CAE底层网格算法的无穷美学【附专用网格处理工具】
1 部分论文成果图
[2] Perceptually Guided Rendering of Texture Point-based Models. Lijun Qu, Xiaoru Yuan, Minh X. Nguyen, Gary Meyer and Baoquan Chen In Proceeding of the 3rd IEEE/Eurographics Symposium on Point-Based Graphics (PBG06), Pages 95-102. Boston, MA, USA. July 29-30, 2006.
[3] All-Hex Meshing using Closed-Form Induced Polycube. Xianzhong Fang, Weiwei Xu, Hujun Bao, Jin Huang，ACM Transactions on Graphics (TOG), 35(4), 2016.
[4] Integrating Mesh and Meshfree Methods for Physics-Based Fracture and Debris Cloud Simulation. Nan Zhang, Xiangmin Zhou, Desong Sha, Xiaoru Yuan, Kumar K. Tamma, and Baoquan Chen. In Proceeding of the 3rd IEEE/Eurographics Symposium on Point-Based Graphics (PBG06), Pages 145-154. Boston, MA, USA. July 29-30, 2006.
[5] A Convolutional Decoder for Point Clouds using Adaptive Instance Normalization. Isaak Lim, Moritz Ibing, Leif Kobbelt.Eurographics Symposium on Geometry Processing 2019.
[6] All-Hex Meshing using Singularity-Restricted Field. Yufei Li,Yang Liu,Weiwei Xu,Wenping Wang,Baining Guo. ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012.
[7] Structured Volume Decomposition via Generalized Sweeping.Gao X, Martin T, Deng S, Cohen E, Deng Z, Chen G.IEEE Trans Vis Comput Graph. 2016 Jul;22(7):1899-911. doi: 10.1109/TVCG.2015.2473835. Epub 2015 Aug 27.
[8] Surface Smoothing and Quality Improvement of Quadrilateral/Hexahedral Meshes with Geometric Flow. Zhang Y, Bajaj C, Xu G. Computational Visualization Center, Institute for Computational Engineering and Sciences, The University of Texas at Austin, USA. jessica@ices.utexas.edu.
2 软件工具推荐
最后，推荐几个轻型的专用网格处理软件（非Hypermesh、ANSA），如果自己研究底层程序编写或者自定义一些模型求解过程，可以作为网格生成工具使用。
2.2 Libigl
Libigl是由瑞士Ethz大学的Olga Sorkine研究小组开发的C++网格处理库，使用说明文档比较齐全，很容易上手使用。它具有较好的构造稀疏离散微分算子和有限元稀疏方程组等功能。有很多研究人员对其有贡献，包括：Alec Jacobson, Daniele Panozzo, Christian Schüller, Olga Diamanti, Qingnan Zhou, Nico Pietroni, Stefan Bruggerr , Kenshi Takayama, Wenzel Jakob, Nikolas De Giorgis, Luigi Rocca, Leonardo Sacht, Olga Sorkine-Hornung。
2.3 Trimmesh
Trimesh是由美国Princeton大学的Thomas Funkhouser研究小组开发的C++网格处理库。非常容易上手，使用不难，适合初学者。但是其中的相关算法实现比较少。
2.5 TetGen
2.7 VEGA FEM
Vega is a computationally efficient and stable C/C++ physics library for three-dimensional deformable object simulation. It is designed to model large deformations, including geometric and material nonlinearities, and can also efficiently simulate linear systems. Vega contains about 145,000 lines of code, and is open-source and free. It is released under the 3-clause BSD license, which means that it can be used freely both in academic research and in commercial applications.
以上，是关于有限元程序开发以及使用过程中可能涉及的底层离散算法。这些算法充满艺术美学，让人眼前一亮，有门槛又非常脑洞有趣，希望对大家产生一些帮助，拓展一些技术边界，如果觉得文章内容不错，欢迎“在看”和分享~
