Re: extracting points and projecting

*To*: mathgroup at smc.vnet.net*Subject*: [mg98127] Re: [mg98099] extracting points and projecting*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Tue, 31 Mar 2009 04:16:12 -0500 (EST)*Reply-to*: hanlonr at cox.net

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); {j1[##], j2[##], j3[##]} & @@@ {{x1, y1}, {x2, y2}, {x3, y3}} {{(2*x1)/(x1^2 + y1^2 + 1)^2, (2*y1)/(x1^2 + y1^2 + 1)^2, (x1^2 + y1^2 - 1)/ (x1^2 + y1^2 + 1)}, {(2*x2)/(x2^2 + y2^2 + 1)^2, (2*y2)/(x2^2 + y2^2 + 1)^2, (x2^2 + y2^2 - 1)/ (x2^2 + y2^2 + 1)}, {(2*x3)/(x3^2 + y3^2 + 1)^2, (2*y3)/(x3^2 + y3^2 + 1)^2, (x3^2 + y3^2 - 1)/ (x3^2 + y3^2 + 1)}} pts3D = {j1[##], j2[##], j3[##]} & @@@ pts; ListPointPlot3D[pts3D, PlotRange -> Full, ImageSize -> 600] Bob Hanlon ---- 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