POV-Ray : Newsgroups : povray.advanced-users : How to distribute points equally on sqhere surface? : Re: How to distribute points equally on sqhere surface? Server Time
30 Jul 2024 20:32:02 EDT (-0400)
  Re: How to distribute points equally on sqhere surface?  
From: Uwe Zimmermann
Date: 20 Jul 1999 11:40:55
Message: <37949886.BA284B6C@ele.kth.se>
I don't know why I didn't see this thread earlier... it's already one
month old...

However, I just recently wrote and published a macro for geodesic
spheres which happen to be bodies that are constructed by dividing the
surface of a sphere into triangles. The principle behind it starts from
the three basic polyhedra with triangular faces:
  tetrahedron  4 faces
  octahedron   8 faces
  icosahedron  20 faces
and divides each triangular face into smaller triangles. Though it is
NOT possible to put any number of points (or triangles/corners) onto a
sphere you can choose from quite a variety of values by just selecting
the basic polyhedron and the "frequency" of subdivision for each face.
The number of faces on the final sphere is then calculated as 

  number of faces on polyhedron * (freq^2)

so you can get the following values:

freq      tetrahedron    octahedron   icosahedron
  1             4             8            20
  2            16            32            80
  3            36            72           180
  4            64           128           320
  5           100           200           500
  6           144           288           720
  8           256           512          1280
etc.    

By defining your own "drawing" (better: object placing) routine for each
face, edge and corner, you can easily distribute whatever object you
want on the faces.

You can download the macro, documentation  and see some examples at
http://www.geocities.com/SiliconValley/Lakes/5432/povray/geodesic.html


Uwe.


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