3D spherical histogram

Question

Abhinendra 2011-8-8

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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...

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Bjorn Gustavsson 2011-8-9

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.

Abhinendra 2011-8-9

Yeah Bjorn,

You are totally correct, in fact I am doing this.

The problem finally comes when I have to plot this data. Can you help me with final plotting of my data?

Abhi...

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Answer 1

Honglei Chen 2011-8-8

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在 MATLAB Online 中打开

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

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Honglei Chen 2011-8-9

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

Abhinendra 2011-8-9

Hi Honglei,

The histogram is set of discrete points. Where each element is the matrix represent the number of lines with orientation between theta(i) and theta(i+1) and between phi(j) and phi(j+1).

So finally I have N(which is discrete data points), theta and phi vectors and I have to plot a 3D polar histogram out of it.

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