Draws a 3D hidden function iso-high line

I used the isosurface function to draw an image of the hidden function, and I wanted to show contours below the 3D graph.

The code is followed.

function sita45

[x,y,z]=meshgrid(linspace(0,0.04,300),linspace(0,0.5,300),linspace(0,0.2,200));

v=(3*log10(x)-182*x-15.079*y+2*log10(z)-48.912*z+15.62);

p=patch(isosurface(x,y,z,v,0));

view(3)

set(p, 'FaceColor', 'blue', 'Edgecolor', 'none');

camlight('headlight');lighting phong

Thank you for your help！

Answer 1

[Vidhi Agarwal]

Hi @跻 陈

To enhance your 3D plot with contours below the graph in MATLAB, you can use the "contour" or "contourf" functions to add contour lines to the 2D projection on one of the coordinate planes.

Below is the modified code for the same:

function sita45
    % Define the grid
    [x, y, z] = meshgrid(linspace(0, 0.04, 300), linspace(0, 0.5, 300), linspace(0, 0.2, 200));
    
    % Define the function values
    v = (3*log10(x) - 182*x - 15.079*y + 2*log10(z) - 48.912*z + 15.62);
    
    % Create the isosurface
    p = patch(isosurface(x, y, z, v, 0));
    set(p, 'FaceColor', 'blue', 'EdgeColor', 'none');
    
    % Add lighting and view
    camlight('headlight');
    lighting phong;
    view(3);
    hold on;
    
    % Add contours on the bottom plane (z = 0)
    % Extract the slice at z = 0
    [X, Y] = meshgrid(linspace(0, 0.04, 300), linspace(0, 0.5, 300));
    % Use a small z value to avoid log(0)
    V_slice = (3*log10(X) - 182*X - 15.079*Y + 2*log10(0.0001) - 48.912*0.0001 + 15.62);
    
    % Plot contours
    contour(X, Y, V_slice, 20, 'LineColor', 'black'); % Adjust the number of contour levels as needed
    
    % Set axis labels
    xlabel('X');
    ylabel('Y');
    zlabel('Z');
    
    % Set other plot properties
    axis tight;
    grid on;
    hold off;
end

For better understanding of "contour" or "contourf" refer to the following documentation:

• contour: https://www.mathworks.com/help/matlab/ref/contour.html
• contourf: https://www.mathworks.com/help/matlab/ref/contourf.html

Hope this helps!