Coloring Intersection of Circles/Patches in Matplotlib - matplotlib

Question

The following code:
# in ipython notebook, enable inline plotting with:
# %pylab inline --no-import-all
import matplotlib.pyplot as plt
# create some circles
circle1 = plt.Circle((-.5,0), 1, color='r', alpha=.2)
circle2 = plt.Circle(( .5,0), 1, color='b', alpha=.2)
# add them to the plot (bad form to use ;, but saving space)
# and control the display a bit
ax = plt.gca()
ax.add_artist(circle1); ax.add_artist(circle2)
ax.set_xlim(-2, 2); ax.set_ylim(-2, 2)
ax.set_aspect('equal')
# display it
plt.plot()
Produces the following plot:
I would like to specify the colors of the four regions (1) the background (currently white), (2 and 3) each individual event (the non-overlapping areas, currently blue and red), and (4) the intersection event (currently blended to purple). For example, I might color them red, green, blue, yellow -or- I might give them four different, precisely specified grayscale values (the later is more likely). [The colors will be generated based on characteristics of the underlying data.]
I specifically do not want to use alpha blending to "infer" a color in the intersection. I need to explicitly control the colors of all four regions.
I can think of a few strategies to solve this:
Ask mpl to extract the "primitive" patch objects that make up the three distinctly colored graphical regions (and do something similar to operate on the background) and then color them.
Given the circles, manually compute their intersections and color that intersection (somehow). Going point by point seems ugly.
Thanks!

Answer 1

I'm not 100% sure but I think matplotlib does not have the functionality to intersect polygons. But you could use shapely:
import shapely.geometry as sg
import matplotlib.pyplot as plt
import descartes
# create the circles with shapely
a = sg.Point(-.5,0).buffer(1.)
b = sg.Point(0.5,0).buffer(1.)
# compute the 3 parts
left = a.difference(b)
right = b.difference(a)
middle = a.intersection(b)
# use descartes to create the matplotlib patches
ax = plt.gca()
ax.add_patch(descartes.PolygonPatch(left, fc='b', ec='k', alpha=0.2))
ax.add_patch(descartes.PolygonPatch(right, fc='r', ec='k', alpha=0.2))
ax.add_patch(descartes.PolygonPatch(middle, fc='g', ec='k', alpha=0.2))
# control display
ax.set_xlim(-2, 2); ax.set_ylim(-2, 2)
ax.set_aspect('equal')
plt.show()