Finding the point of intersection of two line graphs drawn in matplotlib

Question

Is there a way to find the point of intersection of two line graphs in matplotlib?

Consider the code

import numpy as np
import matplotlib.pyplot as          


        

Answer 1

I've expanded @SparkAndShine's solution to work with 3D data, as well as did some performance enhancements using a KD-tree. Full solution is posted here: https://stackoverflow.com/a/51145981/4212158

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from scipy.spatial import cKDTree
from scipy import interpolate

fig = plt.figure()
ax = fig.add_axes([0, 0, 1, 1], projection='3d')
ax.axis('off')

def upsample_coords(coord_list):
    # s is smoothness, set to zero
    # k is degree of the spline. setting to 1 for linear spline
    tck, u = interpolate.splprep(coord_list, k=1, s=0.0)
    upsampled_coords = interpolate.splev(np.linspace(0, 1, 100), tck)
    return upsampled_coords

# target line
x_targ = [1, 2, 3, 4, 5, 6, 7, 8]
y_targ = [20, 100, 50, 120, 55, 240, 50, 25]
z_targ = [20, 100, 50, 120, 55, 240, 50, 25]
targ_upsampled = upsample_coords([x_targ, y_targ, z_targ])
targ_coords = np.column_stack(targ_upsampled)

# KD-tree for nearest neighbor search
targ_kdtree = cKDTree(targ_coords)

# line two
x2 = [3,4,5,6,7,8,9]
y2 = [25,35,14,67,88,44,120]
z2 = [25,35,14,67,88,44,120]
l2_upsampled = upsample_coords([x2, y2, z2])
l2_coords = np.column_stack(l2_upsampled)

# plot both lines
ax.plot(x_targ, y_targ, z_targ, color='black', linewidth=0.5)
ax.plot(x2, y2, z2, color='darkgreen', linewidth=0.5)

# find intersections
for i in range(len(l2_coords)):
    if i == 0:  # skip first, there is no previous point
        continue

    distance, close_index = targ_kdtree.query(l2_coords[i], distance_upper_bound=.5)

    # strangely, points infinitely far away are somehow within the upper bound
    if np.isinf(distance):
        continue

    # plot ground truth that was activated
    _x, _y, _z = targ_kdtree.data[close_index]
    ax.scatter(_x, _y, _z, 'gx')
    _x2, _y2, _z2 = l2_coords[i]
    ax.scatter(_x2, _y2, _z2, 'rx')  # Plot the cross point


plt.show()

Answer 2

Here is an ugly solution (an improved version is at the bottom). After plotting, we know that two line graphs make a cross at the range of (6, 7)

Now, we plot this cross point with the following source code,

import numpy as np
import matplotlib.pyplot as plt

fig = plt.figure()
ax = fig.add_subplot(111)

x1 = [1,2,3,4,5,6,7,8]
y1 = [20,100,50,120,55,240,50,25]
x2 = [3,4,5,6,7,8,9]
y2 = [25,35,14,67,88,44,120]

ax.plot(x1, y1, color='lightblue',linewidth=3)
ax.plot(x2, y2, color='darkgreen', marker='^')


# Plot the cross point

x3 = np.linspace(6, 7, 1000)        # (6, 7) intersection range
y1_new = np.linspace(240, 50, 1000) # (6, 7) corresponding to (240, 50) in y1
y2_new = np.linspace(67, 88, 1000)  # (6, 7) corresponding to (67, 88) in y2

idx = np.argwhere(np.isclose(y1_new, y2_new, atol=0.1)).reshape(-1)
ax.plot(x3[idx], y2_new[idx], 'ro')

plt.show()

---

The end user would not be happy to input the cross range manually. Here is an improved version by looping over every two segments, but it might be a time consumer.

import numpy as np
import matplotlib.pyplot as plt

fig = plt.figure()
ax = fig.add_subplot(111)

x1 = [1,2,3,4,5,6,7,8]
y1 = [20,100,50,120,55,240,50,25]
x2 = [3,4,5,6,7,8,9]
y2 = [25,35,14,67,88,44,120]

ax.plot(x1, y1, color='lightblue',linewidth=3)
ax.plot(x2, y2, color='darkgreen', marker='^')

# Get the common range, from `max(x1[0], x2[0])` to `min(x1[-1], x2[-1])`   
x_begin = max(x1[0], x2[0])     # 3
x_end = min(x1[-1], x2[-1])     # 8

points1 = [t for t in zip(x1, y1) if x_begin<=t[0]<=x_end]  # [(3, 50), (4, 120), (5, 55), (6, 240), (7, 50), (8, 25)]
points2 = [t for t in zip(x2, y2) if x_begin<=t[0]<=x_end]  # [(3, 25), (4, 35), (5, 14), (6, 67), (7, 88), (8, 44)]

idx = 0
nrof_points = len(points1)
while idx < nrof_points-1:
    # Iterate over two line segments
    y_min = min(points1[idx][1], points1[idx+1][1]) 
    y_max = max(points1[idx+1][1], points2[idx+1][1]) 

    x3 = np.linspace(points1[idx][0], points1[idx+1][0], 1000)      # e.g., (6, 7) intersection range
    y1_new = np.linspace(points1[idx][1], points1[idx+1][1], 1000)  # e.g., (6, 7) corresponding to (240, 50) in y1
    y2_new = np.linspace(points2[idx][1], points2[idx+1][1], 1000)  # e.g., (6, 7) corresponding to (67, 88) in y2

    tmp_idx = np.argwhere(np.isclose(y1_new, y2_new, atol=0.1)).reshape(-1)
    if tmp_idx:
        ax.plot(x3[tmp_idx], y2_new[tmp_idx], 'ro')                 # Plot the cross point

    idx += 1

plt.show()