| Control mesh representation of a class of minimal surfaces |
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| 引用本文： | XU Gang,WANG Guo-zhao (Institute of Computer Graphics and Image Processing,Department of Mathematics,Zhejiang University,Hangzhou 310027,China). Control mesh representation of a class of minimal surfaces[J]. 浙江大学学报(A卷英文版), 2006, 7(9): 1544-1549. DOI: 10.1631/jzus.2006.A1544 |
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| 作者姓名： | XU Gang WANG Guo-zhao (Institute of Computer Graphics and Image Processing Department of Mathematics Zhejiang University Hangzhou 310027 China) |
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| 作者单位： | Institute of Computer Graphics and Image Processing，Department of Mathematics，Zhejiang University，Hangzhou 310027，China |
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| 基金项目： | Project supported by the National Natural Science Foundation of China (No. 60473130) and the National Basic Research Program (973) of China (No. 2004CB318000) |
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| 摘 要： | INTRODUCTION The problem of minimal surface is an old and active problem in the field of differential geometry. The minimal surface has been employed in many areas such as architecture, material science, aviation, ship manufacture, biology, crystallogeny, and so on. The history of minimal surface began with La- grange in 1762 (Nitsche, 1989). Many literature on the minimal surface exist in the last two hundred years (Nitsche, 1989; Osserman, 1986), but few on the minimal surface from the…
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| 关 键 词： | 极小曲面 螺旋面 悬索曲面 控制网格 CAD |
| 收稿时间： | 2006-05-20 |
| 修稿时间： | 2006-06-21 |
Control mesh representation of a class of minimal surfaces |
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| Gang Xu,Guo-zhao Wang. Control mesh representation of a class of minimal surfaces[J]. Journal of Zhejiang University Science, 2006, 7(9): 1544-1549. DOI: 10.1631/jzus.2006.A1544 |
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| Authors: | Gang Xu Guo-zhao Wang |
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| Affiliation: | (1) Institute of Computer Graphics and Image Processing, Department of Mathematics, Zhejiang University, Hangzhou, 310027, China |
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| Abstract: | Minimal surface is extensively employed in many areas. In this paper, we propose a control mesh representation of a class of minimal surfaces, called generalized helicoid minimal surfaces, which contain the right helicoid and catenoid as special examples. We firstly construct the Bézier-like basis called AHT Bézier basis in the space spanned by {1, t, sint, cost, sinht, cosht}, t∈[0, α], α∈[0,5π/2]. Then we propose the control mesh representation of the generalized helicoid using the AHT Bézier basis. This kind of representation enables generating the minimal surfaces using the de Casteljau-like algorithm in CAD/CAGD modelling systems. Project supported by the National Natural Science Foundation of China (No. 60473130) and the National Basic Research Program (973) of China (No. 2004CB318000) |
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| Keywords: | Minimal surface Helicoid surface Catenoid Control mesh |
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