Question

I am using matplotlib and numpy to make a polar plot. Here is some sample code:

import numpy as N
import matplotlib.pyplot as P

angle = N.arange(0, 360, 10, dtype=float) * N.pi / 180.0
arbitrary_data = N.abs(N.sin(angle)) + 0.1 * (N.random.random_sample(size=angle.shape) - 0.5)

P.clf()
P.polar(angle, arbitrary_data)
P.show()

You will notice that 0° is at 3 o’clock on the plot, and the angles go counterclockwise. It would be more useful for my data visualization purposes to have 0° at 12 o’clock and have the angles go clockwise. Is there any way to do this besides rotating the data and manually changing the axis labels?

Answer 1

I found it out — matplotlib allows you to create custom projections. I created one that inherits from PolarAxes.

import numpy as np
import matplotlib.pyplot as plt

from matplotlib.projections import PolarAxes, register_projection
from matplotlib.transforms import Affine2D, Bbox, IdentityTransform

class NorthPolarAxes(PolarAxes):
    '''
    A variant of PolarAxes where theta starts pointing north and goes
    clockwise.
    '''
    name = 'northpolar'

    class NorthPolarTransform(PolarAxes.PolarTransform):
        def transform(self, tr):
            xy   = np.zeros(tr.shape, np.float_)
            t    = tr[:, 0:1]
            r    = tr[:, 1:2]
            x    = xy[:, 0:1]
            y    = xy[:, 1:2]
            x[:] = r * np.sin(t)
            y[:] = r * np.cos(t)
            return xy

        transform_non_affine = transform

        def inverted(self):
            return NorthPolarAxes.InvertedNorthPolarTransform()

    class InvertedNorthPolarTransform(PolarAxes.InvertedPolarTransform):
        def transform(self, xy):
            x = xy[:, 0:1]
            y = xy[:, 1:]
            r = np.sqrt(x*x + y*y)
            theta = np.arctan2(y, x)
            return np.concatenate((theta, r), 1)

        def inverted(self):
            return NorthPolarAxes.NorthPolarTransform()

        def _set_lim_and_transforms(self):
            PolarAxes._set_lim_and_transforms(self)
            self.transProjection = self.NorthPolarTransform()
            self.transData = (self.transScale + self.transProjection + (self.transProjectionAffine + self.transAxes))
            self._xaxis_transform = (self.transProjection + self.PolarAffine(IdentityTransform(), Bbox.unit()) + self.transAxes)
            self._xaxis_text1_transform = (self._theta_label1_position + self._xaxis_transform)
            self._yaxis_transform = (Affine2D().scale(np.pi * 2.0, 1.0) + self.transData)
            self._yaxis_text1_transform = (self._r_label1_position + Affine2D().scale(1.0 / 360.0, 1.0) + self._yaxis_transform)

register_projection(NorthPolarAxes)

angle = np.arange(0, 360, 10, dtype=float) * np.pi / 180.0
arbitrary_data = (np.abs(np.sin(angle)) + 0.1 * 
    (np.random.random_sample(size=angle.shape) - 0.5))

plt.clf()
plt.subplot(1, 1, 1, projection='northpolar')
plt.plot(angle, arbitrary_data)
plt.show()