在 python 中查找交点坐标

Question

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.

Answer 1

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.