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CLC number: TP391.72

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Received: 2006-05-20

Revision Accepted: 2006-06-21

Crosschecked: 0000-00-00

Cited: 1

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Journal of Zhejiang University SCIENCE A 2006 Vol.7 No.9 P.1544-1549

http://doi.org/10.1631/jzus.2006.A1544


Control mesh representation of a class of minimal surfaces


Author(s):  XU Gang, WANG Guo-zhao

Affiliation(s):  Institute of Computer Graphics and Image Processing, Department of Mathematics, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   yln41@hotmail.com

Key Words:  Minimal surface, Helicoid surface, Catenoid, Control mesh


XU Gang, WANG Guo-zhao. Control mesh representation of a class of minimal surfaces[J]. Journal of Zhejiang University Science A, 2006, 7(9): 1544-1549.

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journal="Journal of Zhejiang University Science A",
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year="2006",
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T1 - Control mesh representation of a class of minimal surfaces
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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.

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Reference

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