How I can plot a funtion of three variables r, z and t. What is the algorithm to plot such type of difficult functions.

How I can plot a funtion of three variables r, z and t. What is the algorithm to plot such type of difficult functions.

[Dyuman Joshi]

Since you have a function, see fsurf and fimplicit3.

[Sam Chak]

It depends on what you really want to plot. In this example, the volume of a cuboid is a function of three parameters, which is the product of its dimensions: length (x), width (y), and height (z): .

Can you describe how exactly you would like to visualize the volume of a cuboid in graphical representation? This will provide insights into determining which plotting functions in MATLAB should be used.

Answer 1

[TED MOSBY]

Hi,

To plot a data having 3 variables which I assume you mean 3 inputs and 1 output which is a 4D data, it is difficult to visualise it but I found some functions in MATLAB with which you can visualise it:

1. Slice Plots

You can visualize the function by fixing one of the variables and plotting slices of the function in the remaining two-variable space. For example, you can fix ( t ) and plot ( f(r, z, t) ) as a 2D surface plot for different values of ( t ).

% Define your function 
f = @(r, z, t) r.^2 + z.^2 + t.^2; % Example function 
% Define ranges for each variable 
r = linspace(-10, 10, 100); 
z = linspace(-10, 10, 100); 
t_values = [-5, 0, 5]; % Different t values to slice 
[R, Z] = meshgrid(r, z); 
figure; 
for i = 1:length(t_values) 
    t = t_values(i); 
    F = f(R, Z, t); 
    
    subplot(1, length(t_values), i); 
    surf(R, Z, F); 
    title(['t = ', num2str(t)]); 
    xlabel('r'); 
    ylabel('z'); 
    zlabel('f(r, z, t)'); 
    shading interp; 
end 

2. Isosurfaces

If you want to visualize the function as a 3D volume, you can use isosurfaces. This method shows surfaces where the function has a constant value.

% Define the function as an anonymous function 
f = @(r, z, t) r.^2 + z.^2 + t.^2; % Example function 
% Define a grid 
r = linspace(-10, 10, 50); 
z = linspace(-10, 10, 50); 
t = linspace(-10, 10, 50); 
[R, Z, T] = meshgrid(r, z, t); 
% Compute the function values on the grid 
F = f(R, Z, T); 
% Plot isosurfaces 
figure; 
isosurface(R, Z, T, F, 50); % 50 is the isovalue 
xlabel('r'); 
ylabel('z'); 
zlabel('t'); 
title('Isosurface of f(r, z, t)'); 
axis equal;

3. Animated Plots

You can create an animation by varying one of the variables over time, effectively creating a dynamic 3D plot.

% Define the function as an anonymous function 
f = @(r, z, t) r.^2 + z.^2 + t.^2; % Example function 
% Define the range for r and z 
r = linspace(-10, 10, 100); 
z = linspace(-10, 10, 100); 
% Create a 2D grid for r and z 
[R, Z] = meshgrid(r, z); 
% Define the range for t 
t_values = linspace(-10, 10, 50); 
% Create a figure for the animation 
figure; 
% Loop through each t value to create the animation 
for t = t_values 
    % Evaluate the function at the current value of t 
    F = f(R, Z, t); 
    % Plot the surface 
    surf(R, Z, F); 
    xlabel('r'); 
    ylabel('z'); 
    zlabel('f(r, z, t)'); 
    title(['t = ', num2str(t)]); 
    shading interp; % Optional: make the surface look smoother 
    axis([-10 10 -10 10 0 400]); % Adjust axis limits as needed 
    grid on; 
    % Pause to control the speed of the animation 
    pause(0.1); 
end 

4. Contour Slices

Another approach is to use contour slices, which can give you a sense of the function's behavior in different planes.

% Define the function as an anonymous function 
f = @(r, z, t) r.^2 + z.^2 + t.^2; % Example function 
% Define a grid 
r = linspace(-10, 10, 50); 
z = linspace(-10, 10, 50); 
t = linspace(-10, 10, 50); 
[R, Z, T] = meshgrid(r, z, t); 
% Compute the function values on the grid 
F = f(R, Z, T); 
% Plot contour slices 
figure; 
slice(R, Z, T, F, [], [], t_values); % Slices at specified t values 
xlabel('r'); 
ylabel('z'); 
zlabel('t'); 
title('Contour Slices of f(r, z, t)'); 
colorbar; 

Try out these methods, hope this helps!

To know more about "meshgrid" refer the following documentation:

www.mathworks.com/help/matlab/ref/meshgrid.html?s_tid=doc_ta