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MathGroup Archive 1992

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Re: Plotting Quadric Surfaces

  • To: mathgroup-adm at yoda.physics.unc.edu
  • Subject: Re: Plotting Quadric Surfaces
  • From: Silvio Levy <levy at math.berkeley.edu>
  • Date: Thu, 16 Jan 92 12:21:13 PST

Richard Christensen asks:

> Does anyone know an easy was to plot a Quadric surface in the form
> Ax^2 + By^2 + Cz^2 + Exy + Fxz + Gyz = 1.

Well, parametric plotting is much easier than implicit plotting.
So I suggest you find the eigenvalues and eigenvectors of the matrix

A    E/2  F/2
E/2  B    G/2
G/2  F/2  C

The eigenvalues give the directions of the axes of the ellipsoid, the
eigenvectors are the inverses of the semiaxes.  Normalize the axes so
they have the right length (call them e1, e2, e3), then apply
ParametricPlot3D to the surface:

e1 Cos[phi] + e2 Sin[phi]Sin[theta] + e3 Sin[phi]Cos[theta]

Silvio





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