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] How about: 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