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CLC number: TP391.72
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
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Control mesh representation of a class of minimal surfaces
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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.
@article{title="Control mesh representation of a class of minimal surfaces",
author="XU Gang, WANG Guo-zhao",
journal="Journal of Zhejiang University Science A",
volume="7",
number="9",
pages="1544-1549",
year="2006",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2006.A1544"
}
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%T Control mesh representation of a class of minimal surfaces
%A XU Gang
%A WANG Guo-zhao
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%@ 1673-565X
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%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2006.A1544
TY - JOUR
T1 - Control mesh representation of a class of minimal surfaces
A1 - XU Gang
A1 - WANG Guo-zhao
J0 - Journal of Zhejiang University Science A
VL - 7
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SP - 1544
EP - 1549
%@ 1673-565X
Y1 - 2006
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2006.A1544
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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