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I have a function expressed in spherical coordinates:

f(r,theta,phi) = 4*exp(-r)*cos(theta)*sin(phi)

I'd like to plot this in MATLAB in these ways:

  1. R3
  2. R2 Contour Plot (x-y plane or x-z plane or y-z plane)

Is there a straightforward way to do this?

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2 Answers 2

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Just do the conversion and plot in Cartesian coordiantes:

f = @(r, theta, phi) 4*exp(-r).*cos(theta).*sin(phi)
[XX YY ZZ] = meshgrid(x_range, y_range, z_range)
% R = sqrt(XX.^2 + YY.^2 + ZZ.^2)
% Th = acos(XX./YY)
% Phi = acos(ZZ./R)
% This is faster. . . and significantly more correct.  See the comments below.
[Th,Phi,R] = cart2sph(XX,YY,ZZ)
fvals = f(R, Th, Phi)

I like isosurface to visualize 3D data like this. For the 2D slice through Z=0 you could use imagesc(fvals(:,:,N)) or contour(fvals(:,:,N))

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6 Comments

The conversion is a bit off, should be: Th=atan2(YY,XX); Phi=asin(ZZ./R);, but preferably use CART2SPH as it is designed to avoid numerical issues
Is there a less ugly way to do this?
@Amro : How could the above code be modified to use sph2cart()?
@nick_name: [Th,Phi,R] = cart2sph(XX,YY,ZZ). Also looks to me you have volumetric data (ie for each (x,y,z) you have a value), so you want to use functions like ISOSURFACE and SLICE as suggested..
Thanks for the peer review @Amro. I was a bit careless. I've updated the answer to make it better.
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You can use sph2cart() to convert the coordinates, then use plot()/plot3() to plot the function.

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