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CLC number: TN391.72

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Received: 2008-11-26

Revision Accepted: 2009-02-16

Crosschecked: 2009-02-16

Cited: 4

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Journal of Zhejiang University SCIENCE A 2009 Vol.10 No.4 P.570-576


NURBS curve blending using extension

Author(s):  Yong-jin LIU, Rong-qi QIU, Xiao-hui LIANG

Affiliation(s):  Tsinghua National Lab for Information Science and Technology, Tsinghua University, Beijing 100084, China; more

Corresponding email(s):   liuyongjin@tsinghua.edu.cn

Key Words:  Curve blending, Curve fairing, Curve extension, Non-uniform rational B-spline (NURBS)

Yong-jin LIU, Rong-qi QIU, Xiao-hui LIANG. NURBS curve blending using extension[J]. Journal of Zhejiang University Science A, 2009, 10(4): 570-576.

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A1 - Yong-jin LIU
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A1 - Xiao-hui LIANG
J0 - Journal of Zhejiang University Science A
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DOI - 10.1631/jzus.A0820819

Curve and surface blending is an important operation in CAD systems, in which a non-uniform rational B-spline (NURBS) has been used as the de facto standard. In local corner blending, two curves intersecting at that corner are first made disjoint, and then the third blending curve is added-in to smoothly join the two curves with G1- or G2-continuity. In this paper we present a study to solve the joint problem based on curve extension. The following nice properties of this extension algorithm are exploited in depth: (1) The parameterization of the original shapes does not change; (2) No additional fragments are created. Various examples are presented to demonstrate that our solution is simple and efficient.

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


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

[2] Mo, G.L., Zhao, Y.N., 2006. A new extension algorithm for cubic B-splines based on minimal strain energy. J. Zhejiang Univ. Sci. A, 7(12):2043-2049.

[3] Piegl, L., Tiller, W., 1997. The NURBS Book. Springer-Verlag, New York, NY.

[4] Poeschl, T., 1984. Detecting surface irregularities using isophotes. Computer Aided Geometric Design, 1(2):163-168.

[5] Press, W., Teukolsky, S., Vetterling, W., Flannery, B., 2002. Numerical Recipes in C++ (2nd Ed.). Cambridge University Press, Cambridge, UK.

[6] Vida, J., Martin, R.R., Varady, T., 1994. A survey of blending methods that use parametric surfaces. Computer-Aided Design, 26(5):341-365.

[7] Wallner, J., 2007. Note on curve and surface energies. Computer Aided Geometric Design, 24(8-9):494-498.

[8] Wang, J., Wang, G., Zheng, J., 2001. Computer Aided Geometric Design. China Higher Education Press, Beijing, China (in Chinese).

[9] Zang, Y., Liu, Y., Lai, Y., 2008. Note on industrial applications of Hu’s surface extension algorithm. LNCS, 4975:304-314.

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