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从具有x，y和z坐标的点生成网格

[英]Mesh generation from points with x, y and z coordinates

原文 2011-02-03 05:59:46 5 3 algorithm/ geometry/ 3d/ delaunay

Problem: Mesh generation from 3D points (with x, y and z coordinates). 问题：从3D点生成网格（使用x，y和z坐标）。

在此输入图像描述

What I have is points in 3D space (with x, y and z coordinates) you can see it in image 1. 我所拥有的是3D空间中的点（使用x，y和z坐标），您可以在图像1中看到它。
What would be the output is image 2 or image 3, or image 4. In short it would be mesh. 输出的是图像2或图像3，或图像4.简而言之，它将是网格。 Material on it can be provided if I have the mesh. 如果我有网格，可以提供它上面的材料。

I have seen many people say about Delaunay triangulations or constrained Delaunay triangulations will help me in mesh generation, but what I mostly found is its implementation in 2D points (with only x and Y coordinates). 我见过很多人都说Delaunay三角剖分或受约束的Delaunay三角剖分将帮助我进行网格生成，但我发现它主要是在2D点（仅有x和Y坐标）中实现。

But my problem is: I have points in 3D as you can see from image 1. 但我的问题是：我从图像1中可以看到3D点。

Will Delaunay triangulations or constrained Delaunay triangulations work fine with 3D Points? Delaunay三角测量或受约束的Delaunay三角测量是否适用于3D点？ If yes, then how? 如果是，那怎么样？ Or do I have to find another algorithm for generating mesh from 3D points? 或者我是否必须找到另一种从3D点生成网格的算法？

Note: One good explanation of Delaunay triangulations for 2D points can be found here 注意： 这里可以找到关于2D点的Delaunay三角剖分的一个很好的解释

3 个解决方案

here are some other good links for mesh generation and its related work. 这里是网格生成及其相关工作的一些其他好的链接。

• TetGen : A Quality Tetrahedral Mesh Generator http://wias-berlin.de/software/tetgen/ • TetGen：质量四面体网格生成器http://wias-berlin.de/software/tetgen/

• GTSLibrary – The GNU Triangulated Surface Library. • GTSLibrary - GNU三角形曲面库。 http://gts.sourceforge.net/index.html http://gts.sourceforge.net/index.html

• Jonathan Shewchuk - http://www.cs.berkeley.edu/~jrs/ http://www.cs.cmu.edu/~quake/robust.html • Jonathan Shewchuk - http://www.cs.berkeley.edu/~jrs/ http://www.cs.cmu.edu/~quake/robust.html

• VTK: The Visualization Toolkit (VTK) is an open-source, freely available software system http://www.vtk.org/ . • VTK：可视化工具包（VTK）是一个开源，免费提供的软件系统http://www.vtk.org/ 。

• Volume and Surface Meshing – http://www.cse.ohio-state.edu/~tamaldey/mesh.htm . • 体积和表面网格划分 - http://www.cse.ohio-state.edu/~tamaldey/mesh.htm 。

• Poly2Tri: An open source CDT library http://code.google.com/p/poly2tri/ . • Poly2Tri：开源CDT库http://code.google.com/p/poly2tri/ 。

• CM2Mesh Tools – http://www.computing-objects.com/index.php . • CM2Mesh工具 - http://www.computing-objects.com/index.php 。

• Adaptive tessellation – http://fluxionsdividebyzero.com/p1/math/geometry/g046.html#_3D • 自适应曲面细分 - http://fluxionsdividebyzero.com/p1/math/geometry/g046.html#_3D

• CUBIT – The CUBIT Geometry and Mesh Generation Toolkit. • CUBIT - CUBIT几何和网格生成工具包。 http://cubit.sandia.gov/index.html http://cubit.sandia.gov/index.html

• Geometry in Action - http://www.ics.uci.edu/~eppstein/geom.html • 几何行动 - http://www.ics.uci.edu/~eppstein/geom.html

• SlimDX - SlimDX is a free open source framework that enables developers to easily build DirectX applications using .NET technologies such as C#, VB http://slimdx.org/ • SlimDX - SlimDX是一个免费的开源框架，使开发人员能够使用.NET技术轻松构建DirectX应用程序，例如C＃，VB http://slimdx.org/

3D Delauny triangulation will result in a (3D) volume mesh. 3D Delauny三角测量将产生（3D）体积网格。 I suppose what you want is a (2D) surface mesh embedded in 3D which approximates the given point set. 我想你想要的是嵌入在3D中的（2D）表面网格，它近似于给定的点集。

Depending on the type of data (little or big noise, outliers, etc.) you can take different approaches. 根据数据类型（噪声小，噪声大，异常值等），您可以采用不同的方法。 Note that you can always pre-process your data (eg to remove outliers, smooth the data, or estimate normals). 请注意，您始终可以预处理数据（例如，删除异常值，平滑数据或估计法线）。

For oriented point set with little noise and no outliers, you can consider Poisson Surface Reconstruction (eg in Michael Kazhdan, M. Bolitho, and Hugues Hoppe. Poisson Surface Reconstruction. In Symp. on Geometry Processing, pages 61-70, 2005 .). 对于具有很小噪声且没有异常值的定向点集，您可以考虑泊松表面重建 （例如，在Michael Kazhdan，M。Bolitho和Hugues Hoppe。泊松表面重建。在Symp.on Geometry Processing，第61-70页，2005年 。）。
Note that you can pre-process your data to fullfill the requirements, see for example Normal estimation . 请注意，您可以预处理数据以满足要求，例如参见正常估算。 Here is a C++ library implementing Poisson Surface Reconstruction (with nice explanations): CGAL Surface Reconstruction from Point Sets 这是一个实现泊松表面重建的C ++库（有很好的解释）：点集的CGAL表面重建
For scattered point data see for example Ohtake, Y.; 对于散点数据，请参见例如Ohtake，Y。 Belyaev, A. & Seidel, HP A multi-scale approach to 3D scattered data interpolation with compactly supported basis functions Shape Modeling International, 2003, 2003, 153-161 . Belyaev，A。和Seidel，HP使用紧凑支持的基函数进行3D散射数据插值的多尺度方法Shape Modeling International，2003,2003,153-161 。 It uses a hierarchical approach to create multiple interpolation levels. 它使用分层方法创建多个插值级别。
Another approach for highly non-uniform or noisy scattered data is Zhao, H.-K.; 对于高度不均匀或噪声分散的数据的另一种方法是Zhao，H.-K。 Osher, S. & Fedkiw, R. Fast surface reconstruction using the level set method Variational and Level Set Methods in Computer Vision, 2001. Proceedings. Osher，S。和Fedkiw，R。使用水平集方法快速表面重建计算机视觉中的变分和水平集方法，2001年。会议录。 IEEE Workshop on, 2001, 194-201 . IEEE研讨会，2001,194-201 。 It uses variatonal methods and PDEs (particularly level set methods). 它使用变异方法和偏微分方程（特别是水平集方法）。

ENigMA - Developed mostly to solve PDEs it also has a constrained surface and volume mesh generator. ENIGMA - 主要用于解决PDE，它还具有受约束的表面和体积网格生成器。 Still not sure if going to release it as open source in the future. 仍然不确定将来是否会将其作为开源发布。

https://www.sites.google.com/site/billyaraujo/enigma/volume-mesh-generation https://www.sites.google.com/site/billyaraujo/enigma/volume-mesh-generation