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CLC number: TP391.72

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Received: 2006-05-20

Revision Accepted: 2006-06-21

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


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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A1 - XU Gang
A1 - WANG Guo-zhao
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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.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1] Chen, Q.Y., Wang, G.Z., 2003. A class of Bézier-like curves. Computer Aided Geometric Design, 20(1):29-39.

[2] Jin, W.B., Wang, G.Z., 1999. Geometry design of a class of minimal surface with negative Gauss curvature. Chinese Journal of Computers, 22(12):1277-1279.

[3] Li, Y.J., Wang, G.Z., 2005. Two kinds of B-basis of the algebraic hyperbolic space. Journal of Zhejiang University SCIENCE, 6A(7):750-759.

[4] Man, J.J., Wang, G.Z., 2002. Polynomial minimal surface in Isothermal parameter. Chinese Journal of Computers, 25(2):197-201.

[5] Man, J.J., Wang, G.Z., 2003. Approximating to nonparameterzied minimal surface with B-spline surface. Chinese Journal of Software, 14(4):824-829.

[6] Man, J.J., Wang, G.Z., 2005. Representation and geometric construction of catenoids and helicoid. Journal of Computer-aided Design and Computer Graphics, 17(5):431-436.

[7] Monterde, J., 2004. Bézier surfaces of minimal area: the Dirichlet approach. Computer Aided Geometric Design, 21(2):117-136.

[8] Nitsche, J.C.C., 1989. Lectures on Minimal Surfaces, Vol. 1. Cambridge Univ. Press, Cambridge.

[9] Osserman, R., 1986. A Survey of Minimal Surfaces (2nd Ed.). Dover Publications, New York.

[10] Zhang, J.W., 1996. C-curves: An extension of cubic curves. Computer Aided Geometric Design, 13(3):199-217.

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