rotate a matrix with a fixed grid position

Hi,

I have a matrix of values A with their corresponding coordinate contained within the matrices X and Y. I can visualise the data by simply typing pcolor(X,Y,A). Visually, the data seems rotated around its centre. So, I tried to rotate A using imrotate or affine2d but the resulting matrix B has different dimensions and I can no longer relate it to the coordinate system X,Y without changing it also. It is possible to rotate A without changing X,Y ? Maybe I have to interpolate?

Thank you very much, this is quite confusing for me.

[Image Analyst]

Attach your data and code, and a screenshot.

[Daniel Mella]

B=imrotate(A,1) produces a bigger matrix filled with zeros and I cannot relate it to [X,Y] With B=imrotate(A,1,'crop') I lose information on the corners introducing zero values.

Basically, I need to change the orientation of the matrix A without losing information and without losing its correspondence with the grid [X,Y]

Answer 1

[Akanksha]

Hey Daniel Mella,

The following code changes the orientation of matrix A by the desired angle (here 1 degrees) while being in correspondence with grid [X,Y] :

%% Grid of X and Y coordinates from -10 to 10 (200 points each) 
[X, Y] = meshgrid(linspace(-10, 10, 200), linspace(-10, 10, 200)); 

% Matrix A  
A = exp(- (X.^2 + Y.^2) / 50); 

% Visualizing the original data  
figure; 
pcolor(X, Y, A); 
shading interp; 
colorbar; 
title('Original Data'); 


%%Defining the Rotation Transformation 
theta = 1; % rotation angle in degrees 
tform = affine2d([cosd(theta) -sind(theta) 0;  
    sind(theta)  cosd(theta) 0;  
    0            0           1]); 

%% Creating the Spatial Referencing Object 
% The imref2d object defines the world coordinate limits for A. 
Rin = imref2d(size(A), [min(X(:)), max(X(:))], [min(Y(:)), max(Y(:))]); 

%% Applying the Transformation with imwarp 
% Use the 'OutputView' parameter to force the output to have the same coordinate grid as Rin. 
B = imwarp(A, tform, 'OutputView', Rin); 

%% Visualizing the Rotated Data 
figure; 
pcolor(X, Y, B); 
shading interp; 
colorbar; 
title('Rotated Data'); 

I have run the above code locally, and successfully produced the required output. I will attach the original and transformed data visualizations for your reference below -

Also find the links to required documentation for further reference :

https://www.mathworks.com/help/images/ref/imref2d.html

https://www.mathworks.com/help/images/ref/imwarp.html

https://www.mathworks.com/help/images/ref/affine2d.html

https://www.mathworks.com/help/matlab/ref/pcolor.html

Hope this helps. Thanks.