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Re: Implicit surface plotting

• To: mathgroup at christensen.cybernetics.net
• Subject: [mg1529] Re: Implicit surface plotting
• From: "Kenneth D. Ham" <hamkd at ornl.gov>
• Date: Sun, 25 Jun 1995 02:29:39 -0400
• Organization: Martin Marietta Energy Systems

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bengtmn at algonet.se (Bengt Mansson) wrote:
>How can I use Mathematica to plot surfaces implicitly given, eg an 
>ellipsoid x^2+2y^2+3z^2=1.
>
>Regards, Bengt M.
>
>
>
Try the following MMa Code to plot the ellipsoid:

Needs[ "Graphics`ContourPlot3D`"]
ContourPlot3D[ (X)^2 + 2 (Y)^2 + 3 (Z)^2 -1 ,{X,-2 ,2 },{Y,-1 ,1 },{Z,-1 ,1 
},PlotPoints->{17 ,9 ,9 },MaxRecursion->0,Axes->True];

The equation is assumed equal to zero as I have entered it. 

The real challenge in making the plot look right is setting the plot limits if you 
don't know them in advance. The numbers in PlotPoints combine with the plot limits 
for each variable to set the spacing of the "wireframe" independently in each 
dimension.