Constructing discrete minimal surfaces with quadrilateral meshes from described boundary

被引：0
|
作者：
Xu G. [1 ,2 ]
Zhu Y.-G. [1 ]
Li X. [1 ]
Xu J.-L. [1 ,2 ]
Wang G.-Z. [3 ]
Hui K.-C. [4 ]
机构：
[1] School of Computer Science and Technology, Hangzhou Dianzi University, Hangzhou
[2] Key Laboratory of Complex Systems Modeling and Simulation, Ministry of Education, Hangzhou
[3] School of Mathematics, Zhejiang University, Hangzhou
[4] Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong
来源：
Ruan Jian Xue Bao/Journal of Software | 2016年 / 27卷 / 10期
基金：
中国国家自然科学基金;
关键词：
Architectural geometry; Discrete minimal surface; Mesh generation; Quadrilateral mesh; Radial basis function interpolation;
D O I：
10.13328/j.cnki.jos.005087
中图分类号：
学科分类号：
摘要：
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. © Copyright 2016, Institute of Software, the Chinese Academy of Sciences. All rights reserved.
引用
收藏
页码：2499 / 2508
页数：9
相关论文
共 35 条
  • [1] Johannes C.C.N., Lectures on Minimal Surfaces, 1, (1989)
  • [2] Robert O., A survey of Minimal Surfaces, (1986)
  • [3] Wang Y., Periodic surface modeling for computer aided nano design, Computer Aided Design, 39, 3, pp. 179-189, (2007)
  • [4] Jin W.B., Wang G.Z., Geometry design of a class of minimal surface, Chinese Journal of Computers, 23, 12, pp. 1277-1279, (1999)
  • [5] Xu G., Wang G.Z., Research development of minimal surface modeling in computer aided geometric design, Journal of Systems Science and Mathematical Sciences, 28, 8, pp. 984-992, (2008)
  • [6] Man J.J., Wang G.Z., Representation and geometric construction of helicoids and catenoids, Journal of Computer-Aided Design and Computer Graphics, 17, 3, pp. 431-436, (2005)
  • [7] Xu G., Wang G.Z., AHT Bézier surfaces and NUAHT B-spline curves, Journal of Computer Science and Technology, 22, 4, pp. 597-607, (2007)
  • [8] Xu G., Wang G.Z., Control mesh representation of a class of minimal surfaces, Journal of Computer-Aided Design and Computer Graphics, 19, 2, pp. 240-244, (2007)
  • [9] Man J.J., Wang G.Z., Polynomial minimal surface in Isothermal parameter, Chinese Journal of Computers, 25, 2, pp. 197-201, (2002)
  • [10] Xu G., Wang G.Z., Quintic parametric polynomial minimal surfaces and their properties, Differential Geometry and Its Applications, 28, 6, pp. 697-704, (2010)
1234