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Interpolating meshes of arbitrary topology by Catmull–Clark surfaces with energy constraint

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Abstract

We propose an efficient method with energy constraints for constructing a Catmull–Clark surface that interpolates a given mesh. We approximate the surface energy of Catmull–Clark surfaces near extraordinary points by summing their finite subpatches and then represent the energy of the subpatches as linear combinations of the vertices of control mesh. By minimizing the surface energy as a constraint, we generate a new control mesh whose limit surfaces interpolate a given mesh. Numerous examples and comparisons demonstrate that our method has the following characteristics: (1) The limit surfaces are fairer, reducing unnecessary undulations and having minimal surface energy, and (2) the approximation process is simple and intuitive, requiring only a small number of computational steps and avoiding complex parameterization processes.

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The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The authors wish to thank all anonymous referees for their valuable comments and suggestions. This work was supported by the National Natural Science Foundation of China (NSFC) under the project numbers 61872121.

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  1. School of Science, Hangzhou Dianzi University, Hangzhou, 310018, China

    Zinan Lin, Yajuan Li & Chongyang Deng

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  1. Zinan Lin
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  2. Yajuan Li
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Correspondence to Chongyang Deng.

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Lin, Z., Li, Y. & Deng, C. Interpolating meshes of arbitrary topology by Catmull–Clark surfaces with energy constraint. Vis Comput (2023). https://doi.org/10.1007/s00371-023-03154-9

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