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Triangular domain extension of algebraic trigonometric Bézier-like basis

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Abstract

In computer aided geometric design (CAGD), Bézier-like bases receive more and more considerations as new modeling tools in recent years. But those existing Bézier-like bases are all defined over the rectangular domain. In this paper, we extend the algebraic trigonometric Bézier-like basis of order 4 to the triangular domain. The new basis functions defined over the triangular domain are proved to fulfill non-negativity, partition of unity, symmetry, boundary representation, linear independence and so on. We also prove some properties of the corresponding Bézier-like surfaces. Finally, some applications of the proposed basis are shown.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China

    Yong-wei Wei, Wan-qiang Shen & Guo-zhao Wang

  2. Department of Applied Mathematics, Shanghai Maritime University, Shanghai, 201306, China

    Yong-wei Wei

Authors
  1. Yong-wei Wei
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  2. Wan-qiang Shen
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  3. Guo-zhao Wang
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Corresponding author

Correspondence to Yong-wei Wei.

Additional information

Supported by the National Natural Science Foundation of China ( 60933008,60970079).

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Wei, Yw., Shen, Wq. & Wang, Gz. Triangular domain extension of algebraic trigonometric Bézier-like basis. Appl. Math. J. Chin. Univ. 26, 151–160 (2011). https://doi.org/10.1007/s11766-011-2672-z

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  • DOI: https://doi.org/10.1007/s11766-011-2672-z

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