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MathGroup Archive 2001

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RE: ImplicitPlot3d

  • To: mathgroup at smc.vnet.net
  • Subject: [mg32022] RE: [mg32006] ImplicitPlot3d
  • From: "Wolf, Hartmut" <Hartmut.Wolf at t-systems.de>
  • Date: Wed, 19 Dec 2001 04:28:57 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

> -----Original Message-----
> From:	Daniel Meisel [SMTP:Daniel.Meisel at Physik.UNI-Karlsruhe.de]
To: mathgroup at smc.vnet.net
> Sent:	Tuesday, December 18, 2001 8:34 AM
> To:	mathgroup at smc.vnet.net
> Subject:	[mg32006] ImplicitPlot3d
> 
> Hi,
> 
> I'm searching for a way to plot for example the equation
> 
> x^2 + y^2 + z^2 =1
> 
> ( a sphere around the origin with radius 1) in 3d.
> 
> I cannot use the parametric plot command.
> 
> thanks in advance
> 
[Hartmut Wolf]  

Daniel, as I read your problem, you want to know from where to get the
package ImplictPlot3D. It is ever rewarding to start a search at
http://www.mathsource.com/
It will return
http://www.mathsource.com/Content/Enhancements/Graphics/3D/0203-409 
the package and illustrations. 

If you put the package into 
"C:\Programme\Wolfram
Research\Mathematica\4.1\AddOns\StandardPackages\Graphics" 
and then load

<<Graphics`ImplicitPlot3D`

?ImplicitPlot3D

"ImplicitPlot3D[eqn,{x,a,b},{y,c,d},{z,e,f}] draws a graph of the set of
points with coordinates (x,y,z) in the box a2x2b, c2y2d, e2z2f that satisfy
the equation eqn.
ImplicitPlot3D[func,{x,a,b},{y,c,d},{z,e,f}] draws a graph of the set of
points with coordinates (x,y,z) in the box a2x2b, c2y2d, e2z2f that satisfy
the equation func = 0."

you may plot the sphere:

ImplicitPlot3D[x^2+y^2+z^2-1,{x,-1,1},{y,-1,1},{z,-1,1}]//Timing

{54.038 Second, -Graphics3D-}

There are options

Options[ImplicitPlot3D]

{Compiled -> True, PlotPoints -> {{5,5,5},{3,3,3}},
  Passes -> Automatic} 

I couldn't see any effect from changing passes. However explicitly including
the subdivision into PlotPoints, e.g.

PlotPoints -> {{4},{3},{3}}

works. But beware of the calculation time!

PlotPoints -> {{5},{3}} is equivalent to PlotPoints -> {{5,5,5},{3,3,3}},
etc.



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