Пересечение линии и контуров

import numpy as np
import matplotlib.pyplot as plt
 
fig=plt.figure()
ax=fig.add_subplot()
 
'10'
x_10=np.array([0.28, 0.29, 0.355, 0.415, 0.52, 0.6, 0.68, 0.74, 0.76, 0.68, 0.62, 0.545, 0.43, 0.325])
y_10=np.array([0.399, 0.5, 0.57, 0.625, 0.665, 0.67, 0.665, 0.64, 0.57, 0.44, 0.39, 0.35, 0.33, 0.35])
z_10 = np.full(shape=14, fill_value=10,dtype=np.int8)
 
'9'
x_9=np.array([0.15, 0.14, 0.17, 0.3, 0.485, 0.65, 0.8, 0.9, 0.93, 0.9, 0.75, 0.55, 0.43, 0.325, 0.22])
y_9=np.array([0.335, 0.44, 0.55, 0.7, 0.78, 0.8, 0.79, 0.75, 0.6, 0.46, 0.31, 0.235, 0.24, 0.28, 0.265])
z_9 = np.full(shape=15, fill_value=9,dtype=np.int8)
 
'8'
x_8=np.array([0, 0, 0.105, 0.215, 0.4, 0.6, 0.825, 1, 1, 0.885, 0.65, 0.4, 0.2, 0.1, 0])
y_8=np.array([0.4, 0.565, 0.7, 0.785, 0.87, 0.92, 0.94, 0.87, 0.4, 0.31, 0.2, 0.15, 0.17, 0.21, 0.315])
z_8 = np.full(shape=15, fill_value=8,dtype=np.int8)
 
'7'
x_7=np.array([0, 0.1, 0.18, 0.25, 0.45, 0.55, 1, 1, 0.8, 0.6, 0.4, 0.25, 0.15, 0])
y_7=np.array([0.73, 0.815, 0.86, 0.9, 0.97, 1, 1, 0.31, 0.2, 0.14, 0.12, 0.105, 0.11, 0.145])
z_7 = np.full(shape=14, fill_value=7,dtype=np.int8)
 
 
ax.set(xlim=(0, 1), ylim=(0.1, 1))
 
ax.tricontourf(x_7, y_7, z_7, colors='orange')
ax.tricontourf(x_8, y_8, z_8, colors='g')
ax.tricontourf(x_9, y_9, z_9, colors='r')
ax.tricontourf(x_10, y_10, z_10, colors='b')
 
B=1.5
x=np.arange(0, 1.01, 0.01)
y=B*x*x
ax.plot(x, y, 'k')
print(x)
print(y)
 
plt.show()

import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate import CubicSpline
 
fig=plt.figure()
ax=fig.add_subplot()
#'8'
x_8=np.array([0, 0, 0.105, 0.215, 0.4, 0.6, 0.825, 1, 1, 0.885, 0.65, 0.4, 0.2, 0.1, 0])
y_8=np.array([0.4, 0.565, 0.7, 0.785, 0.87, 0.92, 0.94, 0.87, 0.4, 0.31, 0.2, 0.15, 0.17, 0.21, 0.315])
z_8 = np.full(shape=15, fill_value=8,dtype=np.int8)
 
ax.set(xlim=(0, 1), ylim=(0.1, 1))
ax.tricontourf(x_8, y_8, z_8, colors='g')
 
B=1.5
x=np.arange(0, 1.01, 0.01)
y=B*x*x
ax.plot(x, y, 'k')
 
###############
x=x_8
y=y_8-B*x_8*x_8 # условие пересечения - равенство нулю y
 
theta_8 = np.linspace(0, 1, len(x)+1) # параметр, на 1 больше, т.к. кривая замкнута
f_8 = np.c_[np.r_[x,x[0]], np.r_[y,y[0]]] # "замыкание" кривой для периодичности сплайна
cs = CubicSpline(theta_8, f_8, bc_type='periodic') # построение сплайна
roots=cs.roots()[1] # параметр, при котором y=0, корни
x_roots=cs(roots)[:,0] # нахождение x
y_roots=B*x_roots**2 # нахождение y
ax.plot(x_roots, y_roots, 'o',c='r')
print(x_roots, y_roots)