Plotting a radial function f(r), in a 3d isotropic way, with axes (x,y,z=f(x^2+y^2)).

I have a function f(r), where r=sqrt(x^2+y^2). In my data r, is an array which takes values from [0,8], for example: f(r)=sin(r). I don't have data for an array of x or y seperately. The function is perfectly isotropic. How can I create a 3-dimensional plot, where the function f(x^2+y^2) is presented versus x and y in the correct range?

Further explanation:

The vector of the values of f(r) is given. It was calculated from some numerical simulation (I don't have its analytic form). I don't have the vectors for x and y. The function is isotropic, so one can imagine that I just draw the same curve f(r) in every direction. But the problem I encounter for example, is how to create the vector Theta, x and y, so that they will have the correct number of sites, like f(r), and that they will represent f(r) in the 3-dimensional plot.

Answer 1

[Dimitris Kalogiros]

I reshaped my code.

Lets say that we have loaded values of r and f(r) from a file. Cause I haven't these files , I must create these values.

Then for every value of r , I rotate a vector of length r , in order to take values of x and y. This is a reason for the arbitrary creation of this angle, which varies from 0 to 2pi.

For any given value of r, we have f(r) from our file and a very dense set of possible pairs (x,y) which form a vecor with magnitude r. In that way we can claim that we have "transformed" our function from f(r) to f(x,y) .... in fact to f(sqrt(x^2+y^2))

clc; clear; close all;

%%input data ( predefined)
% values of r (they are predefined and stored to a file)
r=0:0.1:8;

% values of f(r) (they are predefined stored to a file) 
f=sin(r);

%%creation of x and y and connect them with f() stored values

% Angle between 0 and 2*pi, with arbitrary small step
% (small step means better accuracy)
phi=0:0.1:2*pi-0.1;

% creation of x and y
x=[];
y=[];
f_xy=[];

for n=1:length(r)
    xtemp=r(n)*cos(phi);
    ytemp=r(n)*sin(phi);

      x=[x xtemp];
      y=[y ytemp];

      f_xy=[f_xy f(n)*ones(1, length(xtemp))];
  end

%%plot
plot3(x,y,f_xy); zoom on; grid on;
xlabel('x'); ylabel('y'); zlabel('f');
grid on; zoom on;

..if you run the script you will receive this:

[Erez]

Fantastic! That's what I was looking for! Thank you very much.

[Erez]

 Quick follow-up: How can I color this curve, so that the color scheme will indicate height, like in a topographical map for instance? Thanks!

Answer 2

[Dimitris Kalogiros]

Dear Erez

Here you are my suggestion:

clc; clear; close all;

% values of r
r=0:0.1:8;

% create values of x and y
phi=0:0.1:2*pi-0.1;

x=[];
y=[];

for n=1:length(r)
    xtemp=r(n)*cos(phi);
    ytemp=r(n)*sin(phi);

      x=[x xtemp];
      y=[y ytemp];
  end

%calculate values of f()
f=sin(sqrt(x.^2 + y.^2));

% plot
plot3(x,y,f); zoom on; grid on;
xlabel('x'); ylabel('y'); zlabel('z');
grid on; zoom on;

My code is not optimum from the point of view of speed , but showes clearly how to overcome your problem

[Erez]

Dear Dimitris, thanks for you reply. However perhaps I did not explain my question correctly. In your code you have : "%calculate values of f() f=sin(sqrt(x.^2 + y.^2));". The point is, that for me, the vector of the values of f(r) is given. It was calculated from some numerical simulation (I don't have its analytic form either). What I don't have, is the vectors for x and y, nor do I have Theta. The function is isotropic, so you can imagine that I just draw the same curve f(r) in every direction. But the problem I encounter for example, is how to create the vector Theta, x and y, so that they will have the correct number of sites, like f(r), and that they will represent f(r) in the 3-dimensional plot. I hope my explanation made it more clear...