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Polygons on spheres

  • To: mathgroup at
  • Subject: [mg54710] Polygons on spheres
  • From: Steve Gray <stevebg at>
  • Date: Mon, 28 Feb 2005 03:26:56 -0500 (EST)
  • Sender: owner-wri-mathgroup at

	I have a need to draw and display "polygons" on spheres. The edges of the polygons will all
be arcs of great circles. Examples are triangles, etc., and n-sided polygons which usually
self-intersect. The great circle arcs must stop at the vertices, which presumably can be done by
correctly setting the range in the parametric plots of the edges. Obviously several edges must be
displayed at the same time, up to a dozen or two.
	I want to see what these figures look like when the vertices are moved around on the sphere,
probably one at a time, constrained by certain rules.  I would like to see the sphere as a colored
surface with the lines standing out. I can specify the vertices by theta-phi or whatever. My main
concern is getting a good display, not the actual math. I will need to vary the point of view to
look at different parts of the sphere and maybe make an animation.
	The part I'm uncertain about is getting a sphere and the lines to show at the same time, and
how to choose whether the lines on the back side of the sphere are visible or not, so options should
be transparent vs. translucent vs. opaque sphere.
	Any suggestions will be welcome. Does anyone know if Trott's book on Mathematica display coding
covers this? If it will help, I'm willilng to buy it.

Steve Gray

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