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Re: implicit surfaces from older version of Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg119639] Re: implicit surfaces from older version of Mathematica
• From: Heike Gramberg <heike.gramberg at gmail.com>
• Date: Wed, 15 Jun 2011 07:21:40 -0400 (EDT)
• References: <201106071047.GAA05975@smc.vnet.net> <isnllv$n7h$1@smc.vnet.net> <201106141013.GAA06207@smc.vnet.net>

This seems to work better:

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]

I'm using the fact that Det[m2]==(Det[d])^2 which means Det[m2] =
Tr[m2]==1 is equivalent
to Det[d] Sqrt[Tr[m2]]==-1 or Det[d] Sqrt[Tr[m2]]==1.

Heike.

On 14 Jun 2011, at 11:13, Roger Bagula wrote:

> Heike Gramberg,
> Thank you for your help.
> I have done some further experiments using your forms.
> I have trouble with edges of the surfaces,
> even when I get them connected right:
> Clear[ x, y, z, f, g, FermiPlot,d,d,d1,m2]
> 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]
> f[x_, y_, z_] = Det[m2]*Tr[m2] - 1
> ContourPlot3D[
> f[kx, ky, -kz], {kx, -Pi, Pi}, {ky, -Pi, Pi}, {kz, -Pi, Pi},
> PlotPoints -> 30, Contours -> {0.000001}, Boxed -> False,
> Axes -> False]
> FermiPlot[energy_] :=
>  ContourPlot3D[
>   f[kx, ky, -kz], {kx, -Pi, Pi}, {ky, -Pi, Pi}, {kz, -Pi, Pi},
>   PlotPoints -> 20, Contours -> {energy}, Boxed -> False,
>   Axes -> False];
> Row[Show[FermiPlot[0.000001], ViewPoint -> #,
>    ImageSize -> 300] & /@ {{0, -0.045, 3.384}, {0.009, -3.331,
>    0.597}, {-3.329, 0.088, 0.597}}]
> (* decomposition matrix in Killing's vectors*)
> d1 = {{1, -1, 0, 0, 0},
>   {1, 0, -1, 0, 0},
>   {0, 1, 0, -1, 0},
>   {0, 0, 1, 0, -1},
>   {0, 0, 0, 1, -1}};
> (* Cartan Matrix:)
> c = d1.Transpose[d1]
>
> Roger Bagula
>

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