圖像中某點繞點旋轉后的坐標，圖像旋轉坐標位置

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在平面坐標上，任意點P(x1,y1)，繞一個坐標點Q(x2,y2)旋轉θ角度后,新的坐標設為(x, y)的計算公式：

x= (x1 - x2)*cos(θ) - (y1 - y2)*sin(θ) + x2 ; y= (x1 - x2)*sin(θ) + (y1 - y2)*cos(θ) + y2 ;

這是在平面上的坐標旋轉公式，但在圖像中某個像素點旋轉一個角度后的坐標不能用上述公式直接求出，因為圖像(0,0)點的坐標的原點是在圖像的左上角。

假設圖像的寬度x高度為col x row,圖像中某個像素P(x1,y1)，繞某個像素點Q(x2,y2)旋轉θ角度后,則該像素點的新坐標位置為(x, y)，其計算公式為：

x1 = x1; y1 = row - y1; x2 = x2; y2 = row - y2; x = (x1 - x2)*cos(pi / 180.0 * θ) - (y1 - y2)*sin(pi / 180.0 * θ) + x2; y = (x1 - x2)*sin(pi / 180.0 * θ) + (y1 - y2)*cos(pi / 180.0 * θ) + y2; x=x; y = row - y;

下面給出OpenCV的實現代碼：原圖像的大小500x577，像素點P(100,100)，繞圖像中心Q(250,288.5)旋轉θ角度后,則該像素點的新坐標位置為(173, 60)

? ?關于OpenCV實現圖像旋轉的方法，可參考本人的博客：《OpenCV圖像旋轉,指定填充背景顏色邊界顏色》 http://blog.csdn.net/guyuealian/article/details/77993410

#include "stdafx.h" #include <iostream> #include<vector> #include<algorithm> #include <opencv2\opencv.hpp> #include <opencv2\highgui\highgui.hpp> using namespace std; using namespace cv; #define pi 3.1415926vector<cv::Point2i> getRotatePoint(cv::Mat srcImage, vector<cv::Point2i> Points, const cv::Point rotate_center, const double angle) {vector<cv::Point2i> dstPoints;int x1 = 0, y1 = 0;int row = srcImage.rows;for (size_t i = 0; i < Points.size(); i++){x1 = Points.at(i).x;y1 = row - Points.at(i).y;int x2 = rotate_center.x;int y2 = row - rotate_center.y;int x = cvRound((x1 - x2)*cos(pi / 180.0 * angle) - (y1 - y2)*sin(pi / 180.0 * angle) + x2);int y = cvRound((x1 - x2)*sin(pi / 180.0 * angle) + (y1 - y2)*cos(pi / 180.0 * angle) + y2);y = row - y;dstPoints.push_back(Point2i(x, y));}return dstPoints; }int main() {Mat src = imread("D:\\OpencvTest\\16.jpg");Point2i point(100, 100);vector<cv::Point2i> Points;Points.push_back(point);cv::circle(src, point, 2, cv::Scalar(255, 0, 0),2); cv::imshow("src image ", src);cv::Mat dst; //旋轉角度-20度 double angle =- 20;//輸出圖像的尺寸與原圖一樣 cv::Size dst_sz(src.cols, src.rows);//指定旋轉中心 cv::Point2f center(src.cols / 2., src.rows / 2.);//獲取旋轉矩陣（2x3矩陣） cv::Mat rot_mat = cv::getRotationMatrix2D(center, angle, 1.0);//設置選擇背景邊界顏色：綠色 cv::Scalar borderColor = Scalar(0, 238, 0);cv::warpAffine(src, dst, rot_mat, dst_sz, INTER_LINEAR, BORDER_CONSTANT, borderColor);//cv::warpAffine(src, dst, rot_mat, dst_sz, INTER_LINEAR, BORDER_REPLICATE); vector<cv::Point2i> dstPoints = getRotatePoint(dst, Points, center, angle);cv::circle(dst, dstPoints.at(0), 5, cv::Scalar(0, 0, 255), 2);cv::imshow("Rotation Image", dst);waitKey(0);return 0; }

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python代碼：

def rotate_point(point1, point2, angle, height):"""點point1繞點point2旋轉angle后的點======================================在平面坐標上，任意點P(x1,y1)，繞一個坐標點Q(x2,y2)旋轉θ角度后,新的坐標設為(x, y)的計算公式：x= (x1 - x2)*cos(θ) - (y1 - y2)*sin(θ) + x2 ;y= (x1 - x2)*sin(θ) + (y1 - y2)*cos(θ) + y2 ;======================================將圖像坐標(x,y)轉換到平面坐標(x`,y`)：x`=xy`=height-y:param point1::param point2: base point (基點):param angle: 旋轉角度，正：表示逆時針，負：表示順時針:param height::return:"""x1, y1 = point1x2, y2 = point2# 將圖像坐標轉換到平面坐標y1 = height - y1y2 = height - y2x = (x1 - x2) * np.cos(np.pi / 180.0 * angle) - (y1 - y2) * np.sin(np.pi / 180.0 * angle) + x2y = (x1 - x2) * np.sin(np.pi / 180.0 * angle) + (y1 - y2) * np.cos(np.pi / 180.0 * angle) + y2# 將平面坐標轉換到圖像坐標y = height - yreturn (x, y)

【尊重原創，轉載請注明出處】https://panjinquan.blog.csdn.net/article/details/78288131

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