add additional parameter to contour plot to generate 3d plot

I have an equation which has 3 unknown variables V, s, and T. I want to produce a contour plot that shows what happens when each of these variables changes. Currently I can do this by creating a vector for both V and T but keep s as a constant:

V = 1:250; 
T = linspace(1,25,length(V));
s = 30;
for j = 1:length(T)
    D(j,:) = (3.*V.*(s^2))./(T(j).*((T(j).^2)-...
        (3.*T(j).*s)+(3.*(s.^(2)))));
end

Then by plotting D as a contour plot:

pcolor(T,V,D');shading interp

we can see that when V is large and T is small, D will be large. From here, I would like to generate a 3d plot where I can also show the influence of changing 's'. At the moment 's' is a constant, so I can show how s affects the outcome by producing say 4 different figures for 4 different values of s. However, it would be better if I could generate one plot with 3 axis showing how D varies with V, T, and s. Could anyone provide some information about the best way of doing this?

Answer 1

[José-Luis]

What you are asking is basically how to plot four-dimensional data in a two dimensional plane. It is not easy, and tends to be messy, IMO. They way you do it sounds reasonable to me, but if you really want to have everything in a single plot, you could always use the slice() function:

V = 1:250; 
T = linspace(1,25,length(V));
ii = 10:10:40;
all_data = nan(250,250,4);
counter = 1;
for s = ii
    for j = 1:length(T)
        D(j,:) = (3.*V.*(s^2))./(T(j).*((T(j).^2)-...
            (3.*T(j).*s)+(3.*(s.^(2))))); %This could be vectorized
    end
    all_data(:,:,counter) = D';
    counter = counter + 1;
end

[x y z] = meshgrid(V,T,ii);
sH = slice(x,y,z,all_data,[],[],ii);
set(sH,'EdgeColor','none');

Answer 2

[Thorsten]

You can use scatter3 and experiment with the size and the color of the dots

scatter3(X(:), Y(:), Z(:), 100*map01(V(:))+0.1, 255*(map01(V(:))), 'filled')