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Volume 41, Issue 4
Construction of Bézier Surfaces from Prescribed Boundary

Yongxia Hao & Ting Li

DOI: 10.4208/jcm.2106-m2021-0050

J. Comp. Math., 41 (2023), pp. 551-568.

Published online: 2023-02

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  • Abstract

In this paper, we present a method for generating Bézier surfaces from the boundary information based on a general second order functional and a third order functional associated with the triharmonic equation. By solving simple linear equations, the internal control points of the resulting Bézier surface can be obtained as linear combinations of the given boundary control points. This is a generalization of previous works on Plateau-Bézier problem, harmonic, biharmonic and quasi-harmonic Bézier surfaces. Some representative examples show the effectiveness of the presented method.

  • Keywords

Bézier surface, Boundary control points, Quadratic functional, Triharmonic equation.

  • AMS Subject Headings

65D17, 65D18

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

yongxiahaoujs@ujs.edu.cn (Yongxia Hao)

17865578531@163.com (Ting Li)

  • BibTex
  • RIS
  • TXT
@Article{JCM-41-551, author = {Hao , Yongxia and Li , Ting}, title = {Construction of Bézier Surfaces from Prescribed Boundary}, journal = {Journal of Computational Mathematics}, year = {2023}, volume = {41}, number = {4}, pages = {551--568}, abstract = {

In this paper, we present a method for generating Bézier surfaces from the boundary information based on a general second order functional and a third order functional associated with the triharmonic equation. By solving simple linear equations, the internal control points of the resulting Bézier surface can be obtained as linear combinations of the given boundary control points. This is a generalization of previous works on Plateau-Bézier problem, harmonic, biharmonic and quasi-harmonic Bézier surfaces. Some representative examples show the effectiveness of the presented method.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2106-m2021-0050}, url = {http://global-sci.org/intro/article_detail/jcm/21405.html} }
TY - JOUR T1 - Construction of Bézier Surfaces from Prescribed Boundary AU - Hao , Yongxia AU - Li , Ting JO - Journal of Computational Mathematics VL - 4 SP - 551 EP - 568 PY - 2023 DA - 2023/02 SN - 41 DO - http://doi.org/10.4208/jcm.2106-m2021-0050 UR - https://global-sci.org/intro/article_detail/jcm/21405.html KW - Bézier surface, Boundary control points, Quadratic functional, Triharmonic equation. AB -

In this paper, we present a method for generating Bézier surfaces from the boundary information based on a general second order functional and a third order functional associated with the triharmonic equation. By solving simple linear equations, the internal control points of the resulting Bézier surface can be obtained as linear combinations of the given boundary control points. This is a generalization of previous works on Plateau-Bézier problem, harmonic, biharmonic and quasi-harmonic Bézier surfaces. Some representative examples show the effectiveness of the presented method.

Yongxia Hao & Ting Li. (2023). Construction of Bézier Surfaces from Prescribed Boundary. Journal of Computational Mathematics. 41 (4). 551-568. doi:10.4208/jcm.2106-m2021-0050
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