CGAL-2D查询包围点的所有相邻边(Regulation) using incident&dual

其他 2018-10-24 20:53:58 阅读次数: 0
版权声明：本文为博主原创文章，未经博主允许不得转载。 https://blog.csdn.net/OOFFrankDura/article/details/81665905

综述

注意到cgal中的dual没有点到面的对偶，所以我们需要自己遍历完成。
这里使用Edge_Circulator。需要注意的是，Circulator要求边闭合（无射线边）。所以我们使用一个包围盒进行框定。

环境

cgal 4.12
IDE clion
项目管理 cmake
macos

更新

2018.8.14给出第二种计算方案：
使用cgal本身
finite_edge_iterator
的特性.

说明

这是使用powerdiagram进行展示（正则三角剖分后求对偶），如果您希望得到Voronoi可以使用Delaunay三角剖分后做相同的处理。

效果

这里写图片描述
其中白色区域就是点——绿色点的包围边。

代码

第一种

//作者：SDU窦志扬
//日期：2018/8/14
//联络：[email protected]
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Regular_triangulation_2.h>
#include <CGAL/Weighted_point_2.h>
#include <CGAL/Polygon_2.h>
#include <GLUT/glut.h>
#include <CGAL/bounding_box.h>
#include <fstream>
#include<iostream>
typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef CGAL::Regular_triangulation_2<K> Regular_triangulation;
typedef K::Vector_2                                     Vector;
typedef K::Point_2 Point;
typedef K::Weighted_point_2 Wp;
typedef K::Point_2                                     Point;
typedef CGAL::Regular_triangulation_2<K>               Rt;

int window_size = 600;
using namespace std;

std::vector<Regular_triangulation::Weighted_point> wpoints;
std::vector<Point> points;


const int n=100;
const GLfloat Pi=3.1415926536f;
#define MAX_CHAR        128
void MyDisplay(double x,double y ,double R)
{
    glBegin(GL_POLYGON);
    glColor3f(1,0,0);
    R  =sqrt(R);
    for(int i=0;i<n;i++){
        glVertex2f(R*cos(2*Pi/n*i)+x,R*sin(2*Pi/n*i)+y);
    }
    glEnd();
}

void add_point(int x, int y, double w){
    //绘制圆形

    wpoints.push_back( Wp(Point(x,y), w) );
    points.push_back(Point(x,y) );
    MyDisplay(x,y,w);
    glPointSize(7);
    glBegin(GL_POINTS);
    glColor3f( 0.0, 1.0, 0.0 );
    glVertex2f( x,y);
    glEnd();
}
void display(void)
{
    add_point(100, 400,10000); //左中
    add_point(200,200,15000);
    add_point(240,310,8000);   //目标点
    add_point(210, 560,20000);
    add_point(340, 80, 12000);
    add_point(560,120, 10000);
    add_point(600, 500,12002);
    add_point(450, 550,8000);

    Regular_triangulation rt(wpoints.begin(), wpoints.end());
    rt.is_valid();
    Regular_triangulation::Edge_iterator eit;
    Regular_triangulation::Point_iterator pit;
    Regular_triangulation::Finite_faces_iterator fit;

    //遍历Delaunay的所有边，绘制Delaunay图的对偶图，即Voronoi图
    glEnable( GL_LINE_STIPPLE );//使用点画模式，即使用虚线来绘制Voronoi图
    glLineStipple( 1, 0x3333 );
    glColor3f( 0.0, 1.0,1.0 );

    cout << "====all points in rt====" << endl;
    for (auto vit = rt.vertices_begin(); vit != rt.vertices_end(); ++vit){
        cout << vit->point() << endl;

    }
    cout << "========" << endl;
    vector<Point> dual_points;

    cout << "====all points in powerdiagram====" << endl;
    //遍历Regular triangulation的所有面
    for( fit = rt.faces_begin(); fit != rt.faces_end(); fit ++)
    {
        dual_points.push_back(rt.dual(fit));
        //在其对偶图中所对应的点
    }
    for (int j = 0; j <dual_points.size() ; ++j) {
        cout << dual_points[j] << endl;
    }
    cout << "========" << endl;


    for( eit = rt.edges_begin(); eit != rt.edges_end(); eit ++)
    {
        CGAL::Object o = rt.dual(eit);
        //在其对偶图中所对应的边
        if (CGAL::object_cast<K::Segment_2>(&o)) //如果这条边是线段，则绘制线段
        {
            glBegin(GL_LINES);
            glVertex2i( CGAL::object_cast<K::Segment_2>(&o)->source().hx(), CGAL::object_cast<K::Segment_2>(&o)->source().hy() );
            glVertex2i( CGAL::object_cast<K::Segment_2>(&o)->target().hx(), CGAL::object_cast<K::Segment_2>(&o)->target().hy() );
            glEnd();
        }
        else if (CGAL::object_cast<K::Ray_2>(&o))//如果这条边是射线，则绘制射线
        {
            glBegin(GL_LINES);
            glVertex2i( CGAL::object_cast<K::Ray_2>(&o)->source().hx(), CGAL::object_cast<K::Ray_2>(&o)->source().hy() );
            glVertex2i( CGAL::object_cast<K::Ray_2>(&o)->point(1).hx(), CGAL::object_cast<K::Ray_2>(&o)->point(1).hy() );
            glEnd();
        }
    }
    glDisable( GL_LINE_STIPPLE );//关闭点画模式

    auto box = CGAL::bounding_box(points.begin(), points.end());
    auto center2 = CGAL::ORIGIN + 0.5 * (box.max() - CGAL::ORIGIN) + 0.5 * (box.min() - CGAL::ORIGIN);
    double sideLen = max(box.xmax() - box.xmin(), box.ymax() - box.ymin());
    Point center = CGAL::ORIGIN;
    double maxW = -100000;
    map<Point,int>  fromSite2ID;
    for (int i = 0; i < wpoints.size(); ++i)
    {
        //fromSite2ID是一个点Point到int的map
        //这里对每个点进行标记"i"
        fromSite2ID[wpoints[i].point()] = i;
        center = center + (wpoints[i].point() - CGAL::ORIGIN);
        if (maxW < wpoints[i].weight())
        {//负值越大说明
            maxW = wpoints[i].weight();
        }
    }
    center = CGAL::ORIGIN + (center - CGAL::ORIGIN) / (double)wpoints.size();
    //center计算距离原点的平均偏移量
    vector<Wp> exteriorPoints;
    Wp p1(center + sideLen * Vector(1, 0), maxW);
    exteriorPoints.push_back(p1);
    Wp p2(center + sideLen * Vector(-1, 0), maxW);
    exteriorPoints.push_back(p2);
    Wp p3(center + sideLen * Vector(0, 1), maxW);
    exteriorPoints.push_back(p3);
    Wp p4(center + sideLen * Vector(0,-1), maxW);
    exteriorPoints.push_back(p4);
    //用一个更大的区域包围起来（一定包在里面）
    rt.insert(exteriorPoints.begin(), exteriorPoints.end());
    for (int i = 0; i < exteriorPoints.size(); ++i)
    {
        fromSite2ID[exteriorPoints[i].point()] = -1; //means the extra sites
    }
    //遍历显示
    cout << "====all edges bounding the point====" << endl;
    int con = 0;

    for (Rt::Finite_vertices_iterator siteIt = rt.finite_vertices_begin();
        siteIt != rt.finite_vertices_end(); ++siteIt)
    {
        con++;
        Point site = siteIt->point().point();
//      cout <<"powerdiagram :" << con++<<"--" <<site << endl;

        int curSiteID = fromSite2ID.find(site)->second;//找到点对应的id
        if (curSiteID == -1){
            cout << "这是边界点" << endl;
            continue;
        }
        Rt::Edge_circulator beg = rt.incident_edges(siteIt);
        Rt::Edge_circulator it = beg;
        vector<Point> cell;
        do
        {
            K::Segment_2 s;
            CGAL::Object o = rt.dual(it);
            if (CGAL::assign(s, o))
            {
                cell.push_back(s.source());

            }
        } while (++it != beg);
        glLineWidth(8);
        glBegin(GL_LINE_LOOP);
        glLineWidth(20);
        glColor3f(1,1,1);
        for (int j = 0; j <cell.size() ; ++j) {
            if (site == Point(240,310)){
                glVertex2f(cell[j].x(), cell[j].y());
                cout << cell[j] << "  ---  " << site << endl;
            }
        }
        glEnd();





    }
}
void InitEnvironment()
{
    //一些初始化操作
    glClearColor(0.0,0.0,0.0,0);
    glClear(GL_COLOR_BUFFER_BIT);
    glPointSize(7);
    glMatrixMode(GL_MODELVIEW);
    glLoadIdentity();
    gluOrtho2D(0,window_size,0,window_size);
}
void init_Display(void)
{
    glClear(GL_COLOR_BUFFER_BIT);
    glColor3f(0.98f, 0.625f, 0.12f);
    display();
    glFlush();
}
int main(int argc, char *argv[])
{
    glutInit(&argc, argv);   //初始化GLUT
    glutInitDisplayMode(GLUT_RGB | GLUT_SINGLE);
    glutInitWindowPosition(300, 100);
    glutInitWindowSize(window_size, window_size);
    glutCreateWindow("RT");
    InitEnvironment();   //初始化
    glutDisplayFunc(&init_Display);   //回调函数
    glutMainLoop();    //持续显示，当窗口改变会重新绘制图形
    return 0;
}

第二种

//作者：SDU窦志扬
//日期：2018/8/14
//联络：[email protected]
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Regular_triangulation_2.h>
#include <CGAL/Weighted_point_2.h>
#include <CGAL/Polygon_2.h>
#include <GLUT/glut.h>
#include <CGAL/bounding_box.h>
#include <fstream>
#include<iostream>
#include <set>
typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef CGAL::Regular_triangulation_2<K> Regular_triangulation;
typedef K::Vector_2                                     Vector;
typedef K::Point_2 Point;
typedef K::Weighted_point_2 Wp;
typedef K::Point_2                                     Point;
typedef CGAL::Regular_triangulation_2<K>               Rt;
int window_size = 600;
using namespace std;

std::vector<Regular_triangulation::Weighted_point> wpoints;
std::vector<Point> points;

std::set<Point> Point_set;

const int n=100;
const GLfloat Pi=3.1415926536f;
#define MAX_CHAR        128
void MyDisplay(double x,double y ,double R)
{
    glBegin(GL_POLYGON);
    glColor3f(1,0,0);
    R  =sqrt(R);
    for(int i=0;i<n;i++){
        glVertex2f(R*cos(2*Pi/n*i)+x,R*sin(2*Pi/n*i)+y);
    }
    glEnd();
}

void add_point(int x, int y, double w){
    //绘制圆形

    wpoints.push_back( Wp(Point(x,y), w) );
    points.push_back(Point(x,y) );
    Point_set.insert(Point(x,y));
    MyDisplay(x,y,w);
    glPointSize(7);
    glBegin(GL_POINTS);
    glColor3f( 0.0, 1.0, 0.0 );
    glVertex2f( x,y);
    glEnd();
}
void display(void)
{
    add_point(100, 400,10000); //左中
    add_point(200,200,15000);
    add_point(240,310,8000);   //目标点
    add_point(210, 560,20000);
    add_point(340, 80, 12000);
    add_point(560,120, 10000);
    add_point(600, 500,12002);
    add_point(450, 550,8000);

    Regular_triangulation rt(wpoints.begin(), wpoints.end());
    rt.is_valid();
    Regular_triangulation::Finite_edges_iterator eit;
    Regular_triangulation::Point_iterator pit;
    Regular_triangulation::Finite_faces_iterator fit;

    //遍历Delaunay的所有边，绘制Delaunay图的对偶图，即Voronoi图
    glEnable( GL_LINE_STIPPLE );//使用点画模式，即使用虚线来绘制Voronoi图
    glLineStipple( 1, 0x3333 );
    glColor3f( 0.0, 1.0,1.0 );

    cout << "====all points in rt====" << endl;
    for (auto vit = rt.vertices_begin(); vit != rt.vertices_end(); ++vit){
        cout << vit->point() << endl;

    }
    cout << "========" << endl;
    vector<Point> dual_points;

    cout << "====all points in powerdiagram====" << endl;
    //遍历Regular triangulation的所有面
    for( fit = rt.faces_begin(); fit != rt.faces_end(); fit ++)
    {
        dual_points.push_back(rt.dual(fit));
        //在其对偶图中所对应的点
    }
    for (int j = 0; j <dual_points.size() ; ++j) {
        cout << dual_points[j] << endl;
    }
    cout << "========" << endl;


    for( eit = rt.finite_edges_begin(); eit != rt.finite_edges_end(); eit ++)
    {
        cout << eit->second << endl;
//        cout << "processing seg"<< eit->first->vertex(eit->second)->point().point() << endl;
//        cout << "processing seg2"<< eit->first->vertex(0)->point().point() << endl;
        CGAL::Object o = rt.dual(eit);
        //在其对偶图中所对应的边
        set<Point>::iterator it;
        Point a = (eit->first->vertex(0)->point().point() );
        Point b = (eit->first->vertex(1)->point().point() );
        it=Point_set.find(a);    //查找键值为5的元素
        set<Point>::iterator it2;
        it2=Point_set.find(eit->first->vertex(1)->point().point());    //查找键值为5的元素

        if(it!=Point_set.end()&&it2!=Point_set.end()&& (a==Point(240,310)||Point(240,310)==b)){
//            cout << "a" << a<<endl;
//            cout << "b" << b<< endl;
        if (CGAL::object_cast<K::Segment_2>(&o)) //如果这条边是线段，则绘制线段
        {
            glBegin(GL_LINES);
            glVertex2i( CGAL::object_cast<K::Segment_2>(&o)->source().hx(), CGAL::object_cast<K::Segment_2>(&o)->source().hy() );
            glVertex2i( CGAL::object_cast<K::Segment_2>(&o)->target().hx(), CGAL::object_cast<K::Segment_2>(&o)->target().hy() );
            glEnd();
        }

        }
    }
    glDisable( GL_LINE_STIPPLE );//关闭点画模式

    auto box = CGAL::bounding_box(points.begin(), points.end());
    auto center2 = CGAL::ORIGIN + 0.5 * (box.max() - CGAL::ORIGIN) + 0.5 * (box.min() - CGAL::ORIGIN);
    double sideLen = max(box.xmax() - box.xmin(), box.ymax() - box.ymin());
    Point center = CGAL::ORIGIN;
    double maxW = -100000;
    map<Point,int>  fromSite2ID;
    for (int i = 0; i < wpoints.size(); ++i)
    {
        //fromSite2ID是一个点Point到int的map
        //这里对每个点进行标记"i"
        fromSite2ID[wpoints[i].point()] = i;
        center = center + (wpoints[i].point() - CGAL::ORIGIN);
        if (maxW < wpoints[i].weight())
        {//负值越大说明
            maxW = wpoints[i].weight();
        }
    }
    center = CGAL::ORIGIN + (center - CGAL::ORIGIN) / (double)wpoints.size();
    //center计算距离原点的平均偏移量
    vector<Wp> exteriorPoints;
    Wp p1(center + sideLen * Vector(1, 0), maxW);
    exteriorPoints.push_back(p1);
    Wp p2(center + sideLen * Vector(-1, 0), maxW);
    exteriorPoints.push_back(p2);
    Wp p3(center + sideLen * Vector(0, 1), maxW);
    exteriorPoints.push_back(p3);
    Wp p4(center + sideLen * Vector(0,-1), maxW);
    exteriorPoints.push_back(p4);
    //用一个更大的区域包围起来（一定包在里面）
    rt.insert(exteriorPoints.begin(), exteriorPoints.end());
    for (int i = 0; i < exteriorPoints.size(); ++i)
    {
        fromSite2ID[exteriorPoints[i].point()] = -1; //means the extra sites
    }
    //遍历显示
    cout << "====all edges bounding the point====" << endl;
    int con = 0;

    for (Rt::Finite_vertices_iterator siteIt = rt.finite_vertices_begin();
         siteIt != rt.finite_vertices_end(); ++siteIt)
    {
        con++;
        Point site = siteIt->point().point();
//      cout <<"powerdiagram :" << con++<<"--" <<site << endl;
        int curSiteID = fromSite2ID.find(site)->second;//找到点对应的id
        if (curSiteID == -1){
            cout << "这是边界点" << endl;
            continue;
        }
        Rt::Edge_circulator beg = rt.incident_edges(siteIt);
        Rt::Edge_circulator it = beg;
        vector<Point> cell;
        do
        {
            K::Segment_2 s;
            CGAL::Object o = rt.dual(it);
            if (CGAL::assign(s, o))
            {
                cell.push_back(s.source());

            }
        } while (++it != beg);
        glLineWidth(8);
//        glBegin(GL_LINE_LOOP);
//        glLineWidth(20);
//        glColor3f(1,1,1);
//        for (int j = 0; j <cell.size() ; ++j) {
//            if (site == Point(240,310)){
//                glVertex2f(cell[j].x(), cell[j].y());
//                cout << cell[j] << "  ---  " << site << endl;
//            }
//        }
//        glEnd();





    }
}
void InitEnvironment()
{
    //一些初始化操作
    glClearColor(0.0,0.0,0.0,0);
    glClear(GL_COLOR_BUFFER_BIT);
    glPointSize(7);
    glMatrixMode(GL_MODELVIEW);
    glLoadIdentity();
    gluOrtho2D(0,window_size,0,window_size);
}
void init_Display(void)
{
    glClear(GL_COLOR_BUFFER_BIT);
    glColor3f(0.98f, 0.625f, 0.12f);
    display();
    glFlush();
}
int main(int argc, char *argv[])
{
    glutInit(&argc, argv);   //初始化GLUT
    glutInitDisplayMode(GLUT_RGB | GLUT_SINGLE);
    glutInitWindowPosition(300, 100);
    glutInitWindowSize(window_size, window_size);
    glutCreateWindow("RT");
    InitEnvironment();   //初始化
    glutDisplayFunc(&init_Display);   //回调函数
    glutMainLoop();    //持续显示，当窗口改变会重新绘制图形
    return 0;
}

往期实现

CGAL单纯的2D Power diagram样例展示（展示暂时使用openGL）：
CGAL 2D Power diagram
CGAL单纯的2D Voronoi diagram样例展示：
CGAL 2F Voronoi diagram
CGAL单纯的3D Voronoi diagram样例展示：
CGAL 3D Voronoi

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