Question

我试图实现算法来获取给定点集的凸包，并使用opencv在c ++上使用以下代码可视化结果：

#include "opencv2/opencv.hpp"
#include "StdAfx.h"
#include <vector>
#include <cv.h>
#include <cv.hpp>
#include <cxcore.h>
#include <highgui.h>
#include <iostream>
#include <utility>
#include <math.h>
#include <time.h>  
#include <algorithm>
#include <stack>
using namespace std; 
using namespace cv;

vector<pair<int,int> > testPoints;
pair<int , int> pivot;
stack< pair<int , int> > hull;
const int frameSize=600;
const double PI = 3.141592653589793238462;
vector< pair <int,int> > points;
Mat img=Mat::zeros(frameSize,frameSize, CV_8UC1);

void drawFilledCircle( Mat img, Point center ,int radius)
{
 int thickness = -1;
 int lineType = 8;

 circle( img,
     center,
     radius,
     255,
     thickness,
     lineType );
}

void drawLine( Mat img, Point start, Point end ,int shade,int thickness)
{
  int lineType = 8;
  shade=shade%256;
  line( img,
    start,
    end,
    shade,
    thickness,
    lineType );
}

float getAngle(pair<int,int> p1 , pair<int,int>p2){
     return atan2(static_cast<double>(p1.second-p2.second) , static_cast<double>       (p1.first-p2.first))*180/PI;
}

bool compareFunction(pair<int,int> p1 , pair<int,int> p2){
    return ( getAngle(p1,pivot)>getAngle(p2,pivot) );
}

void printPoints(vector< pair<int,int> > points){
    for(int i=0;i<points.size();i++)
            cout<<"( "<<(points[i].first-frameSize/2)<<" , "<<(points[i].second-    frameSize/2)<<" )  "<<getAngle(points[i],pivot)<<endl;
     cout<<endl;
}

void mouseEvent(int evt, int x, int y, int flags, void* param){
    if(evt==CV_EVENT_LBUTTONDOWN){
        cout<<"Click at : ( "<<(x-frameSize/2)<<" , "<<(y-frameSize/2)<<" ) , Polar Angle: "<<getAngle(make_pair(x,y),pivot)<<endl;
    }
}

void setUpFrame(){
    int n;
    cout<<"Enter number of points: ";
    cin>>n;

    for(int i=0;i<n;i++)
        points.push_back(make_pair((rand()%static_cast<int>(frameSize*0.75)     +frameSize*0.125) , (rand()%static_cast<int>(frameSize*0.75)  +frameSize*0.125)));

    for(int i=0;i<n;i++)
        drawFilledCircle( img, Point(points[i].first, points[i].second) ,2);
    drawLine(img , Point(frameSize/2,0) , Point(frameSize/2,frameSize),100,1);
    drawLine(img , Point(0,frameSize/2) , Point(frameSize,frameSize/2),100,1);

    cout<<"Settingup frame...\nPress enter to continue."<<endl;
}

void setPivot(){
    int max=-2*frameSize , index=0;
    for(int i=0;i<points.size();i++){
        if(points[i].second>max){
            max=points[i].second;
            index=i;
        }
    }
    pivot=points[index];
    points.erase(points.begin()+index);

    drawFilledCircle( img, Point(pivot.first, pivot.second) ,6);
    cout<<"Pivot chosen at: ( "<<(pivot.first-frameSize/2)<<" , "<<(pivot.second-    frameSize/2)<<" )\nPress enter to continue."<<endl;
}

void sortPoints(){
    cout<<"Sorting points on the basis of polar angles."<<endl;
    std::sort(points.begin(),points.end(),compareFunction);
}

void createHull(){
    pair<int,int> previous,next;
    for(int i=0;i<points.size();i++){
        previous= (hull.size()==0) ? pivot : hull.top();
        next= (i==points.size()-1) ? pivot : points[i+1];

        int x1=(previous.first-points[i].first);
        int x2=(points[i].first-next.first);
        int y1=(previous.second-points[i].second);
        int y2=(points[i].second-next.second);

        if( x1*y2-x2*y1 <0 ) 
                hull.push(points[i]);
        drawFilledCircle( img, Point(hull.top().first, hull.top().second) ,4);
    }

    int size=hull.size();
    pair<int,int> pt;

 drawLine(img,Point(pivot.first,pivot.second),Point(hull.top().first,hull.top().second),200,1);
    for(int i=1;i<size;i++){
        pt=hull.top();
        hull.pop();
        drawLine(img,Point(pt.first,pt.second),Point(hull.top().first,hull.top().second),200,1);
    }
    drawLine(img,Point(pivot.first,pivot.second),Point(hull.top().first,hull.top().second),200,    1);
}

int main(int, char**)
{
    srand (time(NULL));
    namedWindow("Output",1);
    cvSetMouseCallback("Output", mouseEvent, 0);

    setUpFrame();
    setPivot();
    sortPoints();
    createHull();

    imshow("Output", img);
    waitKey(0);
    return 0;
}

我知道有内置的库可以做到这一点，但我想自己实现这个算法。当点数较少时，事情看起来效果很好，例如30点，但随着点数的增加，我开始得到一个奇怪的形状（如下面显示的200和1000）。该算法似乎选择了与枢轴点对角相对的那些额外点（不应包括在船体中的点）（由具有最大半径的实心圆圈表示）。任何人都可以帮我弄清楚我哪里出错或建议我可以在代码中进行一些修改吗？ enter image description here

enter image description here

Answer 1

看起来你想要实施格雷厄姆的扫描，但你没有成功。

格雷厄姆的扫描结构如下：

Find the bottom-most point, then sort the points clockwise around it.
Set hull to the first two points.
For each point, say p, from the third onward:
  While you make a left turn from the last edge of hull to the line from hull.back to p:
    popback(hull);
  push(hull, p)

注意初始化的差异 - 格雷厄姆的扫描以边缘开始，而你从没有点开始。

还要注意循环内部的差异 - 您使用左转标准作为某种拒绝测试，涉及来自points的另一个点，而Graham的扫描使用新点来移除不再存在的点船体的一部分。

凸包算法的意外行为

1 个答案: