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CLC number: TP391.72

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Received: 2006-03-28

Revision Accepted: 2006-07-03

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Journal of Zhejiang University SCIENCE A 2006 Vol.7 No.12 P.2043~2049

http://doi.org/10.1631/jzus.2006.A2043


A new extension algorithm for cubic B-splines based on minimal strain energy


Author(s):  MO Guo-liang, ZHAO Ya-nan

Affiliation(s):  Department of Information and Computational Science, Zhejiang University City College, Hangzhou 310015, China

Corresponding email(s):   mogl@zucc.edu.cn

Key Words:  GC2-continuous, Extension, Minimal strain energy, Knot removal, Reparametrization


MO Guo-liang, ZHAO Ya-nan. A new extension algorithm for cubic B-splines based on minimal strain energy[J]. Journal of Zhejiang University Science A, 2006, 7(12): 2043~2049.

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author="MO Guo-liang, ZHAO Ya-nan",
journal="Journal of Zhejiang University Science A",
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pages="2043~2049",
year="2006",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2006.A2043"
}

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%N 12
%P 2043~2049
%@ 1673-565X
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%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2006.A2043

TY - JOUR
T1 - A new extension algorithm for cubic B-splines based on minimal strain energy
A1 - MO Guo-liang
A1 - ZHAO Ya-nan
J0 - Journal of Zhejiang University Science A
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SP - 2043
EP - 2049
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2006.A2043


Abstract: 
extension of a B-spline curve or surface is a useful function in a CAD system. This paper presents an algorithm for extending cubic B-spline curves or surfaces to one or more target points. To keep the extension curve segment GC2-continuous with the original one, a family of cubic polynomial interpolation curves can be constructed. One curve is chosen as the solution from a sub-class of such a family by setting one GC2 parameter to be zero and determining the second GC2 parameter by minimizing the strain energy. To simplify the final curve representation, the extension segment is reparameterized to achieve C2-continuity with the given B-spline curve, and then knot removal from the curve is done. As a result, a sub-optimized solution subject to the given constraints and criteria is obtained. Additionally, new control points of the extension B-spline segment can be determined by solving lower triangular linear equations. Some computing examples for comparing our method and other methods are given.

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Reference

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[2] Farin, G., 1997. Curves and Surfaces for Computer Aided Geometric Design (4th Ed.). Academic Press, San Diego.

[3] Farin, G., Sapidis, N., 1989. Curvature and the fairness of curves and surfaces. Computer Graphics and Applications, IEEE, 9(2):52-57.

[4] Hoschek, J., Lasser, D., 1993. Fundamentals of Computer Aided Geometric Design. Wellesley, MA.

[5] Hu, S.M., Tai, C.L., Zhang, S.H., 2002. An extension algorithm for B-splines by curve unclamping. Computer-Aided Design, 34(5):415-419.

[6] Piegl, L., Tiller, W., 1997. The NURBS Book. Springer-Verlag, Bernlin, Germany.

[7] Shetty, S., White, P.R., 1991. Curvature-continuous extensions for rational B-spline curves and surfaces. Computer-Aided Design, 23(7):484-491.

[8] Shi, F.Z., 2001. Computer Aided Geometric Design and NURBS. Higher Education Press, Beijing, China (in Chinese).

[9] Su, B.Q., Liu, D.Y., 1982. Computational Geometry. Shanghai Science Press, Shanghai, China (in Chinese).

[10] Tai, C.L., Hu, S.M., Huang, Q.X., 2003. Approximate merging of B-spline curves via knot adjustment and constrained optimization. Computer-Aided Design, 35(10):893-899.

[11] Tiller, W., 1992. Knot-removal algorithms for NURBS curves and surfaces. Computer-Aided Design, 24(8):445-453.

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