Open Access

ARTICLE

Efficient Construction of B-Spline Curves with Minimal Internal Energy

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

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

* Corresponding Author: Gang Xu. 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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Citations