Signature: Path.intersects_path(self, other, filled=True)
Docstring:
Returns *True* if this path intersects another given path.

*filled*, when True, treats the paths as if they were filled.
That is, if one path completely encloses the other,
:meth:`intersects_path` will return True.
File:      ~/anaconda/lib/python2.7/site-packages/matplotlib/path.py
Type:      instancemethod

# -*- coding: utf-8 -*-
import matplotlib.pyplot as plt
from matplotlib.patches import PathPatch
from matplotlib.path import Path

cubic_bezier_codes = [Path.MOVETO, Path.CURVE4, Path.CURVE4, Path.CURVE4]

def plot_ctrls(verts, ax, label='',
               ls='--', marker='o', ms=5, lw=1, alpha=0.6, color='Gray'):
    """Plot the control points of a Bezier curve (debugging purpose)
    """
    ax.plot(*zip(*verts), ls=ls, lw=lw, color=color, ms=ms, marker=marker,
            alpha=alpha, label=label)
    return ax

# For your viewing pleasure when plotting
detection_color = {True: "OliveDrab", False: "Crimson"}

if __name__ == "__main__":
    plt.ion()

    # A dummy path to play with
    verts_1 = [(0.5, 0.01), (0.21, 0.99), (0.99, 0.8), (0.99, 0.99)]
    path_1 = Path(verts_1, cubic_bezier_codes)

    # A path that does intersect with path_1 but for which the ad-hoc test
    # method fails
    verts_2a = [(0.5, 0.8), (0.5, 0.7), (0.6, 0.75), (0.56, 0.7)]
    path_2a = Path(verts_2a, cubic_bezier_codes)

    # Decreasing a bit the y-value of the last control point leads to a
    # correct detection of path intersecting.
    verts_2b = [(0.5, 0.8), (0.5, 0.7), (0.6, 0.75), (0.56, 0.6)]
    path_2b = Path(verts_2b, cubic_bezier_codes)

    # Plot everything to be sure
    fig, (axA, axB) = plt.subplots(ncols=2, sharex=True, sharey=True)
    title_prefix = "path_1.intersects_path(path_2):\n"
    for ax, p1, p2 in [(axA, path_1, path_2a), (axB, path_1, path_2b)]:
        # Detect if the two paths intersect
        detection = p1.intersects_path(p2)
        ax.set_title(title_prefix + "{}".format(detection))

        # Plot the two paths
        patch_1 = PathPatch(p1, lw=2, fc='none', ec='CornFlowerBlue')
        pc1 = ax.add_patch(patch_1)
        patch_2 = PathPatch(p2, lw=2, fc='none', ec=detection_color[detection])
        ax.add_patch(patch_2)

        # Plot the controls nodes for debugging
        ax = plot_ctrls(p1.vertices, ax, marker='s', color=patch_1.get_ec(),
                        label='verts_1')
        ax = plot_ctrls(p2.vertices, ax, color=patch_2.get_ec(),
                        label='verts_2')
        ax.legend(loc='lower right', handlelength=3.5)

    #fig.savefig("Issue_with_intersecting_path_detection.png", dpi=150)