开源四面体网格Netgen使用体验 / 四六文摘

摘要Abstract：本文主是对Netgen的库nglib的用法进行介绍。主要参考资料是Netgen用户指南。最后给出一个具体程序实例。

关键字Key Words：Netgen, nglib, Mesh

一、引言 Introduction

NETGEN是一个二维/三维自动网格剖分工具，并且遵循LGPL开源协议。即可以作为一个带有用户界面的单独程序使用，也可以作为C++的库文件被其它程序链接。Netgen可以跨平台，支持Unix/Linux和Windows。

Netgen最早为奥地利科学家Joachim Schoberl编写的网格剖分程序，是网格划分技术中极为先进与完善的，在3D网格划分领域更是具有极大的优势。可以从sourceforge上获取最新版本的Netgen5.1，网址是：http://sourceforge.net/projects/netgen-mesher/files/netgen-mesher/

Netgen网格生成库nglib是以C++源程序形式提供，可以编译为Unix/Linux或Windows上的库文件。程序开发使用的接口文件是nglib.h。

二、头文件 The Header File

接口文件中包含了一些类型定义和函数调用，所有的Netgen类型和函数都带有前缀Ng。类型和函数首字母大写，所有常量都是大写。

三、类型和常量 Types and Constants

// ** Constants used within Netgen ********************* /// Maximum allowed number of nodes per volume element #define NG_VOLUME_ELEMENT_MAXPOINTS 10


/// Maximum allowed number of nodes per surface element

#define NG_SURFACE_ELEMENT_MAXPOINTS 8
// *** Data-types for accessing Netgen functionality ***

/// Data type for NETGEN mesh

typedef void * Ng_Mesh;
/// Data type for NETGEN CSG geometry

typedef void * Ng_CSG_Geometry;
/// Data type for NETGEN 2D geometry

typedef void * Ng_Geometry_2D;
/// Data type for NETGEN STL geometry

typedef void * Ng_STL_Geometry;
// *** Special Enum types used within Netgen ***********

/// Currently implemented surface element types

enum Ng_Surface_Element_Type

{ NG_TRIG = 1, NG_QUAD = 2, NG_TRIG6 = 3, NG_QUAD6 = 4, NG_QUAD8 = 5 };
/// Currently implemented volume element types

enum Ng_Volume_Element_Type

{ NG_TET = 1, NG_PYRAMID = 2, NG_PRISM = 3, NG_TET10 = 4 };
/// Values returned by Netgen functions

enum Ng_Result

{

NG_ERROR = -1,

NG_OK = 0,

NG_SURFACE_INPUT_ERROR = 1,

NG_VOLUME_FAILURE = 2,

NG_STL_INPUT_ERROR = 3,

NG_SURFACE_FAILURE = 4,

NG_FILE_NOT_FOUND = 5

};
// *** Classes required for use within Netgen **********

/// Netgen Meshing Parameters class

class Ng_Meshing_Parameters

{

public:

int uselocalh; //!< Switch to enable / disable usage of local mesh size modifiers

double maxh; //!< Maximum global mesh size allowed

double minh; //!< Minimum global mesh size allowed

double fineness; //!< Mesh density: 0...1 (0 => coarse; 1 => fine) double grading; //!< Mesh grading: 0...1 (0 => uniform mesh; 1 => aggressive local grading) double elementsperedge; //!< Number of elements to generate per edge of the geometry double elementspercurve; //!< Elements to generate per curvature radius

Ng_Mesh表示Netgen网格的数据结构。Ng_STL_Geometry表示STL几何。可以通过Ng_Meshing_Parameters来指定生成网格时的参数。Netgen函数的返回值类型是Ng_Result。

四、初始化 Initialization

分别调用如下两个函数对netgen初始化和析构：

/*! \brief Initialise the Netgen library and prepare for use */ DLL_HEADER void Ng_Init (); /*! \brief Exit the Netgen meshing kernel in a clean manner */ DLL_HEADER void Ng_Exit ();

五、网格的访问 Mesh access

Netgen网格可以通过如下函数来处理。一个网格包含nodes, surface elements和volume elements。都是从1开始计数的。

// Generates new mesh structure Ng_Mesh * Ng_NewMesh (); void Ng_DeleteMesh (Ng_Mesh * mesh); // feeds points, surface elements and volume elements to the mesh void Ng_AddPoint (Ng_Mesh * mesh, double * x); void Ng_AddSurfaceElement (Ng_Mesh * mesh, Ng_Surface_Element_Type et, int * pi); void Ng_AddVolumeElement (Ng_Mesh * mesh, Ng_Volume_Element_Type et, int * pi); // ask for number of points, surface and volume elements int Ng_GetNP (Ng_Mesh * mesh); int Ng_GetNSE (Ng_Mesh * mesh); int Ng_GetNE (Ng_Mesh * mesh); // return point coordinates void Ng_GetPoint (Ng_Mesh * mesh, int num, double * x); // return surface and volume element in pi Ng_Surface_Element_Type Ng_GetSurfaceElement (Ng_Mesh * mesh, int num, int * pi); Ng_Volume_Element_Type Ng_GetVolumeElement (Ng_Mesh * mesh, int num, int * pi);

更多信息请参考其头文件nglib.h。

在生成网格时，用户可以指定网格大小及一些约束。函数Ng_GenerateVolumeMesh从曲面生成网格。

/*! \brief Apply a global restriction on mesh element size */ DLL_HEADER void Ng_RestrictMeshSizeGlobal (Ng_Mesh * mesh, double h);


/*! \brief Locally restrict the mesh element size at the given point

*/

DLL_HEADER void Ng_RestrictMeshSizePoint (Ng_Mesh * mesh, double * p, double h);

/*! \brief Locally restrict the mesh element size within a specified box */ DLL_HEADER void Ng_RestrictMeshSizeBox (Ng_Mesh * mesh, double * pmin, double * pmax, double h); /*! \brief Create a 3D Volume Mesh given a Surface Mesh */ DLL_HEADER Ng_Result Ng_GenerateVolumeMesh (Ng_Mesh * mesh, Ng_Meshing_Parameters * mp);

六、STL几何 STL Geometry

STL几何数据可以从STL文件（ASCII或二进制）读取，也可以由一个个的三角形组装而成。

// loads geometry from STL file DLL_HEADER Ng_STL_Geometry * Ng_STL_LoadGeometry (const char * filename, int binary = 0);


// generate new STL Geometry

DLL_HEADER Ng_STL_Geometry * Ng_STL_NewGeometry ();
// fills STL Geometry

// positive orientation

// normal vector may be null-pointer

DLL_HEADER void Ng_STL_AddTriangle (Ng_STL_Geometry * geom,

double * p1, double * p2, double * p3,

double * nv = NULL);
// add (optional) edges :

DLL_HEADER void Ng_STL_AddEdge (Ng_STL_Geometry * geom,

double * p1, double * p2);
// after adding triangles (and edges) initialize

DLL_HEADER Ng_Result Ng_STL_InitSTLGeometry (Ng_STL_Geometry * geom);
// automatically generates edges:

DLL_HEADER Ng_Result Ng_STL_MakeEdges (Ng_STL_Geometry * geom,

Ng_Mesh* mesh,

Ng_Meshing_Parameters * mp);

// generates mesh, empty mesh must be already created. DLL_HEADER Ng_Result Ng_STL_GenerateSurfaceMesh (Ng_STL_Geometry * geom, Ng_Mesh * mesh, Ng_Meshing_Parameters * mp);

七、示例程序 Example Code

在Netgen的安装目录下的nglib文件夹中有两个示例程序ng_vol.cpp和ng_stl.cpp。其中ng_vol.cpp程序开始时从cube.surf文件读入点坐标和曲面的三角形，生成的volumne mesh输出到文件：cuve.vol。经过测试，程序可以运行，修改过的代码如下所示：

#include <iostream> #include <fstream>


namespace nglib {

#include <nglib.h>

}
#pragma comment(lib, "nglib.lib")
int main(int argc, char* argv[])

{

std::cout << "Netgen Testing..." << std::endl;
int i = 0;

int np = 0;

int nse = 0;

int ne = 0;

int trig[3] = {0};

int tet[4] = {0};
double point[3] = {0.0};
std::string strMeshFile = (argc > 1)? argv[1]: "cube.surf";

std::ifstream meshFile(strMeshFile.c_str());
// initialize the Netgen library.

nglib::Ng_Init();
// Generate new mesh structure.

nglib::Ng_Mesh* mesh = nglib::Ng_NewMesh();
// Read surface mesh from file.

// feed points to the mesh.

meshFile >> np;

std::cout << "Reading " << np << " points..." << std::endl;

for (int i = 0; i < np; ++i)

{

meshFile >> point[0] >> point[1] >> point[2];

nglib::Ng_AddPoint(mesh, point);

}

std::cout << "done." << std::endl;
// feed surface elements to the mesh.

meshFile >> nse;

std::cout << "Reading " << nse << " faces..." << std::endl;

for (int i = 0; i < nse; ++i)

{

meshFile >> trig[0] >> trig[1] >> trig[2];

nglib::Ng_AddSurfaceElement(mesh, nglib::NG_TRIG, trig);

}

std::cout << "done." << std::endl;
// generate volume mesh.

nglib::Ng_Meshing_Parameters mp;

mp.maxh = 1e6;

mp.fineness = 1;

mp.second_order = 0;
std::cout << "start meshing..." << std::endl;

nglib::Ng_GenerateVolumeMesh(mesh, &mp);

std::cout << "meshing done." << std::endl;
// volume mesh output.

np = nglib::Ng_GetNP(mesh);

std::cout << "Points: " << np << std::endl;

for (int i = 1; i <= np; ++i)

{

nglib::Ng_GetPoint(mesh, i, point);

std::cout << i << ": " << point[0] << ", " << point[1] << ", " << point[2] << std::endl;

}
ne = nglib::Ng_GetNE(mesh);

std::cout << "Elements: " << ne << std::endl;

for (int i = 1; i <= ne; ++i)

{

nglib::Ng_GetVolumeElement(mesh, i, tet);

std::cout << i << ": " << tet[0] << ", " << tet[1] << ", " << tet[2] << ", " << tet[3] << std::endl;

}
// Save mesh.

nglib::Ng_SaveMesh(mesh, "test.vol");
// deconstruct Netgen library.

nglib::Ng_Exit();

return 0; }

开源四面体网格Netgen使用体验