Netgen mesh library : nglib

Netgen mesh library : nglib

[e-mail]

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 = , NG_QUAD = , NG_TRIG6 = , NG_QUAD6 = , NG_QUAD8 =  };

/// Currently implemented volume element types
enum Ng_Volume_Element_Type
   { NG_TET = , NG_PYRAMID = , NG_PRISM = , NG_TET10 =  };

/// Values returned by Netgen functions
enum Ng_Result
   {
     NG_ERROR               = -,
     NG_OK                  = ,
     NG_SURFACE_INPUT_ERROR = ,
     NG_VOLUME_FAILURE      = ,
     NG_STL_INPUT_ERROR     = ,
     NG_SURFACE_FAILURE     = ,
     NG_FILE_NOT_FOUND      =
   };

// *** 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 = );

// 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 = ;
    int np = ;
    int nse = ;
    int ne = ;
    int trig[] = {};
    int tet[] = {};

    double point[] = {0.0};

    std::string strMeshFile = (argc > )? argv[]: "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 = ; i < np; ++i)
    {
        meshFile >> point[] >> point[] >> point[];
        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 = ; i < nse; ++i)
    {
        meshFile >> trig[] >> trig[] >> trig[];
        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 = ;
    mp.second_order = ;

    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 = ; i <= np; ++i)
    {
        nglib::Ng_GetPoint(mesh, i, point);
        std::cout << i << ": " << point[] << ", " << point[] << ", " << point[] << std::endl;
    }

    ne = nglib::Ng_GetNE(mesh);
    std::cout << "Elements: " << ne << std::endl;
    for (int i = ; i <= ne; ++i)
    {
        nglib::Ng_GetVolumeElement(mesh, i, tet);
        std::cout << i << ": " << tet[] << ", " << tet[] << ", " << tet[] << ", " << tet[] << std::endl;
    }

    // Save mesh.
    nglib::Ng_SaveMesh(mesh, "test.vol");

    // deconstruct Netgen library.
    nglib::Ng_Exit();

    return ;
}

PDF Version: Netgen mesh library : nglib