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MathGroup Archive 1997

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Re: Breaking a sphere surface area into equal portions?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg7834] Re: Breaking a sphere surface area into equal portions?
  • From: Lord of Darkness <j.biddiscombe at rl.ac.uk>
  • Date: Mon, 14 Jul 1997 03:01:15 -0400
  • Organization: Rutherford Appleton Laboratory
  • Sender: owner-wri-mathgroup at wolfram.com

> I am looking for a way to break the surface of a sphere into n equal
> area pieces with roughly regular shapes(No jagged points).  Is there a
> simple way to use MMA to do this?  I looked at Graphics`Polyhedra` but
> don't see anything there that is useful unless I already have the
> coordinates of the vertices.

I did almost exactly this very recently, however the jagged points
constraint is a problem. 
The surface area of a sphere is the same as the circumscribing cylinder
with the same height, and therefore strips of equal height on a sphere
(assuming base and top are like a sphere sitting on a desk...with you
looking from the side)..are equal area.

By dividing the sphere into strips of equal height, (latitude) and equal
angle (longitude) you end up with a sphere divided into equal area
chunks. 

Your problem may not allow this aproach because the chunks near the
poles become triangular, whilst the chunks near the equator become
square.

It does work though, and if you want some code, I can send you a routine
which will create polygons and bung them into a list suitable for
display with Show[mypolygons...]

John B
PS - I wanted to do a satellite beam pattern illuminating the earth,
hence my desire to model this particular problem.


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