A new method to solve Plateau-Bézier problems over the triangular domain

作者：Xu Gang^*; Wang Guo Zhao; Chen Xiao Diao

来源：Chinese Journal of Computers, 2011, 34(3): 548-554.

DOI：10.3724/SP.J.1016.2011.00548

• Boundary curves
• Computer aided geometric design
• Control point
• Dirichlet energy
• Energy functions
• Harmonic surface
• Linear energy
• Mean curvature
• Minimal surfaces
• Sufficient and necessary condition
• Triangular domains

This paper solves the Plateau-Be´zier problem over triangular domain from the fact that mean curvature of minimal surface equals zero at every point. A new kind of linear energy function called squared mean curvature energy is firstly proposed. From the minimization of the new energy function, it derives the sufficient and necessary condition that inner control points should satisfy. The method is compared with the method based on the minimization of Dirichlet energy through modeling examples. In particular, if the given boundary curves are the boundary curves of the harmonic Be´zier surface over triangular domain, then the surface constructed by this method is just the harmonic surface; if the given boundary curves are the boundary curves of the parametric polynomial minimal surface with isothermal parameter, then we can reconstruct the minimal surface by this method.

• 出版日期2011
• 单位浙江大学