MATLAB: How to get the new coordinates of a point after rotation of an image (2D)

imrotaterotation matrix

I have got the coordinates of a point (P) in my main image (2D). The main image (im) is now rotated using imrotate and the angle alpha. Now, I want to know what the coordinates of P are in the rotated image.
P = [5;8];    % coordinates of point
alpha = 45;   % angle for rotation
RotatedIm = imrotate(im,alpha);   % rotation of the main image (im)
RotMatrix = [cosd(alpha) -sind(alpha); sind(alpha) cosd(alpha)]; 
ImCenter = (size(im)/2)';         % Center of the main image
RotatedP = RotMatrix*(P-ImCenter)+ImCenter;  % Rotation of point P over center of the image with angle alpha
The rotatedP coordinates are not the right ones. The problem is that there are zeros added on the borders of RotatedIm. I think that that is the reason why the coordinates of RotatedP are not correct. Can someone help me to find the coordinates of point P in the rotated image?

Best Answer

P = [5;8];    % coordinates of point
alpha = 45;   % angle for rotation
RotatedIm = imrotate(im,alpha);   % rotation of the main image (im)
RotMatrix = [cosd(alpha) -sind(alpha); sind(alpha) cosd(alpha)]; 
ImCenterA = (size(im)/2)';         % Center of the main image
ImCenterB = (size(RotatedIm )/2)';  % Center of the transformed image
RotatedP = RotMatrix*(P-ImCenterA)+ImCenterB;
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