3D spherical histogram
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I have a collection of lines of unit length in space that have some orientation. From this I can calculate theta, phi using cart2sph.[THETA,PHI,R] = cart2sph(X,Y,Z) R would be unit, and of not much relevance here. Now I want a histogram matrix (N) using [theta phi]. In the end using N, theta, phi, I would like to plot a spherical histogram which is an extension of 2d polar command in matlab (which is polar(theta,rho)).
Regards Abhi...
5 commentaires
Bjorn Gustavsson
le 9 Août 2011
If you use bins with equal spacing in phi for all theta etc then the area of the solid angle for each bin in not constant, if so it should vary something like dA = sin(theta)*dtheta*dphi. Close to the pole that area decreases as sin theta. To get the pdf you have to normalize it.
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Honglei Chen
le 8 Août 2011
Hi Abhinendra,
You can convert it to rectangular coordinate and then do the surface plot. You just need to make sure that you provide N as the color scale. Here is a quick example.
phi = linspace(0,2*pi,360);
theta = linspace(0,pi,180);
N = ones(180,360);
[P,T] = meshgrid(phi,theta);
surf(N.*sin(T).*cos(P),N.*sin(T).*sin(P),N.*cos(T),N)
HTH
3 commentaires
Honglei Chen
le 9 Août 2011
Hi Abhinendra,
Assuming that your histogram is smooth, you could interpolate your result in a uniformly sampled (phi,theta) grid. This should help in your case.
HTH
Bjorn Gustavsson
le 8 Août 2011
Well if you want a 3-D histogram (that is with bins in R, theta and phi) you should be well helped with these 3 FEX contributions:
http://www.mathworks.co.uk/matlabcentral/fileexchange/30798-n-d-histogram http://www.mathworks.com/matlabcentral/fileexchange/23897-n-dimensional-histogram http://www.mathworks.com/matlabcentral/fileexchange/31889
They should work with 2-D histograms as well - as would a bunch of other FEX-submissions.
HTH
sree kasturi
le 12 Sep 2011
Abhinendra,
Have you looked at Teja's rather elegant solution here? http://www.mathworks.com/matlabcentral/answers/6625-3-d-histogram-in-spherical-coordinates
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