithm for B-patches.

机译：使用矩阵乘法，从一个双变量：n次多项式基础到n个其他双变量多项式基础的基本算法的一般更改的计算复杂度为O（n〜4）。应用开花和对偶，我们得出了用于在CAGD中表示曲面的两个重要的多项式基类之间的计算复杂度为O（n〜3）的基算法的变化：B基和L基。 B基的基础算法的变化取决于它们的开花特性。 L基的基础算法的变化源自L基和B基之间的对偶关系。 Bezier和多项式基是B基和L基的特例，因此这些算法可用于在B6zier和多项式之间进行转换。我们还表明，用于多项式的双变量Horner评估算法对B补丁的双变量de Boor评估算法是双重的。

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来源
《Computer Aided Geometric Design》 |1995年第8期|p.801-824|共24页
作者
Suresh Lodha; Ron Goldman;
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作者单位

Department of Computer and Information Sciences, University of California, Santa Cruz, CA 95064, USA;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类计算机的应用;
关键词
algorithms; blossoming; CAGD; change of basis; de boor evaluation; de boor-fix formula; duality; horner evaluation; polynomials; surfaces;

机译：算法;开花;CAGD;基改变;de boor评估;de boor-fix公式;对偶性;horner评估;多项式;曲面;

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Change of basis algorithms for surfaces in CAGD

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