| Bézier基函数的导出 |
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| 引用本文： | 施法中,韩道康.Bézier基函数的导出[J].航空学报,1980,1(1):92-98. |
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| 作者姓名： | 施法中 韩道康 |
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| 作者单位： | 北京航空学院 |
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| 摘 要： | Bzier教授在《数值控制》一书中,对Bzier曲线曲面作了优美而详尽的说明。Bzier基函数的表达式表于本文（2）和（3）。 Bzier曲线有着很多重要的和有趣的几何性质。这些性质是Bzier基函数性质的直接推论。到目前为止还没有见到关于导出这些基函数的文献。 本文证明了从Bzier曲线的三条简单的、合理的几何要求出发,用两种不同的计算方法可以完全确定并导出这些基函数。
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| 收稿时间： | 1980-04-01; |
ON THE DERIVATION OF BEZIER'S BASIC FUNCTIONS |
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| Shi Fazhong,Han Daokang.ON THE DERIVATION OF BEZIER'S BASIC FUNCTIONS[J].Acta Aeronautica et Astronautica Sinica,1980,1(1):92-98. |
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| Authors: | Shi Fazhong Han Daokang |
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| Institution: | Beijing Institute of Aeronautics and Astronautics |
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| Abstract: | In his book "Numerical Control Professor P. Bezier gives an excellent exposition of his technique in CAGD. Bezier's Basic functions fn,j （ u ） are shown in （ 2 ） and （ 3 ）. Bezier's curves have a number of important and interesting geometric properties of the basic functions. As there has been no literature on the derivation of these basic functions sofar, this paper attempts to prove in two different ways that the expressions of basic functions can be determined completely by three simple and reasonable geometric properties of the Bezier's curves. |
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