Polar 3D plot?

Community matplotlib-users
#1

I'm guessing this is currently impossible with the current mplot3d
functionality, but I was wondering if there was any way I could generate a
3d graph with r, phi, z coordinates rather than x, y, z?

The point is that I want to make a figure that looks like the following:
http://upload.wikimedia.org/wikipedia/commons/7/7b/Mexican_hat_potential_polar.svg

Using the x, y, z system, I end up with something that has long tails like
this:
http://upload.wikimedia.org/wikipedia/commons/4/44/Mecanismo_de_Higgs_PH.png

If I try to artificially cut off the data beyond some radius, I end up with
jagged edges that are not at all visually appealing.

I would appreciate any crazy ideas you can come up with.

Thanks,
Jeff

P.S. Code to produce the ugly jaggedness is included below:

···

-------------------------------------------------------
from mpl_toolkits.mplot3d import Axes3D
import matplotlib
import numpy as np
from matplotlib import cm
from matplotlib import pyplot as plt

step = 0.04
maxval = 1.0
fig = plt.figure()
ax = Axes3D(fig)
X = np.arange(-maxval, maxval, step)
Y = np.arange(-maxval, maxval, step)
X, Y = np.meshgrid(X, Y)
R = np.sqrt(X**2 + Y**2)
Z = ((R**2 - 1)**2) * (R < 1.25)
ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.jet)
ax.set_zlim3d(0, 1)
#plt.setp(ax.get_xticklabels(), visible=False)
ax.set_xlabel(r'$\phi_\mathrm{real}$')
ax.set_ylabel(r'$\phi_\mathrm{im}$')
ax.set_zlabel(r'$V(\phi)$')
ax.set_xticks([])
plt.show()

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#2

I don't see a reason why this can't be implemented. It is probably pretty simple to change the surface plot code to use a polar grid instead of a rectangular grid. Of course this won't change the look of the rectangular axes, but maybe that is not a problem.

I invite you to take a shot at implementing this. You will find the mplot3d code pretty straightforward. (And a lot smaller than you might expect).

-Ben

···

-----Original Message-----
From: klukas [mailto:klukas@…150…]
Sent: Wednesday, March 17, 2010 4:34 PM
To: matplotlib-users@lists.sourceforge.net
Subject: [Matplotlib-users] Polar 3D plot?

I'm guessing this is currently impossible with the current mplot3d functionality, but I was wondering if there was any way I could generate a 3d graph with r, phi, z coordinates rather than x, y, z?

The point is that I want to make a figure that looks like the following:
http://upload.wikimedia.org/wikipedia/commons/7/7b/Mexican_hat_potential_polar.svg

Using the x, y, z system, I end up with something that has long tails like
this:
http://upload.wikimedia.org/wikipedia/commons/4/44/Mecanismo_de_Higgs_PH.png

If I try to artificially cut off the data beyond some radius, I end up with jagged edges that are not at all visually appealing.

I would appreciate any crazy ideas you can come up with.

Thanks,
Jeff

P.S. Code to produce the ugly jaggedness is included below:

-------------------------------------------------------
from mpl_toolkits.mplot3d import Axes3D
import matplotlib
import numpy as np
from matplotlib import cm
from matplotlib import pyplot as plt

step = 0.04
maxval = 1.0
fig = plt.figure()
ax = Axes3D(fig)
X = np.arange(-maxval, maxval, step)
Y = np.arange(-maxval, maxval, step)
X, Y = np.meshgrid(X, Y)
R = np.sqrt(X**2 + Y**2)
Z = ((R**2 - 1)**2) * (R < 1.25)
ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.jet) ax.set_zlim3d(0, 1) #plt.setp(ax.get_xticklabels(), visible=False)
ax.set_xlabel(r'$\phi_\mathrm{real}$')
ax.set_ylabel(r'$\phi_\mathrm{im}$')
ax.set_zlabel(r'$V(\phi)$')
ax.set_xticks([])
plt.show()

–
View this message in context: http://old.nabble.com/Polar-3D-plot--tp27937798p27937798.html
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#3

Hi,

you can create your supporting points on a regular r, phi grid and
transform them then to cartesian coordinates:

from mpl_toolkits.mplot3d import Axes3D
import matplotlib
import numpy as np
from matplotlib import cm
from matplotlib import pyplot as plt
step = 0.04
maxval = 1.0
fig = plt.figure()
ax = Axes3D(fig)

# create supporting points in polar coordinates
r = np.linspace(0,1.25,50)
p = np.linspace(0,2*np.pi,50)
R,P = np.meshgrid(r,p)
# transform them to cartesian system
X,Y = R*np.cos(P),R*np.sin(P)

Z = ((R**2 - 1)**2)
ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.jet)
ax.set_zlim3d(0, 1)
ax.set_xlabel(r'$\phi_\mathrm{real}$')
ax.set_ylabel(r'$\phi_\mathrm{im}$')
ax.set_zlabel(r'$V(\phi)$')
ax.set_xticks([])
plt.show()

hth
Armin

klukas schrieb:

···

I'm guessing this is currently impossible with the current mplot3d
functionality, but I was wondering if there was any way I could generate a
3d graph with r, phi, z coordinates rather than x, y, z?

The point is that I want to make a figure that looks like the following:
http://upload.wikimedia.org/wikipedia/commons/7/7b/Mexican_hat_potential_polar.svg

Using the x, y, z system, I end up with something that has long tails like
this:
http://upload.wikimedia.org/wikipedia/commons/4/44/Mecanismo_de_Higgs_PH.png

If I try to artificially cut off the data beyond some radius, I end up with
jagged edges that are not at all visually appealing.

I would appreciate any crazy ideas you can come up with.

Thanks,
Jeff

P.S. Code to produce the ugly jaggedness is included below:

-------------------------------------------------------
from mpl_toolkits.mplot3d import Axes3D
import matplotlib
import numpy as np
from matplotlib import cm
from matplotlib import pyplot as plt

step = 0.04
maxval = 1.0
fig = plt.figure()
ax = Axes3D(fig)
X = np.arange(-maxval, maxval, step)
Y = np.arange(-maxval, maxval, step)
X, Y = np.meshgrid(X, Y)
R = np.sqrt(X**2 + Y**2)
Z = ((R**2 - 1)**2) * (R < 1.25)
ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.jet)
ax.set_zlim3d(0, 1)
#plt.setp(ax.get_xticklabels(), visible=False)
ax.set_xlabel(r'$\phi_\mathrm{real}$')
ax.set_ylabel(r'$\phi_\mathrm{im}$')
ax.set_zlabel(r'$V(\phi)$')
ax.set_xticks([])
plt.show()

--
Armin Moser
Institute of Solid State Physics
Graz University of Technology
Petersgasse 16
8010 Graz
Austria
Tel.: 0043 316 873 8477

#4

Hi Armin,

Thanks, I added it to the mplot3d examples.

Cheers,
Reinier

···

On Thu, Mar 18, 2010 at 3:46 PM, Armin Moser <armin.moser@...2495...> wrote:

Hi,

you can create your supporting points on a regular r, phi grid and
transform them then to cartesian coordinates:

from mpl_toolkits.mplot3d import Axes3D
import matplotlib
import numpy as np
from matplotlib import cm
from matplotlib import pyplot as plt
step = 0.04
maxval = 1.0
fig = plt.figure()
ax = Axes3D(fig)

# create supporting points in polar coordinates
r = np.linspace(0,1.25,50)
p = np.linspace(0,2*np.pi,50)
R,P = np.meshgrid(r,p)
# transform them to cartesian system
X,Y = R*np.cos(P),R*np.sin(P)

Z = ((R**2 - 1)**2)
ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.jet)
ax.set_zlim3d(0, 1)
ax.set_xlabel(r'$\phi_\mathrm{real}$')
ax.set_ylabel(r'$\phi_\mathrm{im}$')
ax.set_zlabel(r'$V(\phi)$')
ax.set_xticks([])
plt.show()

hth
Armin

klukas schrieb:

I'm guessing this is currently impossible with the current mplot3d
functionality, but I was wondering if there was any way I could generate a
3d graph with r, phi, z coordinates rather than x, y, z?

The point is that I want to make a figure that looks like the following:
http://upload.wikimedia.org/wikipedia/commons/7/7b/Mexican_hat_potential_polar.svg

Using the x, y, z system, I end up with something that has long tails like
this:
http://upload.wikimedia.org/wikipedia/commons/4/44/Mecanismo_de_Higgs_PH.png

If I try to artificially cut off the data beyond some radius, I end up with
jagged edges that are not at all visually appealing.

I would appreciate any crazy ideas you can come up with.

Thanks,
Jeff

P.S. Code to produce the ugly jaggedness is included below:

-------------------------------------------------------
from mpl_toolkits.mplot3d import Axes3D
import matplotlib
import numpy as np
from matplotlib import cm
from matplotlib import pyplot as plt

step = 0.04
maxval = 1.0
fig = plt.figure()
ax = Axes3D(fig)
X = np.arange(-maxval, maxval, step)
Y = np.arange(-maxval, maxval, step)
X, Y = np.meshgrid(X, Y)
R = np.sqrt(X**2 + Y**2)
Z = ((R**2 - 1)**2) * (R < 1.25)
ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.jet)
ax.set_zlim3d(0, 1)
#plt.setp(ax.get_xticklabels(), visible=False)
ax.set_xlabel(r'$\phi_\mathrm{real}$')
ax.set_ylabel(r'$\phi_\mathrm{im}$')
ax.set_zlabel(r'$V(\phi)$')
ax.set_xticks([])
plt.show()

--
Armin Moser
Institute of Solid State Physics
Graz University of Technology
Petersgasse 16
8010 Graz
Austria
Tel.: 0043 316 873 8477

------------------------------------------------------------------------------
Download Intel&#174; Parallel Studio Eval
Try the new software tools for yourself. Speed compiling, find bugs
proactively, and fine-tune applications for parallel performance.
See why Intel Parallel Studio got high marks during beta.
http://p.sf.net/sfu/intel-sw-dev
_______________________________________________
Matplotlib-users mailing list
Matplotlib-users@lists.sourceforge.net
https://lists.sourceforge.net/lists/listinfo/matplotlib-users

--
Reinier Heeres
Tel: +31 6 10852639