| 三调和三角B\'ezier曲面设计 |
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| 引用本文： | 吴岩,朱春钢.三调和三角B\''ezier曲面设计[J].数学研究及应用,2021,41(4):425-440. |
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| 作者姓名： | 吴岩 朱春钢 |
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| 作者单位： | 大连外国语大学软件学院, 辽宁 大连 116044;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.12071057; 11671068). |
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| 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.
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| 关 键 词： | 三角B\''ezier曲面 三调和偏微分方程 偏微分方程曲面 |
| 收稿时间： | 2020/8/3 0:00:00 |
| 修稿时间： | 2020/10/25 0:00:00 |
Design of Triharmonic Triangular B\'{e}zier Surfaces |
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| Yan WU,Chungang ZHU.Design of Triharmonic Triangular B\''{e}zier Surfaces[J].Journal of Mathematical Research with Applications,2021,41(4):425-440. |
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| Authors: | Yan WU Chungang ZHU |
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| Institution: | School of Software, Dalian University of Foreign Languages, Liaoning 116044, P. R. China; School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China |
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| Abstract: | 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. |
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| Keywords: | triangular B\''{e}zier surface triharmonic PDE PDE-based surfaces |
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