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| 插值边界的四边网格离散极小曲面建模方法 |
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徐岗1,2, 朱亚光1, 李鑫1, 许金兰1,2, 汪国昭3, 许健泉4
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1.杭州电子科技大学 计算机学院, 浙江 杭州 310018;2.复杂系统建模与仿真教育部重点实验室, 浙江 杭州 310018;3.浙江大学数学科学学院, 浙江 杭州 310027;4.Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, China
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| 摘要: |
| 如何实现极小曲面的快速三维建模，是几何设计与计算领域中的难点和热点问题.给定一条封闭的边界离散折线，研究如何构造以其为边界的四边网格离散极小曲面.首先从曲面的内蕴微分几何度量出发，给出了离散四边网格极小曲面的数学定义；然后利用保长度边界投影、四边网格生成、径向基函数插值映射和非线性优化技术，提出了由给定边界离散折线快速构造离散四边网格极小曲面的一般技术框架.最后通过若干建模实例验证了所提方法的有效性.该方法可实现四边网格极小曲面的高质量建模，在建筑几何领域具有一定的应用价值. |
| 关键词: 建筑几何 离散极小曲面 四边网格 网格生成 径向基函数插值 |
| DOI：10.13328/j.cnki.jos.005087 |
| 分类号: |
| 基金项目:国家自然科学基金（61472111，61272300，61602138）；浙江省杰出青年自然科学基金（LR16F020003）；浙江省自然科学基金（LQ16F020005） |
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| Constructing Discrete Minimal Surfaces with Quadrilateral Meshes from Described Boundary |
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XU Gang1,2, ZHU Ya-Guang1, LI Xin1, XU Jin-Lan1,2, WANG Guo-Zhao3, HUI Kin-Chuen4
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1.School of Computer Science and Technology, Hangzhou Dianzi University, Hangzhou 310018, China;2.Key Laboratory of Complex Systems Modeling and Simulation, Ministry of Education, Hangzhou 310018, China;3.School of Mathematics, Zhejiang University, Hangzhou 310027, China;4.Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, China
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| Abstract: |
| Efficient modeling of minimal surfaces is a challenging problem and hot topic in the field of geometric design and computation. Taking boundary closed polylines, this paper proposes a general framework to construct discrete minimal surfaces with quadrilateral meshes. First, the mathematical definition of discrete minimal surface with quadrilateral mesh is given from the intrinsic differential-geometry metric of surfaces. Next, based on the length-preserving boundary projection method, quad-mesh generation approach and non-linear numerical optimization technique, a novel framework is presented to construct discrete minimal surfaces with quadrilateral meshes from a described boundary closed discrete polylines. Finally, the effectiveness of the proposed approach is illustrated by several modeling examples. The results show that the proposed method can achieve high-quality modeling of discrete minimal surfaces and provide potential usage in architecture geometry. |
| Key words: architectural geometry discrete minimal surface quadrilateral mesh mesh generation radial basis function interpolation |
