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Adjusting the energy of Ball surfaces by modifying unfixed control balls

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Abstract

Ball surfaces play a crucial role in modeling 3D objects with varying thickness. In this paper, energy functionals for surface design are extended to Ball surfaces and the variational problem of finding the energy-minimizing Ball surface within the constraints imposed by the controls is investigated. Besides, owing to the excellent properties of Bernstein bases, we propose a computationally inexpensive algorithm for the construction of energy-minimizing Ball Bézier surfaces. Finally, an efficient design tool is provided for the construction of Cr continuous energy-minimizing blend surface from two disjoint Ball surfaces. The feasibility of the method is verified by several examples. By adjusting the weighted coefficients, different energy functionals are defined and thus Ball surfaces with different shapes and thickness can be obtained, achieving the deformable modeling of Ball surfaces.

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Funding

This work is supported by the National Natural Science Foundation of China (Grant No. 51875454).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an, Shaanxi, 710072, China

    Huanxin Cao & Hongchan Zheng

  2. Department of Applied Mathematics, Xi’an University of Technology, Xi’an, Shaanxi, 710054, China

    Gang Hu

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  1. Huanxin Cao
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  2. Hongchan Zheng
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  3. Gang Hu
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Correspondence to Hongchan Zheng or Gang Hu.

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Cao, H., Zheng, H. & Hu, G. Adjusting the energy of Ball surfaces by modifying unfixed control balls. Numer Algor 89, 749–768 (2022). https://doi.org/10.1007/s11075-021-01132-7

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