开源四面体网格Netgen使用体验

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;
}