一飞崖、問題

? ? 已知三角形的3個(gè)點(diǎn)p0烂叔、p1和p2」掏幔現(xiàn)希望畫出三角形，并計(jì)算3個(gè)角度的大小逢防。

二、分析

? ? 直線的直線方程：

? ? 已知3個(gè)點(diǎn)p0灰署、p1和p2辜伟，要構(gòu)造三角形必須確保3個(gè)點(diǎn)不在同一直線上，即p0不在直線上：

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

? ?三角形各邊邊長(zhǎng)為：

??由余弦定理得：

三、實(shí)現(xiàn)

#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);

// 判斷3個(gè)點(diǎn)不在同一直線上
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不在直線p1p2上
        return true;
    else
        return false;
}

// 計(jì)算夾角
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;
}

// 畫夾角
void draw_angle(Mat img, Point2d p0, Point2d p1, Point2d p2, double radius, const Scalar color, int thickness)
{
    // 計(jì)算直線的角度
    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;
    // 計(jì)算主軸的角度
    double angle = angle1 <= 0 ? -angle1 : 360 - angle1;
    // 計(jì)算圓弧的結(jié)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;
    }
    // 畫圓弧
    ellipse(img, p0, Size(radius, radius), angle, 0, end_angle, color, thickness);
}

// 鼠標(biāo)回調(diào)函數(shù)
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: // 鼠標(biāo)左鍵點(diǎn)擊
    {
        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)) // 鼠標(biāo)落在中心點(diǎn)g_p0
        {
            n = 0;
            p = g_p0;
        }
        else if (r1.contains(p1)) // 鼠標(biāo)落在g_p1
        {
            n = 1;
            p = g_p1;
        }
        else if (r2.contains(p1)) // 鼠標(biāo)落在g_p2
        {
            n = 2;
            p = g_p2;
        }
        break;
    }
    case cv::EVENT_MOUSEMOVE: // 鼠標(biāo)移動(dòng)
        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: // 鼠標(biāo)左鍵釋放
        p1 = Point2d(0, 0);
        p2 = Point2d(0, 0);
        n = -1;
        break;
    default:
        break;
    }
}

// 主函數(shù)
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); // 調(diào)用鼠標(biāo)回調(diào)函數(shù)
    while (true)
    {
        Mat img = image_original.clone(); // 拷貝空白圖片踩麦，方便重復(fù)畫圖

        line(img, g_p1, g_p2, Scalar(255, 0, 0), 2); // 畫藍(lán)線a
        line(img, g_p2, g_p0, Scalar(0, 255, 0), 2); // 畫綠線b
        line(img, g_p1, g_p0, Scalar(0, 0, 255), 2); // 畫紅線c

        if (same_line(g_p0, g_p1, g_p2)) // 3個(gè)點(diǎn)不在同一條直線上
        {
            draw_angle(img, g_p0, g_p1, g_p2, 15, Scalar(255, 0, 0), 2); // 畫藍(lán)色夾角
            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); // 畫綠色夾角
            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); // 畫紅色夾角
            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：
??鼠標(biāo)左鍵點(diǎn)擊三角形任意一個(gè)頂線并按住移動(dòng)谓谦，由此可修改三角形贫橙。在鍵盤輸入任意的鍵反粥，可退出程序。

運(yùn)行結(jié)果：