[FIXED] finding coordinates of intersection in python

Issue

I have 3 linear line equations.

x1= np.linspace(-1,1,100)

y1= x1
y2=-x1
y3= -2*x1 +2
plt.plot(x1,y1)
plt.plot(x1,y2)
plt.plot(x1,y3)

Is there a simple and a quicker way to find the coordinates of intersection of the three lines?

I have tried Intersection of two graphs in Python, find the x value, and have just the x coordinates.

But in reality I have more linear equations, so the most effective way to get the (x,y) coordinates of intersection would be most helpful.

Solution

If the main purpose is to find intersections, between equations, the symbolic math library sympy could be helpful:

from sympy import symbols, Eq, solve

x, y = symbols('x y')
eq1 = Eq(y, x)
eq2 = Eq(y, -x)
eq3 = Eq(y, -2 * x + 2)
print(solve([eq1, eq2]))
print(solve([eq1, eq3]))
print(solve([eq2, eq3]))

Output:

{x: 0, y: 0}
{x: 2/3, y: 2/3}
{x: 2, y: -2}

To find interpolated intersections between numpy arrays, you can use the find_roots() function from this post:

from matplotlib import pyplot as plt
import numpy as np

def find_roots(x, y):
    s = np.abs(np.diff(np.sign(y))).astype(bool)
    return x[:-1][s] + np.diff(x)[s] / (np.abs(y[1:][s] / y[:-1][s]) + 1)

x1 = np.linspace(-1, 1, 100)

y1 = x1
y2 = -x1
y3 = -2 * x1 + 2
plt.plot(x1, y1, color='dodgerblue')
plt.plot(x1, y2, color='dodgerblue')
plt.plot(x1, y3, color='dodgerblue')

for ya, yb in [(y1, y2), (y1, y3), (y2, y3)]:
    x0 = find_roots(x1, ya - yb)
    y0 = np.interp(x0, x1, ya)
    print(x0, y0)
    plt.plot(x0, y0, marker='o', ls='', ms=4, color='crimson')
plt.show()

Output:

[0.] [0.]
[0.66666667] [0.66666667]
[] []

Zooming in on an intersection, and marking the points of the numpy arrays, you'll notice that the intersection usually doesn't coincide with a common point of the arrays. As such, an interpolation step is necessary.

Answered By - JohanC