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Topic: Re: [mg4908] help!! Plot3D of ellipsoid
Replies: 0

 Paul R. Wellin Posts: 14 Registered: 12/7/04
Re: [mg4908] help!! Plot3D of ellipsoid
Posted: Oct 7, 1996 1:57 AM

> I am trying to get a 3-d plot of an ellipsiod, of the equation
>
> (x^2/a^2) + (y^2/b^2) + (z^2/c^2) = 1
>
> manipulating the equation I can get
>
> z = (c^2 (1- (x^2/a^2) - (y^2/b^2)))^1/2
>
> then, with the constants defined, I write
>
> Plot3D[z,{x,0,a},{y,0,b}]
>
> Mathematica then spits out a bunch of errors

You will have to parametrize the surface. I'll leave the
details to you, but with a bit of work, you can parametrize
the ellipsoid as:

In[1]:=
ellipsoid[u_,v_] := {a Cos[u] Cos[v], b Sin[u] Cos[v], c Sin[v]}

Then you can generate your surface as:

In[2]:=
a = 1;
b = 1;
c = 2;
ParametricPlot3D[ellipsoid[u, v],
{u, 0, 2 Pi}, {v, -Pi/2, Pi/2}]

Out[2]= -Graphics3D-

You can fiddle with the parameters to get stretch the ellipse
in the x, y, or z directions.

---
Paul Wellin
Wolfram Research, Inc.
Champaign, IL 61820

phone: 217-398-0700
fax: 217-398-0747
email: wellin@wolfram.com