Transform a photo according to a function [MATLAB] - matlab

Question

I'm a beginner in matlab and I'm trying to transform a photo according to a function given in the code.
My aim is to see where some points of the R^2 plan go. For example, i'd like to transform :
But I can't figure this out.
I found some good conversations on this topic:
https://www.mathworks.com/matlabcentral/answers/81975-is-it-possible-to-pass-an-image-as-an-input-to-a-function-in-matlab
and good functions like :
https://www.mathworks.com/help/images/ref/imtransform.html
https://www.mathworks.com/help/images/ref/imwarp.html
but I don't understand what to do with that because I don't have a matrix but just like the function "1/z"...
The aim is to do something better than this :
How to plot the Wolfram Alpha grid? [MATLAB]
I've tried to add colors to the mesh graph but I ve not succed in doing so... I could only find how to change uniformly the colors, like setting all in green...
If you have another solution not using an image but constructing a
grid of a range of colors and then deforming it (like in the link) or
even better, instead of a grid, creating a whole plan with an uniform
distribution of the colors... it also fixes the problem!
Thank you !

Answer 1

You can use the surf function to plot a grid with colored patches. If you use the same code in my answer to your previous question, you could visualize the original grid with colors as follows:
C = X.^2 + Y.^2; %change this to any function you like to get different color patterns
surf(X,Y,C);
view([0, 90]); %view the mesh from above
Now, if you want to see how the transformed mesh looks like, you can do:
surf(U,V,C);
view([0, 90]);
where U and V are computed according to my previous answer.
Edit: Added sample code for transforming an image using geometricTransform2d and imwarp.
clear
clc
A = imread('peppers.png');
figure(1)
imshow(A)
t1 = geometricTransform2d(#ftransform);
Rin = imref2d(size(A),[-1 1],[-1 1]);
Rout = imref2d(size(A),[-5 5],[-5 5]);
B = imwarp(A, Rin, t1,'OutputView',Rout);
figure(2);
imshow(B)
function Xt = ftransform(X)
Z = complex(X(:,1),X(:,2));
Zt = 1./Z;
Xt(:,1) = real(Zt);
Xt(:,2) = imag(Zt);
end