90度C ++旋转矩阵/图像的公式

Question

Let's say I have image, which I need to rotate 90 degrees in any direction and I just can't understand how to do that clear. I need to work with matrix, where Width - it's X, and Height - it's Y. I've already done rotating an image 180 degrees, but can't figure out 90 degrees.

Here are the examples. Let's say I have an image 3x4 pixels. Width = 3, Height = 4, the amount of data in each cell - N = Width * Height = 3 * 4 = 12 . Let's make the matrix:

The formula to easily go through the matrix is y*Width + x . And the formula for our rotating 180 degrees is:

N - Width + x - y * Width

So we have:

DataOut [y * Width + x] = DataIn [N - Width + x - y * Width]

Using this formula we get:

But I can't come up with the formula of rotating 90 degrees. Can you help me, please?

Answer 1

you can simply rotate the matrix by this:

for(int i=0; i<cols; i++)
{
    for(int j=1; j<=rows; j++)
    {
        datOut[i][j]= datIn[rows-j][i];
    }
}

and in 1-D array:

for(int i=0; i<cols; i++)
{
    for(int j=1; j<=rows; j++)
    {
        datOut[i * rows + j]= datIn[(rows-j) * cols + i];
    }
}

Answer 2

You can easily convert the (x + y * width) to a simpler (x, y) representation.

using P = point_data_type;
P point(int x, int y){
   return DataIn[x + y * width];  // N - ...?
}

Now a right angle rotation is just a coordinate switch and maybe a sign correction.

P rotate90(int x, int y){
    return point(y, x);
}

This is a positive rotation in a left-handed system. Subtract x from Width if the rotation is in the wrong direction.