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Received: 2004-10-25

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Journal of Zhejiang University SCIENCE A 2005 Vol.6 No.7 P.750~759


Two kinds of B-basis of the algebraic hyperbolic space

Author(s):  LI Ya-juan, WANG Guo-zhao

Affiliation(s):  Department of Mathematics, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   liyajuan9104@sohu.com

Key Words:  Algebraic hyperbolic Bé, zier basis, Algebraic hyperbolic B-Spline basis, Algebraic hyperbolic Bé, zier curve, Algebraic hyperbolic B-Spline curve

LI Ya-juan, WANG Guo-zhao. Two kinds of B-basis of the algebraic hyperbolic space[J]. Journal of Zhejiang University Science A, 2005, 6(7): 750~759.

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T1 - Two kinds of B-basis of the algebraic hyperbolic space
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A1 - WANG Guo-zhao
J0 - Journal of Zhejiang University Science A
VL - 6
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SP - 750
EP - 759
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2005.A0750

In this paper, two new kinds of B-basis functions called algebraic hyperbolic (AH) Bézier basis and AH B-Spline basis are presented in the space Γk=span{1,t,...,tk-3,sinht,cosht}, in which K is an arbitrary integer larger than or equal to 3. They share most optimal properties as those of the Bézier basis and B-Spline basis respectively and can represent exactly some remarkable curves and surfaces such as the hyperbola, catenary, hyperbolic spiral and the hyperbolic paraboloid. The generation of tensor product surfaces of the AH B-Spline basis have two forms: AH B-Spline surface and AH T-Spline surface.

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


[1] Carnicer, J.M., Peña, J.M, 1994. Totally positive for shape preserving curve design and optimality of B-Splines. Computer Aided Geometric Design, 11:635-656.

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

[3] Koch, P.E., Lyche, T., 1991. Construction of Exponential tension B-Splines of Arbitrary Order. In: Laurent, P.J., Le Méhauté, A., Schumaker, L.L. (Eds.), Curves and Surfaces. Academic Press, New York, p.255-258.

[4] Lü, Y.G., Wang, G.Z., Yang, X.N., 2002. Uniform hyperbolic polynomial B-Spline curves. Computer Aided Geometric Design, 19:379-393.

[5] Mainar, E., Peña, J.M., 1999. Corner cutting algorithms associated with optimal shape preserving representations. Computer Aided Geometric Design, 16:883-906.

[6] Mainar, E., Peña, J.M., Sánchez-Reyes, J., 2001. Shape preserving alternatives to the rational Bézier model. Computer Aided Geometric Design, 18:37-60.

[7] Peña., J.M., 1999. Shape Preserving Representations in Computer Aided Geometric Design. Nova Science Publishers, Commack (New York).

[8] Wang, G.Z., Chen, Q.Y., Zhou, M.H., 2004. NUAT B-B-Spline curves. Computer Aided Geometric Design, 21:193-205.

Open peer comments: Debate/Discuss/Question/Opinion


Reenu Sharma@Rani Durgawati University<reenusharma6@rediff.com>

2012-01-17 11:51:25

Dear Editor

I am doing Ph.D. on the various types of B spline curves.

This paper will be very helpful for my Ph.D.

With Regards

Reenu Sharma

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