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Re: extracting points and projecting

  • To: mathgroup at smc.vnet.net
  • Subject: [mg98120] Re: [mg98099] extracting points and projecting
  • From: "David Park" <djmpark at comcast.net>
  • Date: Tue, 31 Mar 2009 04:14:52 -0500 (EST)
  • References: <739352.1238406956778.JavaMail.root@m02>

The following code using the Presentations package will create the contours
and map them to the Riemann sphere. The Riemann sphere even has a north
pole, zero meridian and equator lightly marked (if you want). And tooltips
from the 2D graphics are also transferred to the Riemann sphere.

Needs["Presentations`Master`"]

Draw2D[
 {arg0contours =
   ComplexCartesianContour[
    Arg[Gamma[z]] == 0, {z, -10 - 10 I, 10 + 10 I},
    ContourLabels -> Automatic,
    PlotPoints -> 20,
    MaxRecursion -> 4]},
 Frame -> True, FrameLabel -> {Re, Im},
 PlotLabel -> Row[{Abs@Gamma[z] == 0}],
 ImageSize -> 300]

Draw3DItems[
 {ColoredRiemannSphere[],
  arg0contours // Normal // StereographicMap},
 ViewRiemann,
 ImageSize -> 300]

A PDF file and notebook for this should appear at the following site:

Peter Lindsay at the Mathematical Institute in the University of St Andrews
[ www.mcs.st-and.ac.uk  ] has kindly undertaken to maintain an archive that
provides downloadable notebooks and PDF files for various Presentations
solutions that have appeared on MathGroup.

 http://blackbook.mcs.st-and.ac.uk/~Peter/djmpark/html/ 


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


From: Cristina Ballantine [mailto:cballant at holycross.edu] 

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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