How can I bin the polar angles of a unit sphere for non-equal bin widths?

[susantha]

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

 

[mathman]

Use equal spacing for the cosine of the polar angle.

 

[susantha]

Use equal spacing for the cosine of the polar angle.

Could you please give little more explanation.
Thanks

 

[mathman]

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.

 

[mathman]

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.

 

[susantha]

Now i got it. Thank you very much for your reply.