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MathGroup Archive 1998

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Re: Contour Plotting on a sphere

  • To: mathgroup at smc.vnet.net
  • Subject: [mg15270] Re: Contour Plotting on a sphere
  • From: weber at math.uni-bonn.de (Matthias Weber)
  • Date: Thu, 31 Dec 1998 04:39:27 -0500
  • Organization: RHRZ - University of Bonn (Germany)
  • References: <76cih0$o3s@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

In article <76cih0$o3s at smc.vnet.net>, Rangachari Kidambi
<rkidambi at spock.usc.edu> wrote:

> Hi,
> 
> I want to plot contours of a function f(theta,phi), where theta and phi
> are standard spherical polar coordinates. These contours will be curves
> on the surface of a sphere. Can Mathematica do such a plot? If yes,
> how? As far as i know, Mathematica can do only contours of f(x,y) where
> x,y are cartesian coordinates. Thanks for any help.
> 
> Sincerely,
> Ranga Kidambi

Use stereographic projection or any other (mostly) bijective map to the
sphere to do a 2-dimensional ImplicitPlot (from Graphics`ImplicitPlot`)
of f[StereoGraphic[x,y]]. In other words, do the ImplicitPlot in your
coordinate domain.
The result is a Graphics object to which you can apply the inverse
stereographic projection as in

gr2d=ImplicitPlot[f[StereoGraphic[x,y]]==0,{x,-4,4},{y,-4,4}];

gr3d=Graphics3D[gr2d[[1]]/. {x_Real,y_}:>InverseStereoGraphic[x,y]];


I hope this helps,

Matthias


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