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Topic: Re: [mg4480] Re: Help with ParametricPlot3D in color
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Tom Zeller

Posts: 3
Registered: 12/11/04
Re: [mg4480] Re: Help with ParametricPlot3D in color
Posted: Aug 1, 1996 2:07 AM
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> (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
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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