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Control mesh representation of a class of minimal surfaces 被引量:4

Control mesh representation of a class of minimal surfaces
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摘要 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 mod- elling systems. 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.
出处 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2006年第9期1544-1549,共6页 浙江大学学报(英文版)A辑(应用物理与工程)
基金 Project supported by the National Natural Science Foundation of China (No. 60473130) and the National Basic Research Program (973) of China (No. 2004CB318000)
关键词 Minimal surface Helicoid surface Catenoid Control mesh 极小曲面 螺旋面 悬索曲面 控制网格 CAD
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参考文献1

  • 1Li Ya-juan,Wang Guo-zhao.Two kinds of B-basis of the algebraic hyperbolic space[J].Journal of Zhejiang University SCIENCE A.2005(7)

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