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MathGroup Archive 2002

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Re: 3D plot

  • To: mathgroup at smc.vnet.net
  • Subject: [mg36371] Re: 3D plot
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Wed, 4 Sep 2002 02:56:25 -0400 (EDT)
  • Organization: Universitaet Leipzig
  • References: <al1ib1$kue$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

the volume is 0 because you get two points

Solve[{y == 4 - x^2, y == 3x}, {x, y}]

{{y -> -12, x -> -4}, {y -> 3, x -> 1}}

with
{{y -> -12, x -> -4,z->20}, {y -> 3, x -> 1,z -> 5}}

To get a nonzero volume you neeed a singel implicit equation like

0==f[x,y,z]

or you need 3 parametric equations

{ x==f[1][u,v],
  y==f[2][u,v],
  z==f[3][u,v]}

If you have an implicit equation you can compute the
surface with MathGL3d's MVContourPlot3D[] (not with
the ContourPlot3D[] from the standard addons, because
you need a consistent oriented surface) and than you 
can triangulate the surface an sum the signed voulmes
of the tetrahedrons build from the triangles and a 
fixed point in space.

For parametric surfaces you can do the same with the 
polygons.

Regards
  Jens


Shz Shz Oon wrote:
> 
> Can I use Mathematica to find out the volumn of this 3 dimensional object from
> the equations :
> 
> z=x^2 +4, y=4-x^2, y=3x
> 
> Thanks in advance!
> Shz Shz


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