c++如何計(jì)算矩形重疊面積

#include <iostream>
#include <opencv2/opencv.hpp>

using namespace std;
using namespace cv;

int main()
{
  // 1. 新建一個(gè)畫布，把矩形畫在畫布上, 注意，矩形一定要在畫布里面，不能在畫布外面或者邊上
  Mat canvaCaluateRectangleOverlap(100, 100, CV_8UC1, Scalar(0, 0, 0));

  // 2. 把兩個(gè)矩形都畫在畫布上
  Rect rect1 = Rect(10, 10, 20, 20);
  Rect rect2 = Rect(20, 20, 20, 30);
  //為了使用fillPoly填充畫布需要生成Point
  Point rect1Point[1][4];
  rect1Point[0][0] = Point(rect1.x, rect1.y);
  rect1Point[0][1] = Point(rect1.x + rect1.width, rect1.y);
  rect1Point[0][2] = Point(rect1.x + rect1.width, rect1.y + rect1.height);
  rect1Point[0][3] = Point(rect1.x, rect1.y + rect1.height);

  // 以下是用輪廓法計(jì)算矩形面積的方法，可以看看，但是實(shí)際使用當(dāng)然還是 width*height
  //vector<Point> rect1Contours;
  //rect1Contours.push_back(Point(10, 10));
  //rect1Contours.push_back(Point(30, 10));
  //rect1Contours.push_back(Point(30, 30));
  //rect1Contours.push_back(Point(10, 30));
  //int rect1ContourArea = contourArea(rect1Contours);
  //cout << "rect1ContourArea : " << rect1ContourArea << endl;

  const Point* pointConst1[1] = { rect1Point[0] };
  int npt[] = { 4 };
  fillPoly(canvaCaluateRectangleOverlap, pointConst1, npt, 1, Scalar(255, 255, 255));

  Point rect2Point[1][4];
  rect2Point[0][0] = Point(rect2.x, rect2.y);
  rect2Point[0][1] = Point(rect2.x + rect2.width, rect2.y);
  rect2Point[0][2] = Point(rect2.x + rect2.width, rect2.y + rect2.height);
  rect2Point[0][3] = Point(rect2.x, rect2.y + rect2.height);
  const Point* pointConst2[1] = { rect2Point[0] };
  fillPoly(canvaCaluateRectangleOverlap, pointConst2, npt, 1, Scalar(255, 255, 255));

  // 3. 找出畫布的輪廓
  vector<vector<Point> > canvaContours;
  vector<Vec4i> hierarchy;
  findContours(canvaCaluateRectangleOverlap, canvaContours, hierarchy, RETR_EXTERNAL, CHAIN_APPROX_SIMPLE, Point(0, 0));

  // 修正結(jié)果的偏移量，會(huì)差1個(gè)或0個(gè)像素，這里不考慮這個(gè)，大家有時(shí)間可以列舉出每種情況計(jì)算出來
  int offset = 0;
  // 4. 對(duì)畫布輪廓進(jìn)行判斷 （如果輪廓數(shù)等于1并且這兩個(gè)矩形不是相鄰就可以證明矩形是相交的）
  if (canvaContours.size() == 1 && rect1.x+rect1.width != rect2.x && rect2.x+rect2.width != rect1.x && rect1.y+rect1.height != rect2.y && rect2.y+rect2.height != rect1.y)
  {
    // 當(dāng)矩形相交時(shí)，用計(jì)算輪廓面積的方法計(jì)算出相交多邊形的面積（注意，這邊會(huì)差0個(gè)或1個(gè)偏移量，所以本方式最適合計(jì)算重疊率，一個(gè)近似的數(shù)）
    int canvaContourArea = contourArea(canvaContours[0]) + offset;
    // 重疊的面積數(shù) = 兩個(gè)矩形面積的交集 - 兩個(gè)矩形面積的并集 （要理解這個(gè)，好好去畫圖你就明白了）
    int rectangleOveralpArea = rect1.width * rect1.height + rect2.width * rect2.height - canvaContourArea;
    cout << "The two rectangles are overlapping. " << endl;
    cout << "retangleOverlapArea = " << rectangleOveralpArea << endl;
  }
  else {
    cout << "The two rectangles do not overlap. " << endl;
  }
  return 0;
}