Plotting a 3D Function in Matlab: Visualizing the Evolution of a System

[qspeechc]

Hi everyone.

So, I have a quantity I am computing, say w, a vector. Now w is a function of time t and space x. I have the vectors x and t. At each time step in a loop, I calculate w for that time step. How do I plot w as a 3D plot, as a function of time t and space x, so I can see the evolution of the system?

Here's what I tried. I created a matrix A of dimension NxM, where N is the length of the vector x, and M the length of the vector t. At the mth time step I placed the computed value of w in the mth column of A. Then I tried to plot it like this:

>> plot3(t,x,A)

but that doesn't work, instead I tried t.*x, x.*t in all combinations, but nothing worked. What is the correct way to do it?
Thanks.

 

[KLoux]

I think you want surf() or contour()... plot3 is for plotting (x, y, z) points in 3-space, not for showing z(x, y).

-Kerry

 

[belliott4488]

I think it would help to picture how you'd like to represent this information first, and then try to figure out how to do it in Matlab.

One possibility would be to plot 3-D arrows, one at each (t;x,y,z), such that the length of the arrow was proportional to the magnitude of w (you'll have to choose a scale that looks good), and the direction is given by the direction of w. You could do this by adding the vector w, multiplied by a suitable scaling factor, to each (x,y,z) vector, to get the location of the "head" of the arrow. If you then plot a line from (x,y,z) to this new point, that will represent the vector w. I think you can even put an arrowhead on it, but I don't recall how to do that from the command line or a script.

This would give you something like those plots that show fluid flow by displaying an array of arrows that indicate the velocity of the fluid at each point on a grid.

 

[qspeechc]

I am actually supposed to be showing the interaction of a bunch of waves. I tried mesh and it gives an ok result if I pick a good viewing angle, I can see the direction of the waves, but not really their shapes. I guess it'll do. Thanks.

 

[Choragos]

If you want to do an animation of your motion, here's a suggestion. In the following script I am plotting from a 3-D array 'U'. The third dimension corresponds to time. Surf plots a surface. Xi and Yi are meshes produced using meshgrid(x,y). I fix my axes and loop over time.

h1=surf(Xi,Yi,U(:,:,1),'erasemode','normal');

shading interp;
%colormap(gray);
colorbar;
axis([0 3 0 3 -1 1]);
caxis([-.25 .25]);

for ii = 2:M
set(h1,'zdata',U(:,:,ii));
refreshdata;
drawnow;
% pause(0.01);
% pause(0.3);
end

 

[Choragos]

I think it would help to picture how you'd like to represent this information first, and then try to figure out how to do it in Matlab.

One possibility would be to plot 3-D arrows, one at each (t;x,y,z), such that the length of the arrow was proportional to the magnitude of w (you'll have to choose a scale that looks good), and the direction is given by the direction of w. You could do this by adding the vector w, multiplied by a suitable scaling factor, to each (x,y,z) vector, to get the location of the "head" of the arrow. If you then plot a line from (x,y,z) to this new point, that will represent the vector w. I think you can even put an arrowhead on it, but I don't recall how to do that from the command line or a script.

This would give you something like those plots that show fluid flow by displaying an array of arrows that indicate the velocity of the fluid at each point on a grid.

You can also do this with the 'quiver' plot command. I have never have success using it, but I have seen other people have success so I can only assume it's possible. Hit up the ol' help quiver and see what you can come up with.

 

[BCox]

Hello:

I would like to generate a similar 3D graph in MATLAB. The points are (x,y,z). I would like to have a SCATTER plot on the (x,y) axes. But then each one of these (x,y) points are LINE connected to their respective z point. If anyone has code for this, or know how to do this in SAS, it would be so helpful. Thx!