| 具有特殊坐标曲线网的B\'ezier曲面 |
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| 引用本文： | 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. |
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| 作者姓名： | 孙兰银 朱春钢 |
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| 作者单位： | 信阳师范学院数学与统计学院, 河南 信阳 464000,大连理工大学数学科学学院, 辽宁 大连116024 |
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| 基金项目： | 国家自然科学基金(Grant Nos.11801490; 11671068; 11501488). |
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| 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.
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| 关 键 词： | B\''ezier曲面 坐标曲线网 曲率坐标网 形状约束 |
| 收稿时间： | 2019/8/30 0:00:00 |
| 修稿时间： | 2019/10/22 0:00:00 |
B\'ezier Surfaces with Special Coordinate Curve Nets |
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| Lanyin SUN and Chungang ZHU.B\'ezier Surfaces with Special Coordinate Curve Nets[J].Journal of Mathematical Research with Applications,2019,39(6):700-708. |
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| Authors: | Lanyin SUN and Chungang ZHU |
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| Institution: | School of Mathematics and Statistics, Xinyang Normal University, Henan 464000, P. R. China and School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China |
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| Abstract: | 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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| Keywords: | B\''ezier surfaces coordinate curve nets curvature coordinate nets shape constraints |
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