摘要Abstract：本文主是對Netgen的庫nglib的用法進行介紹。主要參考資料是Netgen使用者指南。最後給出一個具體程式執行個體。 　　關鍵字Key Words：Netgen, nglib, Mesh

Netgen mesh library : nglib

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摘要Abstract：本文主是對Netgen的庫nglib的用法進行介紹。主要參考資料是Netgen使用者指南。最後給出一個具體程式執行個體。 

關鍵字Key Words：Netgen, nglib, Mesh 

一、引言 Introduction

Netgen網格生成庫nglib是以C++源程式形式提供，可以編譯為Unix/Linux或Windows上的庫檔案。程式開發使用的接口檔案是nglib.h。 

二、頭檔案 The Header File

接口檔案中包含了一些類型定義和函數調用，所有的Netgen類型和函數都帶有字首Ng。類型和函數首字母大寫，所有常量都是大寫。 

三、類型和常量 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網格的資料結構。Ng_STL_Geometry表示STL幾何。可以通過Ng_Meshing_Parameters來指定生成網格時的參數。Netgen函數的傳回值類型是Ng_Result。 

四、初始化 Initialization

分别調用如下兩個函數對netgen初始化和析構：

/*! \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、網格的通路 Mesh access

Netgen網格可以通過如下函數來處理。一個網格包含nodes, surface elements和volume elements。都是從1開始計數的。 

// 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);      

更多資訊請參考其頭檔案nglib.h。 

在生成網格時，使用者可以指定網格大小及一些限制。函數Ng_GenerateVolumeMesh從曲面生成網格。

/*! \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幾何 STL Geometry

STL幾何資料可以從STL檔案（ASCII或二進制）讀取，也可以由一個個的三角形組裝而成。

// 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、示例程式 Example Code

在Netgen的安裝目錄下的nglib檔案夾中有兩個示例程式ng_vol.cpp和ng_stl.cpp。其中ng_vol.cpp程式開始時從cube.surf檔案讀入點坐标和曲面的三角形，生成的volumne mesh輸出到檔案：cuve.vol。經過測試，程式可以運作，修改過的代碼如下所示：

#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;
}