4D function plot

I have a function of 3 variables like V= f(r1,p,r2), I want to plot these 4 data in one graph to be able to capture behavior of V with respect to all three variables. I searched a little bit and read about Sliceomatics but not sure how does it work and if it deliveres my requirements. I would appreciate if someone could suggest a way for it. As an example lets say I have: r1 = [1 2 3 4 5 6]; p = [2 4 5 8 9 7]; r2 = [10 45 1 0 7 9]; v= 5.*r1.^2+2.*p.^2+r2.^2;

Answer 1

[Akira Agata]

Using isosurface function, you can do somehow this type of plot. In the following code, I plotted the surfaces of func(x,y,z) = 0.5 (red) and 0.8 (green).

 func = @(x,y,z)(sin(2*x.^2+2*y.^2).*cos(2*z.^2));

 [x,y,z] = meshgrid(-1:0.1:1, -1:0.1:1, -1:0.1:1);
 v = func(x,y,z);

 figure
 p1 = patch(isosurface(x,y,z,v,0.5));
 hold on
 p2 = patch(isosurface(x,y,z,v,0.8));
 isonormals(x,y,z,v,p1);
 isonormals(x,y,z,v,p2);
 p1.FaceColor = 'red';
 p2.FaceColor = 'green';
 p1.EdgeColor = 'none';
 p2.EdgeColor = 'none';
 daspect([1,1,1])
 view(3); axis tight
 camlight 
 lighting gouraud

[F R]

Thanks, this kind of plotting seems to work similar to scatter3, I am wondering where do you see v data, or which axis represents v? in my case, x,y,z and v are vectors, not 3D array.

Answer 2

[Nisha Dhake]

A simple solution will be to keep shifting the array while using the 'hold on' function.

Here is how you can do it:

r1 = [1 2 3 4 5 6]'; 
p = [2 4 5 8 9 7]'; 
r2 = [10 15 1 0 7 9]'; 

for x=0:length(p)
    p=circshift(p,1);
        for w=0:length(r2)
            r2=circshift(r2,1);
            for u =1:1:length(r1)
                v(u)=5*r1(u)^2+2*p(u)^2+r2(u)^2;
            end

              scatter3(r1,p,r2,40,v,'filled')
              xlabel('r1') 
              ylabel('p')
              zlabel('r2')
              hold on
          end
  end
  cb = colorbar;

The plot you will get will be:

Answer 3

[John D'Errico]

You cannot visualize 4-d data in a 2-d plot. And a plot is only 2 dimensions. Even a 3-d plot only makes sense if you rotate things around, or view it using stereo vision. But 4-d simply does not work.

So the classic trick is to use slices in the form of an isosurface. But isosurfaces only are implemented if you have a regular, meshed grid of points, thus a 3-d array in the form of v(x,y,z).

But you have scattered data in 4 dimensions. So nothing will work until you turn that into something regular and well connected. Scattered points are just that, isolated, with no simple way to know what is near what.

Answer 4

[Naveen Pathak]

The solution of Akira Agata will certainly work for you. Just add one more line to represent everything in a transparent manner so that volume can be visualized. Just include an another line: alpha(n), where "n" is some value between 0 to 1. Try, n = 0.3 or 0.4 etc.