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MathGroup Archive 1992

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QuadricSurface and ConicSection

  • To: Mathematica user's group <MathGroup at yoda.physics.unc.edu>
  • Subject: QuadricSurface and ConicSection
  • From: Robby Villegas <Villegas at knox.bitnet>
  • Date: Thursday, January 16, 1992

Richard Christensen <richard at wombat.ee.byu.edu> asked about plotting quadric
surfaces.

     I have a package, QuadricSurface.m, that will take any quadric
polynomial, with or without mixed terms y z, x z, x y, and produce a plot of
the surface after diagonalizing the quadratic and performing translations.  It
also prints a canonical form of the equation in the rotated and translated
coordinate system, and returns a variable QuadricID[] that identifies the type
of quadric, like Hyperboloid1 for "hyperboloid of one sheet", represents the
canonical equation in a list-format, and gives the basis vectors for the
rotated coordinate system along with the translations with respect to the
rotated axes.  This is so the user can have a package of data to
refer to in subsequent computations or plots, such as if the a, b, and c of
v^2/b^2 + w^2/c^2 = u^2/a^2 - 1 need to be known later, or the coordinate
system is desired, or whatever.  Graphically, the coordinate system is
represented by three line segments with arrow heads, red for the first
variable, green for the second, and blue for the third.

     If anyone is interested in this package, I will send it, though I'm
not quite good at file transfers from Macs or NeXT's to our VAX yet.  Also,
there's an equivalent program for the two-dimensional analogues,
ConicSection.m.  Both of these programs run on the Mac and the NeXT.

                                        Robby Villegas
                                        Knox College
                                        E:  Villegas at Knox.Bitnet





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