opencv 旋转 点旋转 以及 逆旋转

#include"opencv2/highgui/highgui.hpp"
#include"opencv2/imgproc/imgproc.hpp"
#include <iostream>
using namespace std;

using namespace cv;



void CalcRotateMatrix(const cv::Mat& img, float degree, cv::Mat& trans_mat, cv::Size& dst_size){
    degree = fmod(degree + 360.0f, 360.0f);
    double angle = degree  * CV_PI / 180.;
    int width = img.cols;
    int height = img.rows;
    double a = sin(angle), b = cos(angle);
    int widthRotate = int(height * fabs(a) + width * fabs(b));
    int heightRotate = int(width * fabs(a) + height * fabs(b));
    
    //    int widthRotate = width;
    //    int heightRotate = height;
    
    // [ m0  m1  m2 ] ===>  [ A11  A12   b1 ]
    // [ m3  m4  m5 ] ===>  [ A21  A22   b2 ]
    trans_mat.create(2, 3, CV_32F);
    float *map = (float *)trans_mat.ptr<float>();
    
    CvPoint2D32f center = cvPoint2D32f(width / 2.0f, height / 2.0f);
    CvMat mapMatrix = trans_mat;
    cv2DRotationMatrix(center, degree, 1.0f, &mapMatrix);
    map[2] += (widthRotate - width) / 2.0f;
    map[5] += (heightRotate - height) / 2.0f;
    
    dst_size = cv::Size(widthRotate, heightRotate);
}

std::vector<cv::Point> PointAffine(const std::vector<cv::Point>& points, const cv::Mat& trans_mat){
    float *m = (float *)trans_mat.ptr<float>();
    vector<Point> transPoints;
    for(size_t i = 0; i < points.size(); i++)
    {
        Point p = points[i];
        int x = p.x * m[0] + p.y * m[1] + m[2];
        int y = p.x * m[3] + p.y * m[4] + m[5];
        transPoints.push_back(Point(x, y));
    }
    return transPoints;
}



int main()
{
    Mat img = imread("/data_2/everyday/1228/plane.png");
    Point pt(285,67);
    circle(img,pt,13,Scalar(0,0,255),2);
    
    float angle = 32.5;
    
    
    Mat M;
    Mat img_rot, img_roi;
    Size dst_size;
    vector<Point> rot_points;
    
    CalcRotateMatrix(img, angle, M, dst_size);
    warpAffine(img, img_rot, M, dst_size, 1, 0, 0);
    
    
    std::vector<cv::Point> points,points_rot;
    points.push_back(pt);
    points_rot = PointAffine(points, M);
    Point pt_rot = points_rot[0];
    circle(img_rot,pt_rot,13,Scalar(255,0,255),2);
        
    imshow("img",img);
    imshow("img_rot",img_rot);
    waitKey(0);

    return 0;
}

通过旋转角度可以求得旋转矩阵，然后原图中的一个点通过旋转矩阵可以对应到旋转之后的图。但是问题来了，已知旋转矩阵，旋转后的图上的一个点，能对应到原图上面去吗？？？

经过分析原图上面点通过防射变换矩阵旋转到旋转之后的图上，这段代码如下：

 Point p = points[i];
        int x = p.x * m[0] + p.y * m[1] + m[2];
        int y = p.x * m[3] + p.y * m[4] + m[5];

我们现在是已知旋转矩阵，旋转后的图上的一个点，即x，y已知，所有m已知，要求的是p.x，p.y，二元一次方程组可以求出来。所以代码如下：

    float *m = (float *)M.ptr<float>();
    int xx = (m[4]*pt_rot.x-m[2]*m[4]-m[1]*pt_rot.y+m[1]*m[5])*1.0/MAX((m[0]*m[4]-m[1]*m[3]),0.01);
    int yy = (pt_rot.y-m[5]-m[3]*xx)*1.0/MAX(m[4],0.01);

#include"opencv2/highgui/highgui.hpp"
#include"opencv2/imgproc/imgproc.hpp"
#include <iostream>
using namespace std;
using namespace cv;

void CalcRotateMatrix(const cv::Mat& img, float degree, cv::Mat& trans_mat, cv::Size& dst_size){
    degree = fmod(degree + 360.0f, 360.0f);
    double angle = degree  * CV_PI / 180.;
    int width = img.cols;
    int height = img.rows;
    double a = sin(angle), b = cos(angle);
    int widthRotate = int(height * fabs(a) + width * fabs(b));
    int heightRotate = int(width * fabs(a) + height * fabs(b));

    //    int widthRotate = width;
    //    int heightRotate = height;

    // [ m0  m1  m2 ] ===>  [ A11  A12   b1 ]
    // [ m3  m4  m5 ] ===>  [ A21  A22   b2 ]
    trans_mat.create(2, 3, CV_32F);
    float *map = (float *)trans_mat.ptr<float>();

    CvPoint2D32f center = cvPoint2D32f(width / 2.0f, height / 2.0f);
    CvMat mapMatrix = trans_mat;
    cv2DRotationMatrix(center, degree, 1.0f, &mapMatrix);
    map[2] += (widthRotate - width) / 2.0f;
    map[5] += (heightRotate - height) / 2.0f;

    dst_size = cv::Size(widthRotate, heightRotate);
}

std::vector<cv::Point> PointAffine(const std::vector<cv::Point>& points, const cv::Mat& trans_mat){
    float *m = (float *)trans_mat.ptr<float>();
    vector<Point> transPoints;
    for(size_t i = 0; i < points.size(); i++)
    {
        Point p = points[i];
        int x = p.x * m[0] + p.y * m[1] + m[2];
        int y = p.x * m[3] + p.y * m[4] + m[5];
        transPoints.push_back(Point(x, y));
    }
    return transPoints;
}

int main()
{
    Mat img = imread("/data_2/everyday/1228/plane.png");
    Point pt(285,67);
    circle(img,pt,13,Scalar(0,0,255),2);

    float angle = 32.5;


    Mat M;
    Mat img_rot, img_roi;
    Size dst_size;
    vector<Point> rot_points;

    CalcRotateMatrix(img, angle, M, dst_size);
    warpAffine(img, img_rot, M, dst_size, 1, 0, 0);


    std::vector<cv::Point> points,points_rot;
    points.push_back(pt);
    points_rot = PointAffine(points, M);
    Point pt_rot = points_rot[0];
    circle(img_rot,pt_rot,13,Scalar(255,0,255),2);


    float *m = (float *)M.ptr<float>();
    int xx = (m[4]*pt_rot.x-m[2]*m[4]-m[1]*pt_rot.y+m[1]*m[5])*1.0/MAX((m[0]*m[4]-m[1]*m[3]),0.01);
    int yy = (pt_rot.y-m[5]-m[3]*xx)*1.0/MAX(m[4],0.01);

    circle(img,Point(xx,yy),33,Scalar(255,0,0),2);

    imshow("img",img);
    imshow("img_rot",img_rot);
    waitKey(0);

    return 0;
}