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Construction of transition surfaces with minimal generalized thin-plate spline-surface energies

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Abstract

Physically based modeling of deformable curves and surfaces has been widely used in computer graphics to meet the needs of both geometry and physics. In this paper, the weighted sum of the first and higher order generalized thin-plate spline-surface energies is introduced for the construction of transition surface. We derive the necessary and sufficient condition that the energy functional of a transition surface reaches its minimum, by which the positions of movable control points can be fully determined within the constraints imposed by the controls and continuity constraints. Furthermore, based on the excellent properties of Bernstein basis functions, we present a simple algorithm to compute energy-minimizing transition surfaces if the given two disjoint tensor product surfaces are in Bézier form. The feasibility of the method is validated by several examples. Compared with previous modeling methods, various physical characteristics are imparted on the modeling of transition surfaces in this paper, thus various energy-minimizing transition surfaces with different characteristics can be obtained.

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Acknowledgements

We thank to the anonymous reviewers for their insightful suggestions and recommendations, which led to the improvements of presentation and content of the paper.

Funding

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

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Authors and Affiliations

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

    Gang Hu & Xinqiang Qin

  2. Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, 710072, Shaanxi, China

    Huanxin Cao

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  1. Gang Hu
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  2. Huanxin Cao
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Correspondence to Gang Hu.

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Communicated by Abimael Loula.

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Hu, G., Cao, H. & Qin, X. Construction of transition surfaces with minimal generalized thin-plate spline-surface energies. Comp. Appl. Math. 41, 317 (2022). https://doi.org/10.1007/s40314-022-02032-9

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  • DOI: https://doi.org/10.1007/s40314-022-02032-9

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