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MathGroup Archive 2009

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extracting points and projecting

  • To: mathgroup at smc.vnet.net
  • Subject: [mg98099] extracting points and projecting
  • From: "Cristina Ballantine" <cballant at holycross.edu>
  • Date: Mon, 30 Mar 2009 04:42:57 -0500 (EST)

I would like to extract the points from the following ContourPlot

g=ContourPlot[Arg[Gamma[x + I*y]] == 0, {x, -10, 10}, {y, -10, 10}, PlotPoints -> 100]

I can do this with

pts = First@Cases[g, x_GraphicsComplex :> First[x]]

Then I would like to map this list of points onto the Riemann sphere. The projection is performed through

j1[x_, y_] := 2 x/(1 + x^2 + y^2)^2
j2[x_, y_] := 2 y/(1 + x^2 + y^2)^2
j3[x_, y_] := (-1 + x^2 + y^2)/(1 + x^2 + y^2)

I need to generate a list of three dimensional points (j1[x,y], j2[x,y], j2[x,y]) from pts and plot them. I am unable to generate the list of three dimensional points. Any help is very much appreciated.

Cristina


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