Intersection of two graphs in Python, find the x value

Question

Let 0 <= x <= 1. I have two columns f and g of length 5000 respectively. Now I plot:

plt.plot(x, f, '-') plt.plot(x, g, '*') 

I want to find the point 'x' where the curve intersects. I don't want to find the intersection of f and g. I can do it simply with:

set(f) & set(g) 

Answer 1

You can use np.sign in combination with np.diff and np.argwhere to obtain the indices of points where the lines cross (in this case, the points are [ 0, 149, 331, 448, 664, 743]):

import numpy as np import matplotlib.pyplot as plt  x = np.arange(0, 1000) f = np.arange(0, 1000) g = np.sin(np.arange(0, 10, 0.01) * 2) * 1000  plt.plot(x, f, '-') plt.plot(x, g, '-')  idx = np.argwhere(np.diff(np.sign(f - g))).flatten() plt.plot(x[idx], f[idx], 'ro') plt.show() 

First it calculates f - g and the corresponding signs using np.sign. Applying np.diff reveals all the positions, where the sign changes (e.g. the lines cross). Using np.argwhere gives us the exact indices.

Answer 2

For those who are using or open to use the Shapely library for geometry-related computations, getting the intersection will be much easier. You just have to construct LineString from each line and get their intersection as follows:

import numpy as np import matplotlib.pyplot as plt from shapely.geometry import LineString  x = np.arange(0, 1000) f = np.arange(0, 1000) g = np.sin(np.arange(0, 10, 0.01) * 2) * 1000  plt.plot(x, f) plt.plot(x, g)  first_line = LineString(np.column_stack((x, f))) second_line = LineString(np.column_stack((x, g))) intersection = first_line.intersection(second_line)  if intersection.geom_type == 'MultiPoint':     plt.plot(*LineString(intersection).xy, 'o') elif intersection.geom_type == 'Point':     plt.plot(*intersection.xy, 'o') 

And to get the x and y values as NumPy arrays you would just write:

x, y = LineString(intersection).xy # x: array('d', [0.0, 149.5724669847373, 331.02906176584617, 448.01182730277833, 664.6733061190541, 743.4822641140581]) # y: array('d', [0.0, 149.5724669847373, 331.02906176584617, 448.01182730277833, 664.6733061190541, 743.4822641140581]) 

or if an intersection is only one point:

x, y = intersection.xy