具有特殊坐标曲线网的B\'ezier曲面

B\'ezier Surfaces with Special Coordinate Curve Nets

中文关键词:  B\'ezier曲面  坐标曲线网  曲率坐标网  形状约束

英文关键词:B\'ezier surfaces  coordinate curve nets  curvature coordinate nets  shape constraints

中文摘要:

      在计算机辅助几何设计中, B\'ezier曲面是一类重要的参数曲面.在微分几何中,坐标曲线网也是重要的研究内容.本文中,我们对具有特殊坐标曲线网(如正交曲线网、曲率曲线网、共轭曲线网等)的B\'ezier曲面进行研究.此外,我们还构造了满足能量约束的特殊B\'ezier曲面,给出了基于控制结构的充分条件并给出具体实例.

英文摘要:

      B\'ezier surfaces play an important role in Computer-aided Geometric Design (CAGD), and coordinate curve nets are widely discussed in differential geometry. In this paper, we study the B\'ezier surfaces with special coordinate curve nets, such as orthogonal coordinate net, curvature coordinate net and asymptotic coordinate net. In addition, we develop the B\'ezier surfaces which satisfy some shape constraints with the help of energy terms. Moreover, some applicable sufficient conditions based on geometrical structure of control nets are deduced and several representative examples are given.