#include <opencv2/opencv.hpp>  
#include <vector>  
  
using namespace cv;  
using namespace std;  
  
// 计算向量叉积  
int crossProduct(Point a, Point b, Point c) {  
    Point v1 = {b.x - a.x, b.y - a.y};  
    Point v2 = {c.x - b.x, c.y - b.y};  
    return v1.x * v2.y - v1.y * v2.x;  
}  
  
// 判断角点类型  
void detectCornerType(const vector<Point>& points) {  
    int n = points.size();  
    for (int i = 0; i < n; i++) {  
        int prev = (i > 0) ? i - 1 : n - 1;  
        int next = (i < n - 1) ? i + 1 : 0;  
          
        int cp = crossProduct(points[prev], points[i], points[next]);  
        if (cp > 0) {  
            cout << "内角点 at: " << points[i] << endl;  
        } else if (cp < 0) {  
            cout << "外角点 at: " << points[i] << endl;  
        } else {  
            cout << "直线点或平角点 at: " << points[i] << endl;  
        }  
    }  
}  
  
int main() {  
    // 加载图像  
    Mat img = imread("path_to_image");      
    // 转换为灰度图  
    Mat gray;  
    cvtColor(img, gray, COLOR_BGR2GRAY);        
    // 二值化  
    Mat binary;  
    threshold(gray, binary, 100, 255, THRESH_BINARY);        
    // 查找轮廓  
    vector<vector<Point>> contours;  
    findContours(binary, contours, RETR_EXTERNAL, CHAIN_APPROX_SIMPLE);        
    // 近似多边形  
    vector<Point> approx;  
    approxPolyDP(contours[0], approx, arcLength(contours[0], true) * 0.02, true);        
    // 判断角点类型  
    detectCornerType(approx);       
    return 0;  
}