Volume 38, Issue 6
The Plateau-Bézier Problem with Weak-Area Functional

Yongxia Hao

J. Comp. Math., 38 (2020), pp. 868-878.

Published online: 2020-06

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  • Abstract

In this paper, we present a new method to solve the Plateau-Bézier problem. A new energy functional called weak-area functional is proposed as the objective functional to obtain the approximate minimal Bézier surface from given boundaries. This functional is constructed based on Dirichlet energy and weak isothermal parameterization condition. Experimental comparisons of the weak-area functional method with existing Dirichlet, quasi-harmonic, the strain energy-minimizing, harmonic and biharmonic masks are performed which show that the weak-area functional method are among the best by choosing appropriate parameters.

  • Keywords

Minimal surface, Plateau-Bézier problem, Weak isothermal parameterization, Weak-area functional.

  • AMS Subject Headings

65D17, 65D18

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

yongxiahaoujs@ujs.edu.cn (Yongxia Hao)

  • BibTex
  • RIS
  • TXT
@Article{JCM-38-868, author = {Hao , Yongxia }, title = {The Plateau-Bézier Problem with Weak-Area Functional}, journal = {Journal of Computational Mathematics}, year = {2020}, volume = {38}, number = {6}, pages = {868--878}, abstract = {

In this paper, we present a new method to solve the Plateau-Bézier problem. A new energy functional called weak-area functional is proposed as the objective functional to obtain the approximate minimal Bézier surface from given boundaries. This functional is constructed based on Dirichlet energy and weak isothermal parameterization condition. Experimental comparisons of the weak-area functional method with existing Dirichlet, quasi-harmonic, the strain energy-minimizing, harmonic and biharmonic masks are performed which show that the weak-area functional method are among the best by choosing appropriate parameters.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1906-m2019-0051}, url = {http://global-sci.org/intro/article_detail/jcm/16971.html} }
TY - JOUR T1 - The Plateau-Bézier Problem with Weak-Area Functional AU - Hao , Yongxia JO - Journal of Computational Mathematics VL - 6 SP - 868 EP - 878 PY - 2020 DA - 2020/06 SN - 38 DO - http://doi.org/10.4208/jcm.1906-m2019-0051 UR - https://global-sci.org/intro/article_detail/jcm/16971.html KW - Minimal surface, Plateau-Bézier problem, Weak isothermal parameterization, Weak-area functional. AB -

In this paper, we present a new method to solve the Plateau-Bézier problem. A new energy functional called weak-area functional is proposed as the objective functional to obtain the approximate minimal Bézier surface from given boundaries. This functional is constructed based on Dirichlet energy and weak isothermal parameterization condition. Experimental comparisons of the weak-area functional method with existing Dirichlet, quasi-harmonic, the strain energy-minimizing, harmonic and biharmonic masks are performed which show that the weak-area functional method are among the best by choosing appropriate parameters.

Yongxia Hao. (2020). The Plateau-Bézier Problem with Weak-Area Functional. Journal of Computational Mathematics. 38 (6). 868-878. doi:10.4208/jcm.1906-m2019-0051
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