Full Text:   <1648>

CLC number: TP391.72

On-line Access: 

Received: 2007-09-15

Revision Accepted: 2007-10-30

Crosschecked: 0000-00-00

Cited: 1

Clicked: 3015

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
1. Reference List
Open peer comments

Journal of Zhejiang University SCIENCE A 2008 Vol.9 No.6 P.816~821

10.1631/jzus.A071490


Paths of algebraic hyperbolic curves


Author(s):  Ya-juan LI, Li-zheng LU, Guo-zhao WANG

Affiliation(s):  School of Science, Hangzhou Dianzi University, Hangzhou 310018, China; more

Corresponding email(s):   liyajuan9104@163.com, wanggz@zju.edu.cn

Key Words:  Algebraic hyperbolic (AH) Bé, zier curve, AH spline curve, Path, Shape modification


Ya-juan LI, Li-zheng LU, Guo-zhao WANG. Paths of algebraic hyperbolic curves[J]. Journal of Zhejiang University Science A, 2008, 9(6): 816~821.

@article{title="Paths of algebraic hyperbolic curves",
author="Ya-juan LI, Li-zheng LU, Guo-zhao WANG",
journal="Journal of Zhejiang University Science A",
volume="9",
number="6",
pages="816~821",
year="2008",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A071490"
}

%0 Journal Article
%T Paths of algebraic hyperbolic curves
%A Ya-juan LI
%A Li-zheng LU
%A Guo-zhao WANG
%J Journal of Zhejiang University SCIENCE A
%V 9
%N 6
%P 816~821
%@ 1673-565X
%D 2008
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A071490

TY - JOUR
T1 - Paths of algebraic hyperbolic curves
A1 - Ya-juan LI
A1 - Li-zheng LU
A1 - Guo-zhao WANG
J0 - Journal of Zhejiang University Science A
VL - 9
IS - 6
SP - 816
EP - 821
%@ 1673-565X
Y1 - 2008
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A071490


Abstract: 
Cubic algebraic hyperbolic (AH) Bé;zier curves and AH spline curves are defined with a positive parameter α in the space spanned by {1, t, sinht, cosht}. Modifying the value of α yields a family of AH Bézier or spline curves with the family parameter α. For a fixed point on the original curve, it will move on a defined curve called “path of AH curve” (AH Bézier and AH spline curves) when α changes. We describe the geometric effects of the paths and give a method to specify a curve passing through a given point.

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

Reference

[1] Hoffmann, M., Juhász, I., 2003. Geometric aspects of knot modification of B-spline surfaces. J. Geom. Graph., 6:141-149.

[2] Hoffmann, M., Juhász, I., 2006. On the family of B-spline surfaces obtained by knot modification. Math. Commun., 11:9-16.

[3] Hoffmann, M., Li, Y.J., Wang, G.Z., 2006. Paths of C-Bézier and C-B-spline curves. Computer Aided Geometric Design, 23(5):463-475.

[4] Juhász, I., Hoffmann, M., 2004. Constrained shape modification of cubic B-spline curves by means of knots. Computer-Aided Design, 36(5):437-445.

[5] Koch, P.E., Lyche, T., 1989. Exponential B-splines in Tension. In: Chui, C.K., Schumaker, L.L., Ward, J.D. (Eds.), Approximation Theory VI. Academic Press, New York, p.361-364.

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

[7] Li, Y.J., Wang, G.Z., 2005. Two kinds of B-basis of the algebraic hyperbolic space. J. Zhejiang Univ. Sci. A, 6:750-759.

[8] Lü, Y.G., Wang, G..Z., Yang, X.N., 2002. Uniform hyperbolic polynomial B-spline curves. Computer Aided Geometric Design, 19(6):379-393.

[9] Mainar, E., Peňa, J.M., Sánchez-Reyes, J., 2001. Shape preserving alternatives to the rational Bézier model. Computer Aided Geometric Design, 18(1):37-60.

[10] Pottmann, H., Wagner, M.G., 1994. Helix splines as example of affine Tchebycheffian splines. Adv. Comput. Math., 2(1):123-142.

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

[12] Zhang, J., 1997. Two different forms of C-B-splines. Computer Aided Geometric Design, 14(1):31-41.

[13] Zhang, J., 1999. C-Bézier curves and surfaces. Graphical Models and Image Processing, 61(1):2-15.

Open peer comments: Debate/Discuss/Question/Opinion

<1>

Please provide your name, email address and a comment





Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - Journal of Zhejiang University-SCIENCE