Plotting 3 variables of a single function

Is it possible to plot three variables x,y and z of a single function f?

i.e. f = x^2 + y^2 + z^2, for example?

I'd want to plot the function 'f' with a range of values for x,y and z.

I've been looking at contour maps for two variables and would now, somehow, like to expand it to three variables and able to represent the function pictorially via a plot in Matlab.

Thanks!

Answer 1

[AJ von Alt]

Sliceomatic on Matlab file exchange is a useful tool for this sort of visualization.

[Kayn]

Thanks for the reply. I'm not very competent at using Matlab and I've no idea how extract the code I would want from the file you linked. Do you have any experience of it? Could you possibly write out a really simple example here so I can go and learn how to use the 'sliceomatic' function please? Many thanks.

[Walter Roberson]

For your purposes are you hoping for interactive use or fixed-parameter use? For interactive use, you would not extract any code from that File Exchange contribution: instead you would download the contribution and call upon it.

[AJ von Alt]

% define an array of values for x y and z
x = -10:0.1:10; 
y = -10:0.1:10; 
z = -10:0.1:10; 

% create a meshgrid
[Xmesh,Ymesh,Zmesh] = meshgrid(x,y,z);

% compute the function value at the meshgrid points
f = Xmesh.^2 + Ymesh.^2 + Zmesh.^2;

% launch sliceomatic
sliceomatic(f,x,y,z)

You can then select slices using the x y and z controls or view layers using the iso surface control

[Giuseppe Naselli]

Hi All,

I need to do the same (plotting F as function of X,Y,Z) but I do not know the relationship between them.

Basically I have 4 column vectors F,X,Y,Z.

I can do the meshgrid(X,Y,Z) but I do not know how to manipulate F in order to use sliceomatic

Any idea?

Thanks in advance

G

Answer 2

[Walter Roberson]

http://www.mathworks.com/help/matlab/ref/slice.html

http://www.mathworks.com/help/matlab/ref/isosurface.html

For a full plot of 3 independent variables and one resultant variable, you need to encode the resultant variable as marker shape (one scatter3 or plot3 call for each different marker shape), or point size (scatter3; or a lot of plot3 calls), or as color (scatter3 or patch or a lot of plot3 calls), or as transparency (patch). (Though transparency by itself is hard to see.)