How to find number of self intersection points on 2D plot?

Question

I have two numpy arrays x and y:

x = [-256.70946838 -188.26946838  -83.86946838   29.81053162  131.89053162
  213.67053162  271.09053162  315.17053162  310.53053162  296.03053162
  252.53053162  184.67053162   82.59053162  -33.40946838 -139.54946838
 -213.78946838 -271.20946838 -317.02946838 -310.64946838 -298.46946838
 -256.70946838]

y = [ 9.71224758e-02 -3.19097822e-02 -4.80388145e-02  6.48644113e-02
 -3.19097822e-02  9.71224758e-02 -1.57807500e-02  6.48644113e-02
 -4.02877524e-01 -1.93200105e-01  6.48644113e-02  1.64773146e-02
  3.48282294e-04 -1.44813008e-01  6.48644113e-02 -1.57807500e-02
  3.48282294e-04 -8.02968790e-02  2.10025702e-01  1.77767637e-01
  9.71224758e-02]

when I use plot command:

plt.plot(x, y)
plt.show()

Below figure would be the output:

Now I want to find the number of self-intersections based on x and y arrays which in this figure it equals six and I don't know how to find it.

Thanks for helping.

Does this answer your question? [Python - Find all intersection points of 2 graphs](https://stackoverflow.com/questions/31541080/python-find-all-intersection-points-of-2-graphs) — Stef, Jan 01 '21 at 17:35
Your lists x,y are equivalent to a list of points (x,y) that define endpoints of line segments. "Counting intersection given a list of segments" is a well known problem. — Vepir, Jan 01 '21 at 18:57

Stef · Accepted Answer · 2021-01-01T19:28:21.833

Just find the intersections between any two line segments:

x = [-256.70946838, -188.26946838,  -83.86946838,   29.81053162,  131.89053162,
  213.67053162,  271.09053162,  315.17053162,  310.53053162,  296.03053162,
  252.53053162,  184.67053162,   82.59053162,  -33.40946838, -139.54946838,
 -213.78946838, -271.20946838, -317.02946838, -310.64946838, -298.46946838,
 -256.70946838]

y = [ 9.71224758e-02, -3.19097822e-02, -4.80388145e-02,  6.48644113e-02,
 -3.19097822e-02,  9.71224758e-02, -1.57807500e-02,  6.48644113e-02,
 -4.02877524e-01, -1.93200105e-01,  6.48644113e-02,  1.64773146e-02,
  3.48282294e-04, -1.44813008e-01,  6.48644113e-02, -1.57807500e-02,
  3.48282294e-04, -8.02968790e-02,  2.10025702e-01,  1.77767637e-01,
  9.71224758e-02]

def intersection(x1,x2,x3,x4,y1,y2,y3,y4):
    d = (x1-x2)*(y3-y4) - (y1-y2)*(x3-x4)
    if d:
        xs = ((x1*y2-y1*x2)*(x3-x4) - (x1-x2)*(x3*y4-y3*x4)) / d
        ys = ((x1*y2-y1*x2)*(y3-y4) - (y1-y2)*(x3*y4-y3*x4)) / d
        if (xs >= min(x1,x2) and xs <= max(x1,x2) and
            xs >= min(x3,x4) and xs <= max(x3,x4)):
            return xs, ys

xs, ys = [], []
for i in range(len(x)-1):
    for j in range(i-1):
        if xs_ys := intersection(x[i],x[i+1],x[j],x[j+1],y[i],y[i+1],y[j],y[j+1]):
            xs.append(xs_ys[0])
            ys.append(xs_ys[1])

from matplotlib import pyplot as plt
plt.plot(x, y)
plt.scatter(xs, ys, color='r')
plt.show()

This is a straightforward implementation of the wikipedia formula which surely can be optimized if needed.

How to find number of self intersection points on 2D plot?

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