Opencv C++ Code for Rotating an Image with the help of a Trackbar

This OpenCV tutorial is about rotating an Image about its centre by varying the slider position on the Trackbar.
Refer the Opencv C++ Code below:

// OpenCV C++ Tutorial of Rotating an Image with the help of Trackbar
#include <opencv2/core/core.hpp> 
#include <opencv2/highgui/highgui.hpp> 
#include <iostream>

using namespace cv;
using namespace std;

//Global Variables
const int rotation_slider_max=360;
const float pi=3.14;
float x,y;
int slider_value=0;

/// Matrices to store images
Mat src1,src2;

void on_trackbar( int, void* )
{
 src2 = Mat::zeros(src1.rows,src1.cols, CV_8UC3);
 for (float i=0; i<src1.cols ; i++){
 for (float j=0 ; j<src1.rows ; j++)
 {
   x=((i-src1.cols/2)*cos(slider_value*pi/180)-(j-src1.rows/2)*sin(slider_value*pi/180)+src1.cols/2);
   y=((i-src1.cols/2)*sin(slider_value*pi/180)+(j-src1.rows/2)*cos(slider_value*pi/180)+src1.rows/2);

   if((x>=0 && x<src1.cols) && (y>=0 && y<src1.rows)){
        Vec3b color1 = src1.at<Vec3b>(Point(i,j));
        Vec3b color2 = src2.at<Vec3b>(Point(i,j));
      color2.val[0] = color1.val[0];
      color2.val[1] = color1.val[1];
      color2.val[2] = color1.val[2];
      src2.at<Vec3b>(Point(x,y)) = color2;
   }
    }
 }
 imshow("Rotated Image", src2); 
}

int main()
{
 src1 = imread("C:\\Users\\arjun\\Desktop\\opencv-logo.png",CV_LOAD_IMAGE_COLOR);
 if( !src1.data ) { printf("Error loading src1 \n"); return -1;}

 namedWindow("Rotated Image",CV_WINDOW_AUTOSIZE); 
    namedWindow("Original Image",CV_WINDOW_AUTOSIZE); 
    imshow("Original Image", src1);

 createTrackbar( "Rotation", "Rotated Image", &slider_value, rotation_slider_max, on_trackbar );
 on_trackbar( slider_value, 0 );
 waitKey(0);
 return 0;
}

Opencv C++ Code for Image Rotation

This Opencv C++ tutorial is about rotating an Image about its centre without using the warpAffine function.
Consider the Figure below:
Point A is rotated from an angle ϴ to an angle ϴ'.

Hence,
x=rCos(ϴ) & y=rSin(ϴ)
And
x'=rCos(ϴ+ϴ') & y'=rSin(ϴ+ϴ')
Thus,
x'=rCos(ϴ)Cos(ϴ')-rSin(ϴ)Sin(ϴ')
x'=xCos(ϴ')-ySin(ϴ')

y'=rSin(ϴ)Cos(ϴ')+rCos(ϴ)Sin(ϴ')
y'=yCos(ϴ')+xSin(ϴ')
Thus,
x'=xCos(ϴ')-ySin(ϴ')
y'=yCos(ϴ')+xSin(ϴ')

This is the matrix obtained when we want to rotate an Image about Origin. If we want to rotate an Image about any other point say(p,q), Then the equation would be,
x'=(x-p)Cos(ϴ')-(y-q)Sin(ϴ')+p
y'=(y-q)Cos(ϴ')+(x-p)Sin(ϴ')+q
Hence the Matrix would be,

Here is the Opencv C++ Example of image rotation about its centre:

// OpenCV Code of rotating an image about its Centre 
#include <opencv2/core/core.hpp> 
#include <opencv2/highgui/highgui.hpp> 
#include <iostream>

using namespace cv;
using namespace std;

int main()
{
 const float pi=3.14;
 int x,y;
 Mat src1,src2;

 //Take the Input Image in src1
 src1 = imread("C:\\Users\\arjun\\Desktop\\opencv-logo.png",CV_LOAD_IMAGE_COLOR);
 if( !src1.data ) { printf("Error loading src1 \n"); return -1;}

 src2 = Mat::zeros(src1.rows,src1.cols, CV_8UC3);

 //Angle by which to rotate an Image
 for (int a=0 ; a<360 ; a++)
 {
 //Logic of Image Rotation
 for (float i=0; i<src1.cols ; i++){
 for (float j=0 ; j<src1.rows ; j++)
 {
   //x'=(x-p)Cos(ϴ')-(y-q)Sin(ϴ')+p
   x=((i-src1.cols/2)*cos(a*pi/180)-(j-src1.rows/2)*sin(a*pi/180)+src1.cols/2);
   //y'=(y-q)Cos(ϴ')+(x-p)Sin(ϴ')+q
   y=((i-src1.cols/2)*sin(a*pi/180)+(j-src1.rows/2)*cos(a*pi/180)+src1.rows/2);

   if((x>=0 && x<src1.cols) && (y>=0 && y<src1.rows)){
  Vec3b color1 = src1.at<Vec3b>(Point(i,j));
  Vec3b color2 = src2.at<Vec3b>(Point(i,j));
  color2.val[0] = color1.val[0];
  color2.val[1] = color1.val[1];
  color2.val[2] = color1.val[2];
  src2.at<Vec3b>(Point(x,y)) = color2;
   }
    }
 }
waitKey(50);
namedWindow("Rotated Image",CV_WINDOW_AUTOSIZE); 
imshow("Rotated Image", src2); 
namedWindow("Original Image",CV_WINDOW_AUTOSIZE); 
imshow("Original Image", src1);

 }
 waitKey(0);
 return 0;
}