trying to model points inside a sphere

if true
clear
clear all
r=randn(0,1);
theta=randn(0,1)*(pi);
phi=randn(0,1)*(2*pi);
for N=1:20
  hold on
  x=r(N).*sin(theta(N)).*cos(phi(N));
  y=r(N).*sin(theta(N)).*sin(phi(N));
  z=r(N).*cos(theta(N));
end
hold off
drawnow
  % code
end
I am trying to model a bunch of points inside a sphere, I put the spherical cooridinates into cartesian, but cannot get it to plot, any help would be appreciated.

[jonas]

The code stops because theta, phi and r are all empty, because randn(0,1) does not output anything. You are also overwriting the variables x,y and z each iteration (consider removing the loop). If you fix those issues, maybe the question becomes more clear.

[Devon Romine]

Thank you very much jonas, I have made some adjustments to the code and it runs now, but am having trouble fine-tuning the graph. What I need is a sphere with the random points inside of it, I will attach my current code, any suggestions would be appreciated.

if true
clear
clear all
n=20;
r=rand(n,1);
theta=rand(n,1)*pi;
phi=rand(n,1)*(2*pi);
x=r.*sin(theta).*cos(phi);
y=r.*sin(theta).*sin(phi);
z=r.*cos(theta);
[X,Y,Z]=sphere;
hold on
scatter3(x,y,z)
plot3(X,Y,Z)
hold off
  % code
end

[jonas]

No problem! I am a bit confused, because running your code gives me what you requested: a sphere with random points inside of it. Just type view(3) to get a 3d-perspective. If you want tips to improve the visualization, then you need to be a bit more specific in what you are trying to achieve. Try this for example:

if true
  clear
  clear all
  n=20;
  r=rand(n,1);
  theta=rand(n,1)*pi;
  phi=rand(n,1)*(2*pi);
  x=r.*sin(theta).*cos(phi);
  y=r.*sin(theta).*sin(phi);
  z=r.*cos(theta);
  sphere;
  hold on
  scatter3(x,y,z)
  hold off
    % code
  end
ha=get(gca,'children')
set(ha(2),'FaceColor',[0 0 0],'FaceAlpha',0.1,'EdgeAlpha',0.2)

[Devon Romine]

I did not know about the view(3), that was what I needed thank you!

[jonas]

Great! I will post an answer for future reference, if anyone else wants to model a sphere with random points

Answer 1

[jonas]

This will generate a sphere with random points inside of it (code adapted from the original question):

 if true
    clear
    clear all
    n=20;
    r=rand(n,1);
    theta=rand(n,1)*pi;
    phi=rand(n,1)*(2*pi);
    x=r.*sin(theta).*cos(phi);
    y=r.*sin(theta).*sin(phi);
    z=r.*cos(theta);
    sphere;
    hold on
    scatter3(x,y,z)
    hold off
      % code
    end
  ha=get(gca,'children')
  set(ha(2),'FaceColor',[0 0 0],'FaceAlpha',0.1,'EdgeAlpha',0.2)

[David Goodmanson]

Hi Jonas / Devin,

This code is pretty good, except if you try it for something like n = 2000 you will see a cluster of points in the middle of the sphere and also along the z axis. It's more usual to be looking for a uniform density of points in the sphere, which would be

r = rand(n,1).^(1/3);
costheta = 2*rand(n,1)-1;
sintheta = sqrt(1-costheta.^2);
phi=rand(n,1)*(2*pi);
x=r.*sintheta.*cos(phi);
y=r.*sintheta.*sin(phi);
z=r.*costheta;