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| Started by | Heike Gramberg <heike.gramberg@gmail.com> |
|---|---|
| First post | 2011-06-08 11:16 +0000 |
| Last post | 2011-06-22 07:57 +0000 |
| Articles | 6 — 2 participants |
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Re: implicit surfaces from older version of Mathematica Heike Gramberg <heike.gramberg@gmail.com> - 2011-06-08 11:16 +0000
Re: implicit surfaces from older version of Mathematica Roger Bagula <roger.bagula@gmail.com> - 2011-06-14 10:13 +0000
Re: implicit surfaces from older version of Mathematica Heike Gramberg <heike.gramberg@gmail.com> - 2011-06-15 11:21 +0000
Re: implicit surfaces from older version of Mathematica Roger Bagula <roger.bagula@gmail.com> - 2011-06-17 04:08 +0000
Re: implicit surfaces from older version of Mathematica Roger Bagula <roger.bagula@gmail.com> - 2011-06-22 07:43 +0000
Re: implicit surfaces from older version of Mathematica Roger Bagula <roger.bagula@gmail.com> - 2011-06-22 07:57 +0000
| From | Heike Gramberg <heike.gramberg@gmail.com> |
|---|---|
| Date | 2011-06-08 11:16 +0000 |
| Subject | Re: implicit surfaces from older version of Mathematica |
| Message-ID | <isnllv$n7h$1@smc.vnet.net> |
If it's only the last three plots you're interested in, you can do
something like
FermiPlot[energy_] :=
ContourPlot3D[
f[kx, ky, -kz], {kx, -Pi/2, Pi/2}, {ky, -Pi/2, Pi/2}, {kz, -Pi/2,
Pi/2}, 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}}]
Heike
On 7 Jun 2011, at 11:47, Roger Bagula wrote:
> This version was developed in version 3 ( I think)
> and was really slow and took up too much memory...
> It works in version 8, but there has to be an easier way...
> Pictures are pretty in 8 and it has the real time effect build it
> where you don't need all the views.
>
> (* <<Graphics`ContourPlot3D`*)
> Clear[A, B, c, rho, x, y, z, f, g, FermiPlot, p, t]
> Clear[g, gg, a, p, q, r, x, y, z, x0, y0, z0]
>
> m = {{x, y, z, 0},
> {y, z, 0, -x},
> {z, 0, -x, -y},
> {0, -x, -y, -z}}
> f[x_, y_, z_] = ExpandAll[Det[m] - 1]
>
> FermiPlot[energy_]:=
> ContourPlot3D[
> f[kx,ky,-kz],
> {kx,-0.001, -Pi/2+0.001},{ky, -0.001, -Pi/2+0.001},{kz,
> -0.001, -Pi/2+0.001},PlotPoints->6,
> Contours -> {energy},Boxed->False];
> g1 = FermiPlot[0.000001]
>
> FermiPlot[energy_]:=
> ContourPlot3D[
> f[kx,ky,-kz],
> {kx,0.001, Pi/2-0.001},{ky, 0.001, Pi/2-0.001},{kz, 0.001, Pi/
> 2-0.001},PlotPoints->6,
> Contours -> {energy}];
> g2 = FermiPlot[0.000001]
>
> FermiPlot[energy_] :=
> ContourPlot3D[
> f[kx, ky, -kz],
> {kx, 0.001, Pi/2 - 0.001}, {ky, -0.001, -Pi/2 + 0.001},
> {kz, -0.001, -Pi/2 + 0.001}, PlotPoints -> 6,
> Contours -> {energy}];
> g3 = FermiPlot[0.000001]
>
> FermiPlot[energy_] :=
> ContourPlot3D[
> f[kx, ky, -kz],
> {kx, 0.001, Pi/2 - 0.001}, {ky, 0.001, Pi/2 - 0.001}, {kz,
> -0.001, -Pi/2 + 0.001}, PlotPoints -> 6,
> Contours -> {energy}];
> g4 = FermiPlot[0.000001]
>
> FermiPlot[energy_] :=
> ContourPlot3D[
> f[kx, ky, -kz],
> {kx, -0.001, -Pi/2 + 0.001}, {ky, -0.001, -Pi/2 + 0.001},
> {kz, 0.001, Pi/2 - 0.001}, PlotPoints -> 6,
> Contours -> {energy}];
> g5 = FermiPlot[0.000001]
>
> FermiPlot[energy_] :=
> ContourPlot3D[
> f[kx, ky, -kz],
> {kx, -0.001, -Pi/2 + 0.001}, {ky, 0.001, Pi/2 - 0.001},
> {kz, -0.001, -Pi/2 + 0.001}, PlotPoints -> 6,
> Contours -> {energy}];
> g6 = FermiPlot[0.000001]
>
> FermiPlot[energy_] :=
> ContourPlot3D[
> f[kx, ky, -kz],
> {kx, 0.001, Pi/2 - 0.001}, {ky, -0.001, -Pi/2 + 0.001},
> {kz, 0.001, Pi/2 - 0.001}, PlotPoints -> 6,
> Contours -> {energy}];
> g7 = FermiPlot[0.000001]
> FermiPlot[energy_] :=
> ContourPlot3D[
> f[kx, ky, -kz],
> {kx, -0.001, -Pi/2 + 0.001}, {ky, 0.001, Pi/2 - 0.001},
> {kz, 0.001, Pi/2 - 0.001}, PlotPoints -> 6,
> Contours -> {energy}];
> g8 = FermiPlot[0.000001]
> ga = Show[{g1, g2, g3, g4, g5, g6, g7, g8}, Boxed -> False, PlotRange \
> [Rule] All, Axes \[Rule] False]
> Show[{g1, g2, g3, g4, g5, g6, g7, g8}, ViewPoint -> {0.000, -0.045,
> 3.384}, PlotRange \[Rule] All, Axes \[Rule] False]
> Show[{g1, g2, g3, g4, g5, g6, g7, g8}, ViewPoint -> {0.009, -3.331,
> 0.597}, Boxed -> False, PlotRange \[Rule] All, Axes \[Rule] False]
> Show[{g1, g2, g3, g4, g5, g6, g7, g8}, ViewPoint -> {-3.329, 0.088,
> 0.597}, Boxed -> False, PlotRange \[Rule] All, Axes \[Rule] False]
>
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| From | Roger Bagula <roger.bagula@gmail.com> |
|---|---|
| Date | 2011-06-14 10:13 +0000 |
| Message-ID | <it7c8q$61t$1@smc.vnet.net> |
| In reply to | #3027 |
Heike Gramberg,
Thank you for your help.
I have done some further experiments using your forms.
I have trouble with edges of the surfaces,
even when I get them connected right:
Clear[ x, y, z, f, g, FermiPlot,d,d,d1,m2]
d = {{z, -x, 0, 0, 0},
{x, 0, -y, 0, 0},
{0, y, 0, -z, 0},
{0, 0, z, 0, -y},
{0, 0, 0, y, -x}};
m2 = d.Transpose[d]
f[x_, y_, z_] = Det[m2]*Tr[m2] - 1
ContourPlot3D[
f[kx, ky, -kz], {kx, -Pi, Pi}, {ky, -Pi, Pi}, {kz, -Pi, Pi},
PlotPoints -> 30, Contours -> {0.000001}, Boxed -> False,
Axes -> False]
FermiPlot[energy_] :=
ContourPlot3D[
f[kx, ky, -kz], {kx, -Pi, Pi}, {ky, -Pi, Pi}, {kz, -Pi, Pi},
PlotPoints -> 20, Contours -> {energy}, Boxed -> False,
Axes -> False];
Row[Show[FermiPlot[0.000001], ViewPoint -> #,
ImageSize -> 300] & /@ {{0, -0.045, 3.384}, {0.009, -3.331,
0.597}, {-3.329, 0.088, 0.597}}]
(* decomposition matrix in Killing's vectors*)
d1 = {{1, -1, 0, 0, 0},
{1, 0, -1, 0, 0},
{0, 1, 0, -1, 0},
{0, 0, 1, 0, -1},
{0, 0, 0, 1, -1}};
(* Cartan Matrix:)
c = d1.Transpose[d1]
Roger Bagula
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| From | Heike Gramberg <heike.gramberg@gmail.com> |
|---|---|
| Date | 2011-06-15 11:21 +0000 |
| Message-ID | <ita4ju$mbn$1@smc.vnet.net> |
| In reply to | #3027 |
This seems to work better:
ContourPlot3D[
Evaluate[(Det[d] Sqrt[Tr[m2]] /. z -> -kz)], {x, -Pi, Pi}, {y, -Pi,
Pi}, {kz, -Pi, Pi}, PlotPoints -> 15, MaxRecursion -> 1,
Contours -> {-1, 1}, Boxed -> False, Axes -> False]
I'm using the fact that Det[m2]==(Det[d])^2 which means Det[m2] =
Tr[m2]==1 is equivalent
to Det[d] Sqrt[Tr[m2]]==-1 or Det[d] Sqrt[Tr[m2]]==1.
Heike.
On 14 Jun 2011, at 11:13, Roger Bagula wrote:
> Heike Gramberg,
> Thank you for your help.
> I have done some further experiments using your forms.
> I have trouble with edges of the surfaces,
> even when I get them connected right:
> Clear[ x, y, z, f, g, FermiPlot,d,d,d1,m2]
> d = {{z, -x, 0, 0, 0},
> {x, 0, -y, 0, 0},
> {0, y, 0, -z, 0},
> {0, 0, z, 0, -y},
> {0, 0, 0, y, -x}};
> m2 = d.Transpose[d]
> f[x_, y_, z_] = Det[m2]*Tr[m2] - 1
> ContourPlot3D[
> f[kx, ky, -kz], {kx, -Pi, Pi}, {ky, -Pi, Pi}, {kz, -Pi, Pi},
> PlotPoints -> 30, Contours -> {0.000001}, Boxed -> False,
> Axes -> False]
> FermiPlot[energy_] :=
> ContourPlot3D[
> f[kx, ky, -kz], {kx, -Pi, Pi}, {ky, -Pi, Pi}, {kz, -Pi, Pi},
> PlotPoints -> 20, Contours -> {energy}, Boxed -> False,
> Axes -> False];
> Row[Show[FermiPlot[0.000001], ViewPoint -> #,
> ImageSize -> 300] & /@ {{0, -0.045, 3.384}, {0.009, -3.331,
> 0.597}, {-3.329, 0.088, 0.597}}]
> (* decomposition matrix in Killing's vectors*)
> d1 = {{1, -1, 0, 0, 0},
> {1, 0, -1, 0, 0},
> {0, 1, 0, -1, 0},
> {0, 0, 1, 0, -1},
> {0, 0, 0, 1, -1}};
> (* Cartan Matrix:)
> c = d1.Transpose[d1]
>
> Roger Bagula
>
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| From | Roger Bagula <roger.bagula@gmail.com> |
|---|---|
| Date | 2011-06-17 04:08 +0000 |
| Message-ID | <itejvd$s3f$1@smc.vnet.net> |
| In reply to | #3027 |
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
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| From | Roger Bagula <roger.bagula@gmail.com> |
|---|---|
| Date | 2011-06-22 07:43 +0000 |
| Message-ID | <its6f4$5uq$1@smc.vnet.net> |
| In reply to | #3136 |
Folium substitution: the x and y are used as
folium variables.
x = 3*t/(1 + t^3); y = 3*t^2/(1 + t^3);
d = (1 + t^3)*{{z, -x, 0, 0},
{x, 0, -y, 0},
{0, -y, 0, z},
{0, 0, -z, t1}};
m2 = d.Transpose[d]
f[t_, t1_, z_] = ExpandAll[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, Mesh -> False]
This works but only slowly.
Roger Bagula
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| From | Roger Bagula <roger.bagula@gmail.com> |
|---|---|
| Date | 2011-06-22 07:57 +0000 |
| Message-ID | <its78j$66a$1@smc.vnet.net> |
| In reply to | #3136 |
Folium substitution: the x and y are used as
folium variables.
x = 3*t/(1 + t^3); y = 3*t^2/(1 + t^3);
d = (1 + t^3)*{{z, -x, 0, 0},
{x, 0, -y, 0},
{0, -y, 0, z},
{0, 0, -z, t1}};
m2 = d.Transpose[d]
f[t_, t1_, z_] = ExpandAll[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, Mesh -> False]
This works but only slowly.
Roger Bagula
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