OpenCV : algorithm for simple image rotation and reduction - c++

Question

I have tried image rotation and reduction(JPEG) with getRotationMatrix2D(center, angle, scale);
and warpAffine(image1, image3, rotation, image3.size());
I got the result I wanted(image as below)
for (int r = 0;r < image1.rows;r++) {
for (int c = r + 1;c < image1.cols;c++) {
Point center = Point(image1.cols / 2, image1.rows / 2);
Point center1 = Point(image1.cols / 2, image1.rows / 2);
double angle = 90.0;
double scale = 1;
double angle1 = 90.0;
double scale1 = 0.5;
rotation = getRotationMatrix2D(center, angle, scale);
rotation1 = getRotationMatrix2D(center1, angle1, scale1);
but I want to learn some simple rotation and reduction algorithm ( simple for beginner like me ) without using any library
to get the same result.
After searching for various solutions, i ended up with this
from https://gamedev.stackexchange.com/questions/67613/how-can-i-rotate-a-bitmap-without-d3d-or-opengl
Can anyone break up bit by bit of the simple linear algebra to explain to me in regards to my pesudo code?
EDIT:
Reduction code
void reduction(Mat image1)
{
for (int r = 0;r < imgC.rows;r++)
{
for (int c = 0;c < imgC.cols;c++)
{
int new_x = c * (125 / 256);
int new_y = r * (125 / 256);
imgC.at<uchar>(r, c) = imgC.at<uchar>(new_y, new_x);
}
}
}

Answer 1

In this example I have loaded two images. One is in gray scale and other is color image. Both are same image so you can understand easily how to handle rotation with mathematical equation. Please see this example which is very easy to understand. Also in the similar manner you can add scaling and reduction. Here each point is converted according to the equation and color value set on new location. Here is the code:
#include <iostream>
#include <string>
#include "opencv/highgui.h"
#include "opencv2/imgproc/imgproc.hpp"
#include "opencv2/objdetect/objdetect.hpp"
using namespace std;
using namespace cv;
#define PIPI 3.14156
int main()
{
Mat img = imread("C:/Users/dell2/Desktop/DSC00587.JPG",0);//loading gray scale image
Mat imgC = imread("C:/Users/dell2/Desktop/DSC00587.JPG",1);//loading color image
Mat rotC(imgC.cols, imgC.rows, imgC.type());
rotC = Scalar(0,0,0);
Mat rotG(img.cols, img.rows, img.type());
rotG = Scalar(0,0,0);
float angle = 90.0 * PIPI / 180.0;
for(int r=0;r<imgC.rows;r++)
{
for(int c=0;c<imgC.cols;c++)
{
float new_px = c * cos(angle) - r * sin(angle);
float new_py = c * sin(angle) + r * cos(angle);
Point pt((int)-new_px, (int)new_py);
//color image
rotC.at<Vec3b>(pt) = imgC.at<Vec3b>(r,c);//assign color value at new location from original image
//gray scale image
rotG.at<uchar>(pt) = img.at<uchar>(r,c);//assign color value at new location from original image
}
}
imshow("color",rotC);
imshow("gray",rotG);
waitKey(0);
return 0;
}