       ParametricPlot Remark

• To: mathgroup at smc.vnet.net
• Subject: [mg7177] ParametricPlot Remark
• From: Andrei Constantinescu <constant at athena.polytechnique.fr>
• Date: Wed, 14 May 1997 01:11:12 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

``` Hellow !

... so I just remarked a pretty unusual thing with ParametricPlot / 3D ,
and theirs Automatic PlotPoints number !

So lets resume:

ParametricPlot  - works fine giving nice smooth courbes ,

wether

ParametricPlot3D - samples largely giving a pretty zigzag form !

SURE , I can be fitted by hand, ... and I did it ! But does someone
understand why this happens ?

You have bellow a sample program of the Lorenz Equations in order to
test it !

Have fun !

a + andrei

s = 10;
b = 8/3;
r = 167;

tmax = 10;

eq = {
x'[t] == s ( y[t] - x[t] ),
y'[t] == r x[t] - y[t] - x[t] z[t],
z'[t] == - b z[t] + x[t] y[t],
x == 0,
y == 1,
z == 0
}

sol = NDSolve[ eq, {x,y,z} , {t, 0, tmax},
MaxSteps -> 5000, StartingStepSize -> 0.001]

ParametricPlot3D[ Evaluate[{x[t], y[t], z[t]} /. sol[] ], {t,0,tmax},
PlotRange -> All  ]
ParametricPlot[ Evaluate[{z[t], x[t]} /. sol[] ], {t,0,tmax} ,
PlotRange -> All ]
ParametricPlot[ Evaluate[{z[t], y[t]} /. sol[] ], {t,0,tmax} ,
PlotRange -> All ]
ParametricPlot[ Evaluate[{x[t], y[t]} /. sol[] ], {t,0,tmax} ,
PlotRange -> All ]

______________________________________________________________________
Andrei Constantinescu               constant at athena.polytechnique.fr

LMS Ecole Polytechnique                  tel:   (33)-1-69.33.33.30
91128 PALAISEAU cedex - FRANCE           fax:   (33)-1-69.33.30.26

```

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