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Binning a unit sphere

  • Thread starter susantha
  • Start date
  • #1
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hello,
I am trying to bin the unit sphere so that each bin has approximately equal area on the sphere. I hope binning the azimuthal angle (0...2*pi) to equal bin widths. Then i need to bin the polar angle(0...pi) so that at poles(angles close to 0 and pi) bin widths are large and close to equator(angles close to pi/2) the bin widths are small. I would appreciate any kind of help for binning the polar angles for non-equal bin widths.
Thanks in advance.
Susantha
 

Answers and Replies

  • #2
mathman
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Use equal spacing for the cosine of the polar angle.
 
Last edited:
  • #3
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Use equal spacing for the cosine of the polar angle.
Could you please give little more explanation.
Thanks
 
  • #4
mathman
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It just comes from the fact that the surface area differential on a sphere is given by: dA=sinφdφdθ, where φ is the polar angle (0,π) and θ is the azimuthal angle (0,2π). Integrate dA over some range in φ results in the cosine difference.
 
  • #5
mathman
Science Advisor
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Further explanation: Unit sphere - then the radius of a small circle at angle φ is sinφ. A circular strip of width dφ would have an area 2πsinφdφ.
 
  • #6
6
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Now i got it. Thank you very much for your reply.
 

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