How to convert polar meshgrid to Cartesian meshgrid?

I prepared a Cartesian meshgrid (10x10) and then converted it to polar. After doing some calculations and filling all 100 elements of the matrix now I want to see the final picture back in Cartesian coordinates. So, I want to map every single index of that 10x10 matrix to its Cartesian counterpart. How can I do that?

Answer 1

[Jacob Mathew]

Hi Sachin,

You can utilize vectorized operations to achieve the transformations. A simple workflow is shown below:

% Creating a Cartesian Meshgrid
x = linspace(-5, 5, 10);
y = linspace(-5, 5, 10);
[X, Y] = meshgrid(x, y);

% Visualize the Original Cartesian Space
figure;
subplot(1, 2, 1);
pcolor(X, Y, zeros(size(X)));
shading flat; 
colorbar;
xlabel('X');
ylabel('Y');
title('Original Cartesian Grid');
axis equal;

% Convert from Cartesian to Polar Coordinates
R = sqrt(X.^2 + Y.^2);
Theta = atan2(Y, X);

% Example calculation in Polar Coordinates
Z = sin(R) .* cos(Theta);

% Convert Polar Back to Cartesian
X_prime = R .* cos(Theta);
Y_prime = R .* sin(Theta);

% Visualize the Transformed Data
subplot(1, 2, 2);
pcolor(X_prime, Y_prime, Z);
shading interp;
colorbar;
xlabel('X');
ylabel('Y');
title('Transformed Data in Cartesian Coordinates');
axis equal;

If you have specific issues with your data or woflow, share the code in comment.