Although approach of energy minimizations has been widely applied in the construction of planar curves, it is seldom used in the construction of spatial curves. In this paper, we first introduce the bending energy and twisting energy of spatial parametric curves. A method of constructing spatial parametric curves aiming at minimizing the bending energy and twisting energy simultaneously is then proposed. Finally, the applications of the proposed method in the construction, extension, and smoothing of the cubic Bézier curve are discussed. The proposed method conforms with the fact that both bending and twisting are important shape features of spatial parametric curves.
Received: 10 September 2021
Published: 13 January 2023
Juncheng LI,Chengzhi LIU,Zhijun LUO,Zhiwen LONG. Bi-objective energy minimization of spatial parametric curves and its applications. Journal of Zhejiang University (Science Edition), 2023, 50(1): 63-68.
Fig.1 Spatial cubic Bézier curves constructed by three energy minimizations
能量极小化方法
弯曲能
扭曲能
弯曲能极小
51.000 0
171.000 0
扭曲能极小
76.000 0
0
双目标能量极小
75.534 9
0.025 4
Table 1Bending energy and twist energy obtained by three energy minimizations
Fig. 2 Extension of the spatial cubic Bézier curve
Fig.3 Smoothing of linked spatial curves
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