Question

I have three functions in spherical coordinates that I want to plot. They are functions of r,theta,phi and I want to view them in the x-y,y-z,x-z planes. I’ve tried accomplishing this for literally 8 hours. Every method I’ve tried has been unsuccessful.

How can I accomplish this phenomenally simple task?

F1 = (r.^2).*abs((1/(8*sqrt(pi))).*r.*exp(-r/2).*sin(theta).*cos(phi)).^2;
F2 = (r.^2).*abs((1/(8*sqrt(pi))).*r.*exp(-r/2).*sin(theta).*sin(phi)).^2;
F3 = (r.^2).*abs((1/(4*sqrt(2*pi))).*r.*exp(-r/2).*cos(theta)).^2;

As you can see, all three of the functions are F(r,theta,phi). That means that there are four dimensions: F,r,theta,phi.

Answer 1

If your functions cannot be expressed as r=f(theta,phi), maybe you can compute the value of f(theta,phi,r) over a grid and then plot an isosurface where your volume data equals your value twoPx.

I tried this small example from which you can expand but I do not know if the shape is correct because I do not know what to expect:

n=20;
rmax=5;
twoPx=0;
%%%%%%%%%%
[theta phi r]=ndgrid(linspace(0,2*pi,n),linspace(-pi/2,pi/2,n),linspace(0,rmax,n));
%%%%%%%%%%
value=(r.^2).*abs((1/(8*sqrt(pi))).*r.*exp(-r/2).*sin(theta).*cos(phi)).^2;
%%%%%%%%%%
[x y z]=sph2cart(theta,phi,r);
%%%%%%%%%%
p=patch(isosurface(x,y,z,value,twoPx));
%%%%%%%%%%
set(p,'FaceColor','b','EdgeColor','k','FaceAlpha',0.5);
daspect([1 1 1])
axis square;
grid on;
camlight;
view([0 0]);

A little explanation of what this snippet does:

1. define a spherical grid (ndgrid)
2. compute the value of your function on that grid
3. compute the cartesian grid corresponding to the spherical grid (sph2cart)
4. plot the isosurface where your volume equals twoPx (patch and isosurface)

Finally you may want to use the Matlab function view to specify which plane you want to look from.