专注网格剖分 - TetGen,NETGEN,Steller
提要
记得大三那一年有一门课叫做高等有限元,最后的作业就是网格剖分算法的实现,我和同学一起花了些时间做了一个Qt程序,他写算法,我写界面,最后成绩竟然出奇的拿了90多...
今天要介绍的这款软件TetGen就是一款网格剖分的软件,算是力学计算中的前处理,他能够将输入的三维模型剖分成一个个的单元,如下图:
最左边的是原三维模型,中间图为Delaunay算法生成的四面体网格,最右边的图为在tetview中查看剖分的结果。
官网的手册里还有一些关于剖分算法的说明,有兴趣的可以去看看。
Netgen也是一款网格剖分软件,为奥地利科学家Joachim Schoeberl负责编写的格网(曲面和实体)剖分程序。是格网划分技术中极为先进与完善的,在3D格网划分领域更是具有极大的优势。
官网:http://www.hpfem.jku.at/netgen/
Stellar的中文意思是恒星,这是一个博士写的用于优化网格的软件,可以将生成的单元模型进行一些smooth、删除重复边的操作。
环境: ubuntu 12.04 32bit
Delaunay算法简介及实现
【定义】三角剖分[1]:假设V是二维实数域上的有限点集,边e是由点集中的点作为端点构成的封闭线段, E为e的集合。那么该点集V的一个三角剖分T=(V,E)是一个平面图G,该平面图满足条件:
1.除了端点,平面图中的边不包含点集中的任何点。
2.没有相交边。
3.平面图中所有的面都是三角面,且所有三角面的合集是散点集V的凸包。
在实际中运用的最多的三角剖分是Delaunay三角剖分,它是一种特殊的三角剖分。
先从Delaunay边说起:
【定义】Delaunay边:假设E中的一条边e(两个端点为a,b),e若满足下列条件,则称之为Delaunay边:存在一个圆经过a,b两点,圆内(注意是圆内,圆上最多三点共圆)不含点集V中任何其他的点,这一特性又称空圆特性。
【定义】Delaunay三角剖分:如果点集V的一个三角剖分T只包含Delaunay边,那么该三角剖分称为Delaunay三角剖分。
算法描述
Bowyer-Watson算法
的基本步骤是:
1、构造一个超级三角形,包含所有散点,放入三角形链表。
2、将点集中的散点依次插入,在三角形链表中找出外接圆包含插入点的三角形(称为该点的影响三角形),删除影响三角形的公共边,将插入点同影响三角形的全部顶点连接起来,完成一个点在Delaunay三角形链表中的插入。
3、根据优化准则对局部新形成的三角形优化。将形成的三角形放入Delaunay三角形链表。
4、循环执行上述第2步,直到所有散点插入完毕。
算法实现
代码是当时的队友小六子的,注释比较详尽。
delaunay.h
- #ifndef DELAUNAY_H_INCLUDED
- #define DELAUNAY_H_INCLUDED
- #include <cstdlib>
- #include <iostream>
- #include <cstring>
- #include <string>
- #include <fstream>
- #include <math.h>
- #include <vector>
- using namespace std;
- typedef struct
- {
- double x;
- double y;
- double z;
- }Point;//定义点类
- typedef vector<Point> PointArray;//定义点类的vector容器
- typedef struct
- {
- int left;
- int right;
- int count;//边的计数,如果计数为0,则删除此边
- }Edge;//定义边类
- typedef vector<Edge> EdgeArray;//定义边类的vector容器
- typedef struct
- {
- int v[3];//三角形的三个顶点
- Edge s[3];//三角形的三条边
- double xc;//三角形外接圆圆心的x坐标
- double yc;//三角形外接圆圆心的y坐标
- double r;//三角形外接圆的半径
- }Triangle;//定义三角形类
- typedef vector<Triangle> TriangleArray;//定义三角形类的vector容器
- typedef vector<int> intArray;//定义int类的vector容器
- class Delaunay//定义Delaunay类
- {
- public:
- Delaunay(Point p1,Point p2,Point p3,Point p4);//Delaunay类的构造函数,创建外边框
- ~Delaunay();//Delaunay类的析构函数
- bool AddPoint(double xx,double yy,double zz);//向已有剖分图形中加点的函数
- void Delete_Frame();//删除外边框
- void Boundary_Recover(int fromPoint,int toPoint);//边界恢复
- void output();//输出ANSYS命令流文件
- private:
- void Cal_Centre(double &x_centre,double &y_centre,double &radius,int n1,int n2,int n3);//计算三角形的外接圆圆心坐标和半径
- void MakeTriangle(int n1,int n2,int n3);//生成指定顶点的三角形
- bool inCircle(double xx,double yy,Triangle currentTris);//判断点是否在圆内
- void DelTriangle(int n,EdgeArray &BoundEdges);//删除指定的三角形
- PointArray m_Pts;//m_Pts用于存储所有点
- EdgeArray m_Edges;//m_Edges用于存储所有边
- TriangleArray m_Tris;//m_Tris用于存储所有三角形
- };
- void GetPoint(double &xx,double &yy,double &zz,string line);//解析从input文件中读取的每一行数据
- #endif // DELAUNAY_H_INCLUDED
delaunary .cpp
- #include "delaunay.h"
- Delaunay::Delaunay(Point p1,Point p2,Point p3,Point p4)
- {
- m_Pts.resize(4);
- m_Pts[0]=p1;
- m_Pts[1]=p2;
- m_Pts[2]=p3;
- m_Pts[3]=p4;//添加四个外边框点
- m_Edges.resize(4);
- Edge l1={0,1,-1};
- Edge l2={1,2,-1};
- Edge l3={0,3,-1};
- Edge l4={2,3,-1};
- m_Edges[0]=l1;
- m_Edges[1]=l2;
- m_Edges[2]=l3;
- m_Edges[3]=l4;//添加四个外边框的边
- MakeTriangle(0,1,2);
- MakeTriangle(0,2,3);//添加初始的两个三角形
- }
- Delaunay::~Delaunay()//清空Delaunay类的数据成员
- {
- m_Pts.resize(0);
- m_Edges.resize(0);
- m_Tris.resize(0);
- }
- void Delaunay::MakeTriangle(int n1,int n2,int n3)
- {
- double x_centre,y_centre,radius;
- Cal_Centre(x_centre,y_centre,radius,n1,n2,n3);//获得顶点为n1,n2,n3的三角形的外接圆圆心坐标和半径
- Triangle newTriangle={{n1,n2,n3},{{n1,n2,1},{n2,n3,1},{n1,n3,1}},x_centre,y_centre,radius};//生成指定的三角形
- m_Tris.push_back(newTriangle);//向m_Tris中添加新构造的三角形
- int EdgeSzie=(int)m_Edges.size();//获得目前的边数
- int flag;
- for (int i=0;i<3;i )
- {
- flag=1;
- for(int j=0;j<EdgeSzie;j )//通过循环判断新构造的三角形的各边是否已经存在于m_Edges中,如果存在则只增加该边的计数,否则添加新边
- {
- if (newTriangle.s[i].left==m_Edges[j].left&&newTriangle.s[i].right==m_Edges[j].right&&m_Edges[j].count!=-1) {flag=0;m_Edges[j].count =1;break;}
- else if(newTriangle.s[i].left==m_Edges[j].left&&newTriangle.s[i].right==m_Edges[j].right&&m_Edges[j].count==-1) {flag=0;break;}
- }
- if (flag==1) m_Edges.push_back(newTriangle.s[i]);
- }
- }
- void Delaunay::Cal_Centre(double &x_centre,double &y_centre,double &radius,int n1,int n2,int n3)
- {
- double x1,x2,x3,y1,y2,y3;
- x1=m_Pts[n1].x;
- y1=m_Pts[n1].y;
- x2=m_Pts[n2].x;
- y2=m_Pts[n2].y;
- x3=m_Pts[n3].x;
- y3=m_Pts[n3].y;
- x_centre=((y2-y1)*(y3*y3-y1*y1 x3*x3-x1*x1)-(y3-y1)*(y2*y2-y1*y1 x2*x2-x1*x1))/(2*(x3-x1)*(y2-y1)-2*((x2-x1)*(y3-y1)));//计算外接圆圆心的x坐标
- y_centre=((x2-x1)*(x3*x3-x1*x1 y3*y3-y1*y1)-(x3-x1)*(x2*x2-x1*x1 y2*y2-y1*y1))/(2*(y3-y1)*(x2-x1)-2*((y2-y1)*(x3-x1)));//计算外接圆圆心的y坐标
- radius= sqrt((x1 - x_centre)*(x1 - x_centre) (y1 - y_centre)*(y1 - y_centre));//计算外接圆的半径
- }
- bool Delaunay::AddPoint(double xx,double yy,double zz)
- {
- EdgeArray BoundEdges;//BoundEdges用于存储在删除三角形后留下的边框,用于构造新的三角形
- Point newPoint={xx,yy,zz};
- m_Pts.push_back(newPoint);//向m_Pts中添加新点
- intArray badTriangle;//badTriangle用于存储不符合空圆规则的三角形的索引号
- int TriSize=(int)m_Tris.size();//获得目前的三角形数
- for (int i=0;i<TriSize;i )//通过循环找到所有不符合空圆规则的三角形,并将其索引号存在badTriangle中
- {
- if (inCircle(xx,yy,m_Tris[i])==true) badTriangle.push_back(i);
- }
- for (int i=0;i<(int)badTriangle.size();i )//通过循环删除所有不符合空圆规则的三角形,同时保留边框
- {
- DelTriangle(badTriangle[i],BoundEdges);
- for (int j=i 1;j<(int)badTriangle.size();j ) badTriangle[j]-=1;
- }
- int PtSize=(int)m_Pts.size();//获得目前的点数
- for (int i=0;i<(int)BoundEdges.size();i )//生成新的三角形
- {
- if (PtSize-1<BoundEdges[i].left) MakeTriangle(PtSize-1,BoundEdges[i].left,BoundEdges[i].right);
- else if (PtSize-1>BoundEdges[i].left && PtSize-1<BoundEdges[i].right) MakeTriangle(BoundEdges[i].left,PtSize-1,BoundEdges[i].right);
- else MakeTriangle(BoundEdges[i].left,BoundEdges[i].right,PtSize-1);
- }
- return true;
- }
- bool Delaunay::inCircle(double xx,double yy,Triangle currentTris)//判断点是否在三角形的外接圆内
- {
- double dis=sqrt((currentTris.xc-xx)*(currentTris.xc-xx) (currentTris.yc-yy)*(currentTris.yc-yy));
- if (dis>currentTris.r) return false;
- else return true;
- }
- void Delaunay::DelTriangle(int n,EdgeArray &BoundEdges)
- {
- for (int i=0;i<3;i )
- {
- for (int j=0;j<(int)m_Edges.size();j )
- {
- if (m_Edges[j].left==m_Tris[n].s[i].left&&m_Edges[j].right==m_Tris[n].s[i].right)
- {
- if (m_Edges[j].count==2)//若要删除三角形的一边的计数为2,则将其计数减1,并将其压入BoundEdges容器中
- {
- m_Edges[j].count=1;
- BoundEdges.push_back(m_Edges[j]);
- }
- else if (m_Edges[j].count==-1) BoundEdges.push_back(m_Edges[j]);//如果是外边框,则直接压入BoundEdges容器中
- else if (m_Edges[j].count==1)//如果删除三角形的一边的计数为1,则删除该边,同时查看BoundEdges中是否有此边,若有,则删除
- {
- for (int k=0;k<(int)BoundEdges.size();k )
- {
- if (BoundEdges[k].left==m_Edges[j].left&&BoundEdges[k].right==m_Edges[j].right)
- {
- BoundEdges.erase(BoundEdges.begin() k);
- break;
- }
- }
- m_Edges.erase(m_Edges.begin() j);
- j--;
- }
- break;
- }
- }
- }
- m_Tris.erase(m_Tris.begin() n);//删除该三角形
- }
- void Delaunay::output()//向“output.log"文件中写入ANSYS命令流
- {
- ofstream outfile("output.log");
- if (!outfile)
- {
- cout<<"Unable to output nodes!";
- exit(1);
- }
- outfile<<"/PREP7"<<endl;
- for (int i=0;i<(int)m_Pts.size();i )
- {
- outfile<<"K,"<<i 1<<","<<m_Pts[i].x<<","<<m_Pts[i].y<<","<<m_Pts[i].z<<endl;
- }
- for (int i=0;i<(int)m_Edges.size();i )
- {
- outfile<<"L,"<<m_Edges[i].left 1<<","<<m_Edges[i].right 1<<endl;
- }
- outfile.close();
- }
- void GetPoint(double &xx,double &yy,double &zz,string line)//从字符串line中解析出点的x,y,z坐标
- {
- int flag=0;
- string tmp="";
- char *cstr;
- for (int i=(int)line.find(',') 1;i<(int)line.size();i )
- {
- if (line[i]==',')
- {
- cstr=new char[tmp.size() 1];
- strcpy(cstr,tmp.c_str());
- if (flag==0) {xx=atof(cstr);tmp.resize(0);flag ;}
- else if (flag==1) {yy=atof(cstr);tmp.resize(0);flag ;}
- continue;
- }
- tmp=tmp line[i];
- }
- if (fabs(xx)<1.0e-6) xx=0.0;
- if (fabs(yy)<1.0e-6) yy=0.0;
- if (fabs(zz)<1.0e-6) zz=0.0;
- }
- void Delaunay::Delete_Frame()//删除外边框
- {
- EdgeArray BoundEdges;
- for (int i=0;i<4;i ) m_Pts.erase(m_Pts.begin());
- for (int i=0;i<(int)m_Tris.size();i )
- {
- if (m_Tris[i].v[0]==0||m_Tris[i].v[0]==1||m_Tris[i].v[0]==2||m_Tris[i].v[0]==3)
- {
- DelTriangle(i,BoundEdges);
- BoundEdges.resize(0);
- i--;
- }
- else
- {
- for (int j=0;j<3;j )
- {
- m_Tris[i].v[j]-=4;
- m_Tris[i].s[j].left-=4;
- m_Tris[i].s[j].right-=4;
- }
- }
- }
- for (int i=0;i<4;i ) m_Edges.erase(m_Edges.begin());
- for (int i=0;i<(int)m_Edges.size();i )
- {
- m_Edges[i].left-=4;
- m_Edges[i].right-=4;
- }
- }
- void Delaunay::Boundary_Recover(int fromPoint,int toPoint)//恢复由指定点组成的边界
- {
- EdgeArray BoundEdges;
- for (int i=0;i<(int)m_Tris.size();i )
- {
- if (m_Tris[i].v[0]>=(fromPoint-1)&&m_Tris[i].v[2]<=(toPoint-1))
- {
- DelTriangle(i,BoundEdges);
- BoundEdges.resize(0);
- i--;
- }
- }
- }
main.cpp
- #include "delaunay.h"
- int main()
- {
- ifstream infile("input.txt");//打开"input.txt"文件
- if (!infile)//判断文件是否正常打开
- {
- cout<<"Unable to input nodes!";
- exit(1);
- }
- string line;
- PointArray p;
- double xx,yy,zz;
- int nodeSize;
- for (int i=0;i<4;i )//读入4外边框点
- {
- getline(infile,line);
- GetPoint(xx,yy,zz,line);
- Point tmp={xx,yy,zz};
- p.push_back(tmp);
- }
- Delaunay MyMesh(p[0],p[1],p[2],p[3]);//实例化Delaunay类
- getline(infile,line);//读入节点数,用于后面循环
- char *cstr;
- cstr=new char[line.size() 1];
- strcpy(cstr,line.c_str());
- nodeSize=atoi(cstr);
- for (int i=0;i<nodeSize;i )//读入每个节点的坐标
- {
- getline(infile,line);
- GetPoint(xx,yy,zz,line);
- MyMesh.AddPoint(xx,yy,zz);
- }
- infile.close();
- MyMesh.Delete_Frame();//删除外边框
- MyMesh.Boundary_Recover(203,466);
- MyMesh.Boundary_Recover(467,487);
- MyMesh.Boundary_Recover(488,511);
- MyMesh.Boundary_Recover(512,537);//以上都是恢复指定边界
- MyMesh.output();//将相应ANSYS命令流输出
- return 0;
- }
测试一组数据后,得到结果:
编译tetgen
下载源码之后cd进目录,然后执行
make
编译完成之后,目录下就会生成一个名为 tetgen 的可执行文件。
运行tetview
这个是用于查看网格模型的工具。 因为这个东西比较老,所以首先要安装一些比较老的库。
g77
下载好之后解压,cd进目录运行:
sudo ./install.sh
stdc 5
sudo apt-get install libstdc 5
将下载好linux版本的tetivew解压,再将example解压到相同的目录,终端cd进目录,执行:
./tetview pmdc.1
一切配置正确的话,tetview就运行了。很简单的一个操作界面,按F1沿着plane剖分,效果就像这样:
网格剖分实战
首先打开blender,Add->Mesh->Torus,添加一个圆环,然后File->Export->Stanford(.ply),导出ply文件,待会用于剖分。
将导出的ply模型放到tetgen的目录,终端执行:
./tetgen -p torus.ply
再将生成的文件拷贝到tetiew的目录下,执行
./tetview torus.1.ele
Netgen
这个东西编译起来还是有点头疼,还在ubuntu的软件中心有带,所以直接在软件中心搜索下载就可以了。
还是选择用blender导出模型。这里一定要记住,所有用于网格剖分的模型都要是封闭的体模型,不然就会出现闪退的情况。
这里选择一个植物模型,File ->Export->stl。记住勾选左边的ascii。
打开netgen,File ->Load Geometry,选择刚才导出的模型。然后点击工具栏中的GnerateMesh,稍等片刻,得到结果。
导出单元
首先选择导出类型:
File -> Export File type ->Elmer Format
然后导出:
File-> Export Mesh
Stellar
从官网下载好源码之后解压,终端进入目录,运行
make
Stellar就编译好了。
将之前的用tetgen生成的 model.1.node 和 model.1.ele 文件拷贝至Stellar的文件夹,终端执行
Stellar model.1
发现报错:
Improving mesh.
***** ALERT Input mesh has non-positive worst quality of -0.85263, dying *****
Starting up smoothing, input tet has quality -0.85263
Stellar: ./src/smoothing.c:1640: nonsmooth: Assertion `worstqual > 0.0' failed.
Aborted (core dumped)
发邮件为问作者,说是单元模型三角面没有遵循右手法则,用meshconvert.py官网给的脚本转化一下就好。
终端执行./meshconvert.py model.1.node model.2.node
执行完成之后会生成新的ele,node文件,这时再在终端运行Stellar,
Stellar model.2
原来的模型有6000多个顶点,经过大概10分钟的优化,生成了一个20000点的模型...T T
原因可能是在平滑处理的过程中插入了很多点,在优化结果中,还会生成一个stats文件,里面描述了整个优化过程。
如果要控制优化的过程的话,需要自己写配置文件,修改一下官网给的模板就可以了,比如我不想增加单元格的数量,则关闭顶点的插入就可以了。
创建一个 conf 文件
- ####################################
- # Stellar mesh improvement options #
- ####################################
- # This file contains all the possible options that can currently be set for
- # mesh improvement. Lines that begin with '#' are comments and are ignored.
- # Other lines take the form 'option intval floatval stringval', where option
- # is the name of the option, and intval floatval and stringval are the possible
- # fields that can be used to set that option. If an option takes an int, only
- # a value for int needs to be given. If it's a float, a dummy int should be
- # inserted before the float. If it's a string, a dummy int and a dummy float
- # should be inserted before the string. This clumsiness is because I don't like
- # coding string processing in C, and this is the easiest way. Any unset options
- # will assume their default values.
- # verbosity: bigger number means more verbose output of improvement.
- # default = 1
- verbosity 0
- # use color in verbose improvement output. default = 0
- usecolor 1
- # just output the mesh unchanged and quit. default = 0
- outputandquit 0
- ## quality measure options
- # qualmeasure: selects which quality measure to use as an objective function
- # for optimizing the tetrahedra. The quality measures are described in
- # Chapter 2 of Bryan's dissertation. default = 0
- # 0 = minimum sine of the dihedral angles (default)
- # 1 = square root of radius ratio (circumradius divided by inradius)
- # 2 = V / l_rms^3 (volume divided by cube of root-mean-squared edge length)
- # 5 = minimum sine with biased obtuse angles
- qualmeasure 5
- # sinewarpfactor: float. for qualmeasure 5 only; sets the factor by which
- # obtuse angles are scaled relative to acute angles. Default is 0.75
- sinewarpfactor 0 0.75
- ## termination options
- # BOTH goal angles must be reached to terminate improvement
- # goalanglemin: float. terminates improvement early if minimum angle reaches
- # this value. default = 90.0 (which precludes early termination)
- goalanglemin 0 90.0
- # goalanglemax: float. terminates improvement early if maximum angle reaches
- # this value. default = 90.0
- goalanglemax 0 90.0
- ## smoothing options
- # nonsmooth: enable optimization-based smoothing. default = 1
- nonsmooth 1
- # facetsmooth: enable smoothing of facet vertices. default = 1
- facetsmooth 1
- # segmentsmooth: enable smoothing of segment vertices. default = 1
- segmentsmooth 1
- # usequadrics: enable use of surface quadric error for smoothing fixed boundary
- # vertices. WARNING: this will allow the domain shape to change slightly. But
- # even a little play sometimes yields much better meshes. default = 0
- usequadrics 0
- # quadricoffset: amount to start quadric error at before subtracting.
- # See alpha in Section 3.2.5 of Bryan's dissertation. default = 0.8
- quadricoffset 0 0.8
- # quadricscale: amount to scale quadric error before subtracting from offset.
- # See beta in Section 3.2.5 of Bryan's dissertation. default = 300.0
- quadricscale 0 300.0
- ## topological transformation options
- # flip22: enable 2-2 flips (for boundary tets). default = 1
- flip22 1
- # multifaceremoval: enable multi-face removal. singlefaceremoval might still
- # be on. default = 1
- multifaceremoval 1
- # singlefaceremoval: enable single face removal (2-3 and 2-2 flips). Has
- # no effect when multifaceremoval is enabled. default = 1
- singlefaceremoval 1
- # edgeremoval: enable edge removal. default = 1
- edgeremoval 1
- ## edge contraction options
- # edgecontraction: enable edge contraction. default = 1
- edgecontraction 1
- ## vertex insertion options
- # enableinsert: enable ALL vertex insertion (overrides others). default = 1
- enableinsert 0
- # insertbody: enable just vertex insertion in body (interior). default = 1
- insertbody 0
- # insertfacet: enable just insertion on facets. default = 1
- insertfacet 0
- # insertsegment: enable just insertion on segments. default = 1
- insertsegment 0
- # insertthreshold: on each insertion pass, try vertex insertion in this
- fraction of the tetrahedra. default = 0.031 (the worst 3.1%)
- insertthreshold 0 0.031
- ## size control options
- # (See Chapter 6 of Bryan's dissertation.)
- # sizing: enable control of element sizes. default = 0
- sizing 0
- # sizingpass: enable edge length correction before quality improvement.
- # default = 0
- sizingpass 0
- # targetedgelength: the target edge length for this mesh. If set to 0.0, the
- # target edge length is initialized automatically to the initial mean edge
- # length. default = 0.0
- targetedgelength 0 0.0
- # longerfactor: factor by which an edge can be longer than the target edge
- # length before being considered "too long". default = 3.0
- longerfactor 0 2.0
- # shorterfactor: factor by which an edge can be shorter than the target edge
- # length before being considered "too short" default = 0.33
- shorterfactor 0 0.50
- ## anisotropy options
- # (See Chapter 7 of Bryan's dissertation.)
- # anisotropic: enable anisotropic meshing. default = 0
- anisotropic 0
- # tensor: which size/anisotropy tensor to use. default = 0
- # 0 = identity
- # 1 = stretch x
- # 2 = stretch y
- # 3 = sink
- # 4 = swirl
- # 5 = center
- # 6 = perimeter
- # 7 = right
- # 8 = sine
- tensor 6
- ## quality file output options
- # These files list, for each tetrahedron, the values of the quality measures
- # minsineout: enable output of .minsine quality file. default = 1
- minsineout 1
- # minangout: enable output of .minang quality file. default = 0
- minangout 0
- # maxangout: enable output of .maxang quality file. default = 0
- maxangout 0
- # vlrmsout: enable output of .vlrms quality file. default = 0
- vlrmsout 0
- # nrrout: enable output of the .nrr quality file. default = 0
- nrrout 0
- ## animation options
- # animate: activate animation file output (a set of output files after each
- # pass). default = 0
- animate 0
- # timeseries: when animate = 1, only output .stats. default = 0
- timeseries 0
- ## output filename option
- # fileprefix: filename prefix that distinguishes the output files from the
- # input files. If none specified, an iteration number is appended to the input
- # filenames.
- #fileprefix 0 5 ../output/testprefix
再次运行,
./Stellar -s conf model.2
运行结果:
顶点从6000多降到了5000多,用tetiew来查看:
相关下载
http://blog.csdn.net/silangquan/article/details/10475015