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Non-Uniform Doo-Sabin Subdivision Surface via Eigen Polygon

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Abstract

This paper constructs a new non-uniform Doo-Sabin subdivision scheme via eigen polygon. The authors proved that the limit surface is always convergent and is G1 continuous for any valence and any positive knot intervals under a minor assumption, that λ is the second and third eigenvalues of the subdivision matrix. And then, a million of numerical experiments are tested with randomly selecting positive knot intervals, which verify that our new subdivision scheme satisfies the assumption. However this is not true for the other two existing non-uniform Doo-Sabin schemes in [32, 33]. In additional, numerical experiments indicate that the quality of the new limit surface can be improved.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, China

    Md Nur Alam & Xin Li

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  1. Md Nur Alam
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  2. Xin Li
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Correspondence to Xin Li.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 61872328, SRF for ROCS SE, and the Youth Innovation Promotion Association CAS, CAS-TWAS president’s fellowship program.

This paper was recommended for publication by Editor-in-Chief GAO Xiao-Shan.

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Alam, M.N., Li, X. Non-Uniform Doo-Sabin Subdivision Surface via Eigen Polygon. J Syst Sci Complex 34, 3–20 (2021). https://doi.org/10.1007/s11424-020-9264-z

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  • DOI: https://doi.org/10.1007/s11424-020-9264-z

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