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Re: implicit surfaces from older version of Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg119674] Re: implicit surfaces from older version of Mathematica
• From: Roger Bagula <roger.bagula at gmail.com>
• Date: Fri, 17 Jun 2011 00:08:08 -0400 (EDT)
• References: <201106071047.GAA05975@smc.vnet.net> <isnllv$n7h$1@smc.vnet.net>

Heike Gramberg
Thanks.
If you put in a Mesh->False,
you get a pretty surface:
d = {{z, -x, 0, 0, 0}, {x, 0, -y, 0, 0}, {0, y, 0, -z, 0}, {0, 0, z,
    0, -y}, {0, 0, 0, y, -x}};
m2 = d.Transpose[d]
ContourPlot3D[
 Evaluate[(Det[d] Sqrt[Tr[m2]] /. z -> -kz)], {x, -Pi, Pi}, {y, -Pi,
  Pi}, {kz, -Pi, Pi}, PlotPoints -> 15, MaxRecursion -> 1,
 Contours -> {-1, 1}, Boxed -> False, Axes -> False, Mesh -> False]
The anti-diagonal I associate with space and the diagonal Killing
vectors with time.
So making time constant:
d = {{1, -x, 0, 0, 0}, {x, 0, -y, 0, 0}, {0, y, 0, -z, 0}, {0, 0, z,
    0, -y}, {0, 0, 0, y, -1}};
m2 = d.Transpose[d]
ContourPlot3D[
 Evaluate[(Det[d] Sqrt[Tr[m2]] /. z -> -kz)], {x, -Pi, Pi}, {y, -Pi,
  Pi}, {kz, -Pi, Pi}, PlotPoints -> 15, MaxRecursion -> 1,
 Contours -> {-1, 1}, Boxed -> False, Axes -> False, Mesh -> False]
Gives a surface with a four fold/ C4rotation axis.
Roger Bagula

• References:
  • implicit surfaces from older version of Mathematica
    • From: Roger Bagula <roger.bagula@gmail.com>