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] == 0,
	y[0] == 1,
	z[0] == 0
 	}
 sol = NDSolve[ eq, {x,y,z} , {t, 0, tmax}, 
	MaxSteps -> 5000, StartingStepSize -> 0.001]
 ParametricPlot3D[ Evaluate[{x[t], y[t], z[t]} /. sol[[1]] ], {t,0,tmax}, 
	PlotRange -> All  ]
 ParametricPlot[ Evaluate[{z[t], x[t]} /. sol[[1]] ], {t,0,tmax} , 
	PlotRange -> All ]
 ParametricPlot[ Evaluate[{z[t], y[t]} /. sol[[1]] ], {t,0,tmax} , 
	PlotRange -> All ]
 ParametricPlot[ Evaluate[{x[t], y[t]} /. sol[[1]] ], {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