孙兰银,朱春钢.具有特殊坐标曲线网的B\'ezier曲面[J].数学研究及应用,2019,39(6):700~708
具有特殊坐标曲线网的B\'ezier曲面
B\'ezier Surfaces with Special Coordinate Curve Nets
投稿时间:2019-08-30  修订日期:2019-10-22
DOI:10.3770/j.issn:2095-2651.2019.06.013
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
基金项目:国家自然科学基金(Grant Nos.11801490; 11671068; 11501488).
作者单位
孙兰银 信阳师范学院数学与统计学院, 河南 信阳 464000 
朱春钢 大连理工大学数学科学学院, 辽宁 大连116024 
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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.
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