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MathGroup Archive 2006

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3D ContourGraphics alternative

  • To: mathgroup at smc.vnet.net
  • Subject: [mg65683] 3D ContourGraphics alternative
  • From: "vasil michev" <michev at gmail.com>
  • Date: Fri, 14 Apr 2006 04:32:07 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Hello,
I need to plot a function of 3 parameters, and later examine different
contours of it. To do so, I've already downloaded and tried
ImplicitPlot3D and ContourPlot3D, but once I have the plot, say

p1 = ImplicitPlot3D[z^2 == 1 - (2 - Sqrt[x^2 +
      y^2])^2, {x, -3, 3}, {y, -3, 3}, {z, -1, 1}, PlotPoints -> {15,
    15, 10}, Passes -> Automatic]

I want to be able to work with the 'pl1' plot. With the 'ordinary'
Plot3D command the outpur it SurfaceGraphics and I can convert it, or
immediately display N contours of it on a single plot using the
ContourGraphics function. For example:

Show[ContourGraphics[Out[80]], ColorFunction -> Hue,
ColorFunctionScaling ->
True, ContourShading -> False, Contours -> 11, PlotRange -> {{-10, 10},
{1, 10}, {0.39999, .4}}]

But when using ContourPlot3D or ImplicitPlot3D packages the output is
more general - Graphics3D, and I cant simply do the trick. Can anyone
help me out, is there any package that will do the trick or any other
way you can think of doing this? I tried making number of plots with
various limitation for z-range, say

Show[p1, PlotRange -> {-.00001, 0}, Axes -> True]

and that seems to do what I want, but problems occur when I try to
convert the output to "ordinary" Graphics object - the range/points are
all wrong, probalby scaled (they vary from 0 to 1 only)
(If you cant understand me just try the following:

p1 = ImplicitPlot3D[E^z Cos[x] == Cos[y], {x, -6, 6}, {y, -6, 6}, {z,
-6, 6}, PlotPoints -> {16, 16, 12}, Passes -> 4]
pp1 = Show[p1, PlotRange -> {-.00001, 0}, Axes -> True]
Show[Graphics[pp1], Axes -> True, PlotRange -> All]

and look at the later 2 graphs - they're not quite the same... any help
working around this will be much appretiated too)

thanks in advance for any help


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