Question

I need to generate a stack of 2D polar plots (a 3D cylindrical plot) so that I can view a distorted cylinder. I want to use matplotlib since I already have it installed and want to distribute my code to others who only have matplotlib. For example, say I have a bunch of 2-D arrays. Is there any way I can do this without having to download an external package? Here’s my code.

#!usr/bin/env python
import matplotlib.pyplot as plt
import numpy as np

x = np.arange(-180.0,190.0,10)
theta = (np.pi/180.0 )*x    # in radians

A0 = 55.0
offset = 60.0

R = [116.225,115.105,114.697,115.008,115.908,117.184,118.61,119.998,121.224,122.216,\
122.93,123.323,123.343,122.948,122.134,120.963,119.575,118.165,116.941,116.074,115.66\
,115.706,116.154,116.913,117.894,119.029,120.261,121.518,122.684,123.594,124.059,\
123.917,123.096,121.661,119.821,117.894,116.225]

fig = plt.figure()
ax = fig.add_axes([0.1,0.1,0.8,0.8],polar=True)     # Polar plot
ax.plot(theta,R,lw=2.5)
ax.set_rmax(1.5*(A0)+offset)
plt.show()

I have 10 more similar 2D polar plots and I want to stack them up nicely. If there’s any better way to visualize a distorted cylinder in 3D, I’m totally open to suggestions. Any help would be appreciated. Thanks!

Answer 1

If you want to stack polar charts using matplotlib, one approach is to use the Axes3D module. You’ll notice that I used polar coordinates first and then converted them back to Cartesian when I was ready to plot them.

from numpy import *
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt

n = 1000

fig = plt.figure()
ax = fig.gca(projection='3d')

for k in linspace(0, 5, 5):
    THETA = linspace(0, 2*pi, n)
    R     = ones(THETA.shape)*cos(THETA*k)

    # Convert to Cartesian coordinates
    X = R*cos(THETA)
    Y = R*sin(THETA)

    ax.plot(X, Y, k-2)

plt.show()

If you play with the last argument of ax.plot, it controls the height of each slice. For example, if you want to project all of your data down to a single axis you would use ax.plot(X, Y, 0). For a more exotic example, you can map the height of the data onto a function, say a saddle ax.plot(X, Y, -X**2+Y**2 ). By playing with the colors as well, you could in theory represent multiple 4 dimensional datasets (though I’m not sure how clear this would be). Examples below: