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 - <p style="text-align: justify;">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.</p>