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MathGroup Archive 1996

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Re: Re: Help with ParametricPlot3D in color

  • To: mathgroup at smc.vnet.net
  • Subject: [mg4556] Re: [mg4480] Re: Help with ParametricPlot3D in color
  • From: tzeller (Tom Zeller)
  • Date: Wed, 7 Aug 1996 04:18:04 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

>ivan at nauplius.rsmas.miami.edu (Ivan Lima) wrote:
>
>>I'm trying to plot some phase portraits of a three-dimensional system
>>with ParametricPlot3D and I'd like it to plot the lines in
>>color. After two days looking at the manuals I can't find any way to
>>do that. Does anybody know how to do that?  Sorry for posting such a
>>stupid question. I'm kind of new to Mathematica graphics and any
>>help will be appreciated
>
>>Bellow are the commands I'm using.
>
>>ParametricPlot3D[Evaluate[{x[t],y[t],z[t]} /. %],
>>                          {t, 100, 20000}, PlotPoints -> 20000,
>>                           PlotRange -> {{0, 6}, {0, 2}, {0, 1}},
>>                           ColorOutput -> RGBColor,
>>                           ViewPoint -> {1.3, 2.4, 2.}]
>

ParametricPlot3D can treat a color function value as a fourth "dimension"
(see Wickham-Jones, Mathematica Graphics pp 209).  His example (with a
simplified
argument to the color function and automatic PlotPoints ) is

 ParametricPlot3D[{r Sin[t], r Cos[t], -r^3 Sin[3 t], Hue[r]},
                   {r,0,1}, {t, 0, 2 Pi}, Lighting -> False]

Turning off the Lighting option is important.


Perhaps something like:

ParametricPlot3D[Evaluate[{x[t],y[t],z[t], Hue[arg]} /. %],
                          {t, 100, 20000}, PlotPoints -> 20000,
                           PlotRange -> {{0, 6}, {0, 2}, {0, 1}},
                           ViewPoint -> {1.3, 2.4, 2.}]

where arg is some osterization of t.  A simple arg would be t (or t/20000
if you only wanted about 1 cycle of Hue's colors).   Haven't tried it but
it should work.

Tom Zeller

Technical Support
Wolfram Research



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