三调和三角B\'ezier曲面设计

Design of Triharmonic Triangular B\'{e}zier Surfaces

中文关键词:  三角B\'ezier曲面  三调和偏微分方程  偏微分方程曲面

英文关键词:triangular B\'{e}zier surface  triharmonic PDE  PDE-based surfaces

中文摘要:

      偏微分方程曲面设计,是由给定边界条件出发构造满足偏微分方程的曲面.本文基于三调和方程,提出三类边界条件,分别通过求解线性方程组,给出三调和三角形B\'ezier曲面的设计方法.证明了在这些边界条件下,生成曲面的唯一性,并分别给出具体曲面设计算法.通过实例验证了本文结论的有效性,并对三种边界条件进行对比分析.

英文摘要:

      Partial differential equation-based (PDE-based) surface design generates surfaces from PDEs with given boundary conditions. In this paper, design of triangular B\'{e}zier surfaces satisfying triharmonic equations is presented. We propose three sets of boundary control points for triharmonic triangular B\'{e}zier surfaces design by solving the systems of the linear equations with unique solutions. Moreover, we compare these three methods by some representative examples.