| 三角域上的调和B-B曲面 |
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| 引用本文： | 徐岗,汪国昭.三角域上的调和B-B曲面[J].计算机学报,2006,29(12):2180-2185. |
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| 作者姓名： | 徐岗 汪国昭 |
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| 作者单位： | 浙江大学数学系,杭州,310027 |
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| 基金项目： | 国家自然科学基金;国家重点基础研究发展计划(973计划) |
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| 摘 要： | 利用方向导数研究了三角域上的调和B—B曲面的性质，给出了三角域上的B—B曲面为调和曲面的充要条件，并且证明了任何一个三角域上的调和B—B曲面的控制网格均由它的第1层和第2层控制顶点完全决定．最后对极小曲面在建筑设计中的应用进行了初步探讨．
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| 关 键 词： | 极小曲面 调和曲面 三角域上的调和B-B曲面 控制网格 建筑设计 |
| 收稿时间： | 2005-07-07 |
| 修稿时间： | 2005-07-072006-06-07 |
Harmonic B-B Surfaces over the Triangular Domain |
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| XU Gang,WANG Guo-Zhao.Harmonic B-B Surfaces over the Triangular Domain[J].Chinese Journal of Computers,2006,29(12):2180-2185. |
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| Authors: | XU Gang WANG Guo-Zhao |
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| Affiliation: | Department of Mathematics, Zhejiang University, Hangzhou 310027 |
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| Abstract: | The minimal surfaces have been extensively employed in many areas. However, the complexity of the minimal surface equation prevents people from modeling minimal surface in CAD. In some special cases, the harmonic surface can be considered as an approximation to the minimal surface. In this paper, the properties of the harmonic B-B surface over the triangular domain are discussed. A sufficient and necessary condition of a B-B surface over the triangular domain being a harmonic surface is obtained. It is proved that the control net of an arbitrary harmonic B-B surface over the triangular domain is fully determined by the first and second layers of control points. This paper also presents some applications of the minimal surface in architectural design. |
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| Keywords: | minimal surface harmonic surface harmonic B-B surface over the triangular domain control net architectural design |
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