How to make the angles in a polar plot go clockwise with 0° at the top

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?

Pico

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()

Pico

Awesome, this should be included with their custom projection examples. – Toy

@Pico - I think the answer needs an update for a commit that was made 2012-01-23 (git log -Sself._r_label1_position). Not sure which version that ended up in. In any case there is no self._r_label1_position anymore and removing that line seems to solve the problems. – Madiemadigan

In that case it should be updated to match whatever PolarAxes looks like now... – Pico

The question was how to get a polar plot with zero at the top and angles increasing clockwise. The example output is a plot with zero to the right and angles increasing counterclockwise. Am I missing something? – Citystate

Answer 2

Updating this question, in Matplotlib 1.1, there are now two methods in PolarAxes for setting the theta direction (CW/CCW) and location for theta=0.

Check out http://matplotlib.sourceforge.net/devel/add_new_projection.html#matplotlib.projections.polar.PolarAxes

Specifically, see set_theta_direction() and set_theta_offset().

Lots of people attempting to do compass-like plots it seems.

Plagiarism

If you have an polar axis ax: ax.set_theta_offset(0.5*numpy.pi) – Moccasin

Answer 3

To expand klimaat's answer, with an example:

from math import radians
import matplotlib.pyplot as plt

angle=[0.,5.,10.,15.,20.,25.,30.,35.,40.,45.,50.,55.,60.,65.,70.,75.,\
       80.,85.,90.,95.,100.,105.,110.,115.,120.,125.]

angle = [radians(a) for a in angle]

lux=[12.67,12.97,12.49,14.58,12.46,12.59,11.26,10.71,17.74,25.95,\
     15.07,7.43,6.30,6.39,7.70,9.19,11.30,13.30,14.07,15.92,14.70,\
     10.70,6.27,2.69,1.29,0.81]

plt.clf()
sp = plt.subplot(1, 1, 1, projection='polar')
sp.set_theta_zero_location('N')
sp.set_theta_direction(-1)
plt.plot(angle, lux)
plt.show()

• matplotlib: Developer's guide for creating scales and transformations

Cosec

Answer 4

You could modify your matplotlib/projections/polar.py.

Where it says:

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

Make it say:

def transform(self, tr):
        xy   = npy.zeros(tr.shape, npy.float_)
        t    = tr[:, 0:1]
        r    = tr[:, 1:2]
        x    = xy[:, 0:1]
        y    = xy[:, 1:2]
        x[:] = - r * npy.sin(t)
        y[:] = r * npy.cos(t)
        return xy

I didn't actually try it, you may need to tweak x[:] and y[:] assignments to your taste. This change will affect all programs that use matplotlib polar plot.

Starflower

This is ingenious, but patching the code is kind of cheating, isn't it? However, you've given me an idea. Matplotlib allows you to create axes with any kind of transformation; perhaps I can write an alternate polar() function with the transform I'm looking for. – Pico

Answer 5

Both invert routines should use the full path to the transforms:

return NorthPolarAxes.InvertedNorthPolarTransform()

and

return NorthPolarAxes.NorthPolarTransform()

Now, automatically created subclasses of NorthPolarAxes such as NorthPolarAxesSubplot can access the transform functions.

Hope this helps.

Jaynajayne