How to find all the intersection points between two contour-set in an efficient way

Question

I\'m wondering about the best way to find all the intersection points (to roundoff error) between two sets of contour lines. Which is the best method? Here is the example:

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Answer 1

import collections
import matplotlib.pyplot as plt
import numpy as np
import scipy.spatial as spatial
import scipy.spatial.distance as dist
import scipy.cluster.hierarchy as hier


def intersection(points1, points2, eps):
    tree = spatial.KDTree(points1)
    distances, indices = tree.query(points2, k=1, distance_upper_bound=eps)
    intersection_points = tree.data[indices[np.isfinite(distances)]]
    return intersection_points


def cluster(points, cluster_size):
    dists = dist.pdist(points, metric='sqeuclidean')
    linkage_matrix = hier.linkage(dists, 'average')
    groups = hier.fcluster(linkage_matrix, cluster_size, criterion='distance')
    return np.array([points[cluster].mean(axis=0)
                     for cluster in clusterlists(groups)])


def contour_points(contour, steps=1):
    return np.row_stack([path.interpolated(steps).vertices
                         for linecol in contour.collections
                         for path in linecol.get_paths()])


def clusterlists(T):
    '''
    http://stackoverflow.com/a/2913071/190597 (denis)
    T = [2, 1, 1, 1, 2, 2, 2, 2, 2, 1]
    Returns [[0, 4, 5, 6, 7, 8], [1, 2, 3, 9]]
    '''
    groups = collections.defaultdict(list)
    for i, elt in enumerate(T):
        groups[elt].append(i)
    return sorted(groups.values(), key=len, reverse=True)

# every intersection point must be within eps of a point on the other
# contour path
eps = 1.0

# cluster together intersection points so that the original points in each flat
# cluster have a cophenetic_distance < cluster_size
cluster_size = 100

x = np.linspace(-1, 1, 500)
X, Y = np.meshgrid(x, x)
Z1 = np.abs(np.sin(2 * X ** 2 + Y))
Z2 = np.abs(np.cos(2 * Y ** 2 + X ** 2))
contour1 = plt.contour(Z1, colors='k')
contour2 = plt.contour(Z2, colors='r')

points1 = contour_points(contour1)
points2 = contour_points(contour2)

intersection_points = intersection(points1, points2, eps)
intersection_points = cluster(intersection_points, cluster_size)
plt.scatter(intersection_points[:, 0], intersection_points[:, 1], s=20)
plt.show()

yields