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De Casteljau Algorithm and Degree Elevation of Toric Surface Patches

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Abstract

De Casteljau algorithm and degree elevation of Bézier and NURBS curves/surfaces are two important techniques in computer aided geometric design. This paper presents the de Casteljau algorithm and degree elevation of toric surface patches, which include tensor product and triangular rational Bézier surfaces as special cases. Some representative examples of toric surface patches with common shapes are illustrated to verify these two algorithms. Moreover, the authors also apply the degree elevation of toric surface patches to isogeometric analysis. And two more examples show the effectiveness of proposed method.

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Authors and Affiliations

  1. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China

    Jinggai Li, Ye Ji & Chungang Zhu

  2. Key Laboratory for Computational Mathematics and Data Intelligence of Liaoning Province, Dalian University of Technology, Dalian, 116024, China

    Jinggai Li, Ye Ji & Chungang Zhu

Authors
  1. Jinggai Li
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  2. Ye Ji
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  3. Chungang Zhu
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Corresponding author

Correspondence to Chungang Zhu.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 11671068 and 11801053.

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

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Li, J., Ji, Y. & Zhu, C. De Casteljau Algorithm and Degree Elevation of Toric Surface Patches. J Syst Sci Complex 34, 21–46 (2021). https://doi.org/10.1007/s11424-020-9370-y

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  • DOI: https://doi.org/10.1007/s11424-020-9370-y

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