Re: Re: extracting points and projecting

• To: mathgroup at smc.vnet.net
• Subject: [mg98163] Re: [mg98150] Re: [mg98099] extracting points and projecting
• From: "David Park" <djmpark at comcast.net>
• Date: Wed, 1 Apr 2009 05:55:19 -0500 (EST)
• References: <200903300942.EAA08024@smc.vnet.net> <833158.1238493917058.JavaMail.root@m02>

```However, the mapping given by the original poster is not the correct mapping
to the Riemann sphere. I believe it should be:

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

And why settle for Points when you can have lines?

David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/

From: DrMajorBob [mailto:btreat1 at austin.rr.com]

g = ContourPlot[Arg[Gamma[x + I*y]] == 0, {x, -10, 10}, {y, -10, 10},
PlotPoints -> 100]
pts = First@Cases[g, x_GraphicsComplex :> First[x]];

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)

Timing[one = pts /. {x_, y_} :> {j1[x, y], j2[x, y], j3[x, y]};]

{0.127167, Null}

one // Dimensions

{8146, 3}

Graphics3D[Point@one]

or

Timing[two = Outer[#2 @@ #1 &, pts, {j1, j2, j3}, 1, 1];]

{0.171188, Null}

one == two

True

Bobby

On Mon, 30 Mar 2009 04:42:57 -0500, Cristina Ballantine
<cballant at holycross.edu> 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
>

--
DrMajorBob at bigfoot.com

```

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