| 曲面转换中的一个定理 |
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| 引用本文： | 王拉柱,左万利,唐泽圣.曲面转换中的一个定理[J].清华大学学报(自然科学版),1998(3). |
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| 作者姓名： | 王拉柱 左万利 唐泽圣 |
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| 作者单位： | 1. 清华大学,计算机科学与技术系,北京,100084
2. 吉林大学计算机科学与技术系,长春,130021 |
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| 摘 要： | Ｃｏｏｎｓ类曲面、Ｂ样条曲面和ＮＵＲＢＳ曲面是ＣＡＧＤ中主要的曲面表达形式。Ｃｏｏｎｓ构造曲面的思想对ＣＡＧＤ的发展起了巨大的推动作用。Ｂ样条曲线、曲面具有许多优点而且已成为ＣＡＧＤ中使用最为广泛的方法之一。文中应用Ｂ样条的递推公式，讨论了Ｃｏｏｎｓ类曲面向ＮＵＲＢＳ曲面转换过程中用到的一个重要定理。给出了这个定理的一种构造性证明。定理的证明过程同时也给出了转换方法。这个定理在Ｃｏｏｎｓ类曲面向ＮＵＲＢＳ曲面的转换过程中起到了重要的桥梁作用。
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| 关 键 词： | Coons曲面 B样条曲面 NURBS曲面 |
Theorem for curved surface conversion |
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| WANG Lazhu,ZUO Wanli,TANG Zesheng.Theorem for curved surface conversion[J].Journal of Tsinghua University(Science and Technology),1998(3). |
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| Authors: | WANG Lazhu ZUO Wanli TANG Zesheng |
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| Abstract: | In the CAGD field, Coons surface, B spline surface and NURBS surface are mainly used. Coons strategy has been of great impact to the development of CAGD. B spline surface is mathematically elegant with many good properties and has become one of the most widely used methods in CAGD. In this paper, an important theorem which is used in the conversion of Coons surface to NURBS surface is discussed. A construction proof of the theorem is proposed and the proof process also gives a method to convert Coons surface to NURBS surface. |
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