学习OpenCV3：画出三角形，并计算3个角的大小

﹏ヽ暗。殇╰゛Y 2023-02-22 03:56 12阅读 0赞

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# 一、问题 #

已知三角形的3个顶点`p0`、`p1`和`p2`。现希望画出三角形，并计算3个角的大小。

![format_png_pic_center][]

# 二、分析 #

直线 a a a的直线方程：  
 y − y 1 y 2 − y 1 = x − x 1 x 2 − x 1 ⇒ \{ a x + b y + c = 0 a = − ( y 2 − y 1 ) b = x 2 − x 1 c = ( y 2 − y 1 ) x 1 − ( x 2 − x 1 ) y 1 \\frac\{y-y\_1\}\{y\_2-y\_1\} = \\frac\{x-x\_1\}\{x\_2-x\_1\} \\Rightarrow \\begin\{cases\} ax+by+c=0 \\\\a=-(y\_2-y\_1) \\\\ b = x\_2-x\_1 \\\\ c = (y\_2-y\_1)x\_1 - (x\_2-x\_1) y\_1\\end\{cases\} y2−y1y−y1=x2−x1x−x1⇒⎩⎪⎪⎪⎨⎪⎪⎪⎧ax\+by\+c=0a=−(y2−y1)b=x2−x1c=(y2−y1)x1−(x2−x1)y1

已知3个顶点`p0`、`p1`和`p2`，要构造三角形必须确保3个顶点不在同一直线上，即`p0`不在直线 a a a上：

a * p0.x + b * p0.y + c != 0

三角形各边边长为：

a = ( p 2. x − p 1. x ) 2 + ( p 2. y − p 1. y ) 2 a = \\sqrt\{(p2.x-p1.x)^2+(p2.y-p1.y)^2\} a=(p2.x−p1.x)2\+(p2.y−p1.y)2

b = ( p 2. x − p 0. x ) 2 + ( p 2. y − p 0. y ) 2 b = \\sqrt\{(p2.x-p0.x)^2+(p2.y-p0.y)^2\} b=(p2.x−p0.x)2\+(p2.y−p0.y)2

c = ( p 1. x − p 0. x ) 2 + ( p 1. y − p 0. y ) 2 c = \\sqrt\{(p1.x-p0.x)^2+(p1.y-p0.y)^2\} c=(p1.x−p0.x)2\+(p1.y−p0.y)2

由余弦定理得：  
 a 2 = b 2 + c 2 − 2 b c cos ⁡ θ ⇒ cos ⁡ θ = b 2 + c 2 − a 2 2 b c ⇒ θ = arccos ⁡ ( b 2 + c 2 − a 2 2 b c ) a^2=b^2+c^2-2bc \\cos \\theta \\Rightarrow \\cos \\theta = \\frac\{b^2+c^2-a^2\}\{2bc\} \\Rightarrow \\theta = \\arccos (\\frac\{b^2+c^2-a^2\}\{2bc\}) a2=b2\+c2−2bccosθ⇒cosθ=2bcb2\+c2−a2⇒θ=arccos(2bcb2\+c2−a2)

# 三、实现 #

#include <opencv2/opencv.hpp>
    #include <iostream>
    #include <string>
    #include <cmath>
    using namespace std;
    using namespace cv;
    
    Point2d g_p0(200, 500), g_p1(400, 100), g_p2(600, 500);
    
    // 判断3个点不在同一直线上
    bool same_line(Point2d p0, Point2d p1, Point2d p2)
    {
        double a = -(p2.y - p1.y);
        double b = p2.x - p1.x;
        double c = (p2.y - p1.y) * p1.x - (p2.x - p1.x) * p1.y;
        if (a * p0.x + b * p0.y + c != 0) // p0不在直线p1p2上
            return true;
        else
            return false;
    }
    
    // 计算夹角
    double calculate_angle(Point2d p0, Point2d p1, Point2d p2)
    {
        double a = sqrt(pow(p2.x - p1.x, 2) + pow(p2.y - p1.y, 2));
        double b = sqrt(pow(p2.x - p0.x, 2) + pow(p2.y - p0.y, 2));
        double c = sqrt(pow(p1.x - p0.x, 2) + pow(p1.y - p0.y, 2));
        double angle = acos((b * b + c * c - a * a) / (2 * b * c)) * 180 / CV_PI;
        return angle;
    }
    
    // 画夹角
    void draw_angle(Mat img, Point2d p0, Point2d p1, Point2d p2, double radius, const Scalar color, int thickness)
    {
        // 计算直线的角度
        double angle1 = atan2(-(p1.y - p0.y), (p1.x - p0.x)) * 180 / CV_PI;
        double angle2 = atan2(-(p2.y - p0.y), (p2.x - p0.x)) * 180 / CV_PI;
        // 计算主轴的角度
        double angle = angle1 <= 0 ? -angle1 : 360 - angle1;
        // 计算圆弧的结束角度
        double end_angle = (angle2 < angle1) ? (angle1 - angle2) : (360 - (angle2 - angle1));
        if (end_angle > 180)
        {
            angle = angle2 <= 0 ? -angle2 : 360 - angle2;
            end_angle = 360 - end_angle;
        }
        // 画圆弧
        ellipse(img, p0, Size(radius, radius), angle, 0, end_angle, color, thickness);
    }
    
    // 鼠标回调函数
    void mouse_callback(int event, int x, int y, int flags, void *param)
    {
        static Point2d p(0, 0), p1(0, 0), p2(0, 0);
        static int n = -1;
        switch (event)
        {
        case cv::EVENT_LBUTTONDOWN: // 鼠标左键点击
        {
            p1 = Point2d(x, y);
            int w = 15, h = 15;
            Rect r0(g_p0.x - w, g_p0.y - h, 2 * w, 2 * h);
            Rect r1(g_p1.x - w, g_p1.y - h, 2 * w, 2 * h);
            Rect r2(g_p2.x - w, g_p2.y - h, 2 * w, 2 * h);
            if (r0.contains(p1)) // 鼠标落在中心点g_p0
            {
                n = 0;
                p = g_p0;
            }
            else if (r1.contains(p1)) // 鼠标落在g_p1
            {
                n = 1;
                p = g_p1;
            }
            else if (r2.contains(p1)) // 鼠标落在g_p2
            {
                n = 2;
                p = g_p2;
            }
            break;
        }
        case cv::EVENT_MOUSEMOVE: // 鼠标移动
            p2 = Point2d(x, y);
            if (n == 0)
            {
                g_p0 = p + p2 - p1;
            }
            else if (n == 1)
            {
                g_p1 = p + p2 - p1;
            }
            else if (n == 2)
            {
                g_p2 = p + p2 - p1;
            }
            break;
        case cv::EVENT_LBUTTONUP: // 鼠标左键释放
            p1 = Point2d(0, 0);
            p2 = Point2d(0, 0);
            n = -1;
            break;
        default:
            break;
        }
    }
    
    // 主函数
    int main()
    {
        string window_name = "image";
        namedWindow(window_name, WINDOW_AUTOSIZE);
        int w = 800, h = 600;
        Mat image_original = Mat(h, w, CV_8UC3, Scalar(255, 255, 255));
        cv::setMouseCallback(window_name, mouse_callback); // 调用鼠标回调函数
        while (true)
        {
            Mat img = image_original.clone(); // 拷贝空白图片，方便重复画图
    
            line(img, g_p1, g_p2, Scalar(255, 0, 0), 2); // 画蓝线a
            line(img, g_p2, g_p0, Scalar(0, 255, 0), 2); // 画绿线b
            line(img, g_p1, g_p0, Scalar(0, 0, 255), 2); // 画红线c
    
            if (same_line(g_p0, g_p1, g_p2)) // 3个点不在同一条直线上
            {
                draw_angle(img, g_p0, g_p1, g_p2, 15, Scalar(255, 0, 0), 2); // 画蓝色夹角
                double b = calculate_angle(g_p0, g_p1, g_p2);
                string s2 = "p0: (" + to_string(g_p1.x) + ", " + to_string(g_p1.y) + ") " + to_string(b);
                putText(img, s2, Point2d(10, 25), cv::FONT_HERSHEY_COMPLEX, 0.5, Scalar(255, 0, 0));
    
                draw_angle(img, g_p1, g_p2, g_p0, 15, Scalar(0, 255, 0), 2); // 画绿色夹角
                double c = calculate_angle(g_p1, g_p2, g_p0);
                string s3 = "p1: (" + to_string(g_p2.x) + ", " + to_string(g_p2.y) + ") " + to_string(c);
                putText(img, s3, Point2d(10, 50), cv::FONT_HERSHEY_COMPLEX, 0.5, Scalar(0, 255, 0));
    
                draw_angle(img, g_p2, g_p0, g_p1, 15, Scalar(0, 0, 255), 2); // 画红色夹角
                double a = calculate_angle(g_p2, g_p0, g_p1);
                string s1 = "p2: (" + to_string(g_p0.x) + ", " + to_string(g_p0.y) + ") " + to_string(a);
                putText(img, s1, Point2d(10, 75), cv::FONT_HERSHEY_COMPLEX, 0.5, Scalar(0, 0, 255));
            }
            else
            {
                putText(img, "error", Point2d(10, 25), cv::FONT_HERSHEY_COMPLEX, 0.5, Scalar(0, 0, 255), 1);
            }
    
            imshow(window_name, img);
            if (waitKey(3) > 0)
                break;
        }
        return 0;
    }

**操作方法：**  
  鼠标左键点击三角形任意一个顶点并按住移动，由此可修改三角形。在键盘输入任意的键，可退出程序。

**运行结果：**

![format_png_pic_center 1][]

![format_png_pic_center 2][]

![format_png_pic_center 3][]

![format_png_pic_center 4][]

[format_png_pic_center]: https://imgconvert.csdnimg.cn/aHR0cHM6Ly91cGxvYWQtaW1hZ2VzLmppYW5zaHUuaW8vdXBsb2FkX2ltYWdlcy8yMDMwMzQzNC03ODUyMTBkM2Q2YmZmYTRlLnBuZw?x-oss-process=image/format,png#pic_center
[format_png_pic_center 1]: https://imgconvert.csdnimg.cn/aHR0cHM6Ly91cGxvYWQtaW1hZ2VzLmppYW5zaHUuaW8vdXBsb2FkX2ltYWdlcy8yMDMwMzQzNC1lMGI0Njg2ZmI2NmRiMWY1LnBuZw?x-oss-process=image/format,png#pic_center
[format_png_pic_center 2]: https://imgconvert.csdnimg.cn/aHR0cHM6Ly91cGxvYWQtaW1hZ2VzLmppYW5zaHUuaW8vdXBsb2FkX2ltYWdlcy8yMDMwMzQzNC1mYmI5ZGU4NmVkZDI4YTQwLnBuZw?x-oss-process=image/format,png#pic_center
[format_png_pic_center 3]: https://imgconvert.csdnimg.cn/aHR0cHM6Ly91cGxvYWQtaW1hZ2VzLmppYW5zaHUuaW8vdXBsb2FkX2ltYWdlcy8yMDMwMzQzNC0xOGZhN2EyMjI4OTY3NDhlLnBuZw?x-oss-process=image/format,png#pic_center
[format_png_pic_center 4]: https://imgconvert.csdnimg.cn/aHR0cHM6Ly91cGxvYWQtaW1hZ2VzLmppYW5zaHUuaW8vdXBsb2FkX2ltYWdlcy8yMDMwMzQzNC01NGMxNWRhNGNjNjUyMjc5LnBuZw?x-oss-process=image/format,png#pic_center