Create a 2D grid to map points over a transformation?

I am trying to create two plots: one showing a grid on the top and the second showing a transformation applied to every point on the grid (bottom). Till now I have been able to figure out the following way which only works when the x and y ranges are symmetric:

x = linspace(-5, 5, 10);
y = linspace(-5, 5, 100);
[X, Y]= meshgrid(x, y);
figure
plot(X, Y, 'blue', Y, X, 'blue');

Z = X + i*Y;
W = Z.^2; % f(z) = z^2 for example
figure
plot(W, 'blue')
Z = Y + i*X;
W = Z.^2;
hold on;
plot(W, 'blue')

So far so good but say I want to create grid that is asymetrical with regards to the axes ranges. For example, the normalized impedance of a transmission line z = r + ix which can only have positive resistance r. Say want a grid in the region 0 < r < 10 and -10 < x < 10 with lines at intervals of 1 say. Is there a general way of doing this? (and perhas a better way of doing the above?)

Answer 1

[Pratyush Swain]

Hi Shovnik,

For handling assymmetric grid ranges we can utilize a general approach as follows:

% Set up the assymmetric ranges %

r = linspace(0, 10, 11);
x = linspace(-10, 10, 21);
[R, X] = meshgrid(r, x);

% Convert to complex domain and apply conformal map %

Z = R + j*X;
W = Z.^2;

For plotting the original and transformed grid:

% Plotting horizontal and vertical lines separately %
figure;
plot(R, X, 'b'); 
hold on;
plot(R', X', 'b'); 
axis equal;
title('Original Grid');

●

% Instead of plotting plot(W), plotting row and column lines %
figure;
plot(real(W), imag(W), 'b'); hold on;
plot(real(W'), imag(W'), 'b');
axis equal;
title('Transformed Grid');

I have utilised the real function: https://www.mathworks.com/help/symbolic/sym.real.html and imag function: https://ww.mathworks.com/help/symbolic/sym.imag.html from the symbolic math toolbox.

Hope this helps.