The problem is really pretty simple.  Imagine putting the stars on a
cylinder instead, and you can see that the distribution would be more uniform.
At the poles, the space is "contracted" because the apparent number of locations
per unit area is much higher.  Think of dots printed on fabric, then gathered in
at the poles.  There will be far more stars where the fabric is gathered up.
    Conversely, imagine the stars printed uniformly on a rubber cylinder, then
stretched over a sphere- the equator will have far fewer than the poles because
the fabric is stretched out there.
    Now, to get rid of the gathering, my intuition says that all you must do it
use a squared radius function.  Imagine a centerline or axis through the sphere.
Any point on the sphere will be from zero to 1 radius from that axis.  So, to
make it more likely that you stars will appear near the equator and less so near
the poles, use the sine of the latitude and square it.  In fact, play with
exponents for the sine from 1 to 2 and you will find a value that will give you
what you want.
    That is the probability for a star appearing there if you write your
algorithm properly. Just multiply the square of the sine of the latitude by the
angle, or some similar idea.
    Time to get out the calculator and play around a bit.

Cheers!

Chip Shults
My robotics, space and CGI web page - http://home.cfl.rr.com/aichip

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