Re: extracting points and projecting

• To: mathgroup at smc.vnet.net
• Subject: [mg98114] Re: extracting points and projecting
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Mon, 30 Mar 2009 05:19:50 -0500 (EST)
• Organization: Uni Leipzig
• References: <gqq3s0\$7ml\$1@smc.vnet.net>

```Hi,

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

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)

toSphere[{x_, y_}] := {j1[x, y], j2[x, y], j3[x, y]}

and

Graphics3D[
g[[1]] /. GraphicsComplex[pnts_, more_, ___] :>
GraphicsComplex[toSphere /@ pnts, more]]

Regards
Jens

Cristina Ballantine wrote:
> 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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