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CLC number: TP391.72
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Received: 2007-09-15
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Paths of algebraic hyperbolic curves
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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"
}
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%A Guo-zhao WANG
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%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
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SP - 816
EP - 821
%@ 1673-565X
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PB - Zhejiang University Press & Springer
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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.
[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.
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