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Efficient Construction of B-Spline Curves with Minimal Internal Energy

Gang Xu1,*, Yufan Zhu1, Lishan Deng1, Guozhao Wang2, Bojian Li1, Kin-chuen Hui3

School of Computer Science and Technology, Hangzhou Dianzi University, Hangzhou, Zhejiang, 310018, China.
Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang, 310018, China.
Department of Mechanical and Automation Engineering, Chinese University of Hong Kong, Hong Kong, 999077, China.

* Corresponding Author: Gang Xu. Email: email.

Computers, Materials & Continua 2019, 58(3), 879-892. https://doi.org/10.32604/cmc.2019.03752

Abstract

In this paper, we propose an efficient method to construct energy-minimizing B-spline curves by using discrete mask method. The linear relations between control points are firstly derived for different energy-minimization problems, then the construction of B-spline curve with minimal internal energy can be addressed by solving a sparse linear system. The existence and uniqueness of the solution for the linear system are also proved. Experimental results show the efficiency of the proposed approach, and its application in G1 blending curve construction is also presented.

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APA Style
Xu, G., Zhu, Y., Deng, L., Wang, G., Li, B. et al. (2019). Efficient construction of b-spline curves with minimal internal energy. Computers, Materials & Continua, 58(3), 879-892. https://doi.org/10.32604/cmc.2019.03752
Vancouver Style
Xu G, Zhu Y, Deng L, Wang G, Li B, Hui K. Efficient construction of b-spline curves with minimal internal energy. Comput Mater Contin. 2019;58(3):879-892 https://doi.org/10.32604/cmc.2019.03752
IEEE Style
G. Xu, Y. Zhu, L. Deng, G. Wang, B. Li, and K. Hui "Efficient Construction of B-Spline Curves with Minimal Internal Energy," Comput. Mater. Contin., vol. 58, no. 3, pp. 879-892. 2019. https://doi.org/10.32604/cmc.2019.03752

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cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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