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ZJUS-A
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2006, Vol. 7 Issue ( 9): 12-    DOI: 10.1631/jzus.2006.A1544
    
Control mesh representation of a class of minimal surfaces
XU Gang, WANG Guo-zhao
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.

Key words： Minimal surface      Helicoid surface      Catenoid      Control mesh     
Received: 20 May 2006     
CLC:  TP391.72  
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XU Gang
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XU Gang, WANG Guo-zhao. Control mesh representation of a class of minimal surfaces. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2006, 7( 9): 12-.

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http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.2006.A1544     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2006/V7/I 9/12

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