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DP 基关于L2 内积的对偶函数及其应用

  

  • 出版日期:2015-04-30 发布日期:2015-06-03

Dual Functions on L2 Inner Product for DP Basis and Their Applications

  • Online:2015-04-30 Published:2015-06-03

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摘要： 给出DP 基关于L2 内积对偶函数的显示表示公式。首先介绍了计算机辅助几何设
计中多项式对偶函数的一般理论；然后根据两组多项式基的转换公式，给出了相应对偶函数的
转换公式。随后利用此转换公式和Bernstein 基对偶函数的表示公式，推导出DP 基关于L2 内积
对偶函数的显示表示。讨论了对偶函数在计算机辅助几何设计中的应用。

关键词: DP 基, 对偶函数, L2 内积, 广义De Boor-Fix 公式, 逼近

Abstract: An explicit formula for the dual functions of DP basis on L2 inner product is derived. The
general theory of polynomial dual functions in computer aided geometric design is first introduced,
and by using conversion formulas between two polynomial basis, the conversion formulas between
two corresponding dual functions are deduced. Then with this conversion formulas and the dual
functions of Bernstein basis, the dual functions of DP basis on L2 inner product are obtained. Finally,
the application of this result in computer aided geometric design is discussed.

Key words: DP basis, dual functions, L2 inner product, generalized De Boor-Fix formula;
approximation