如何找到三角形和二维曲线的交点？

Question

I have plotted a triangle ad two lines. I would like to plot the parts of lines inside the triangle with other style. How to find the intersection, please? Many thanks.

import matplotlib.pyplot as plt
import numpy as np
from sympy import *

a1 = 1080
a2 = 350
c1 = -7
c2 = 0
d = 7
x = np.linspace(0,100,500)

y1 = a1/(x-c1)-d
y2 = a2/(x-c2)

fig, ax = plt.subplots()
plt.rcParams["figure.figsize"] = [10, 3]
 
I1 = 23
x_end = 70
plt.xlim(0,x_end)
plt.ylim(0,50)

# Plot curves
plt.plot(x[10:], y1[10:], c = 'red')
plt.plot(x[10:], y2[10:], c = 'blue')

# Plot triangle
shift = 15
triangle = np.array([[0,I1], [x_end,I1+shift], [x_end, I1-shift]])

plt.scatter(triangle[:, 0], triangle[:, 1], s = 0, color = 'grey')

t1 = plt.Polygon(triangle[:3,:])
plt.gca().add_patch(t1)

x = symbols('x')
intercept = solve(a1/(x-c1)-d, (322+3*x)/14) 
print(intercept)

plt.show()

Answer 1

You can use fill_between and set the triangle as clip_path. The zorder needs to be changed to show the green area on top of the triangle.

import matplotlib.pyplot as plt
import numpy as np

a1 = 1080
a2 = 350
c1 = -7
c2 = 0
d = 7
x = np.linspace(0, 100, 500)

y1 = a1 / (x - c1) - d
y2 = a2 / (x - c2)

fig, ax = plt.subplots(figsize=(10, 3))

I1 = 23
x_end = 70
plt.xlim(0, x_end)
plt.ylim(0, 50)

# Plot curves
ax.plot(x[10:], y1[10:], c='red')
ax.plot(x[10:], y2[10:], c='blue')

# Plot triangle
shift = 15
triangle = np.array([[0, I1], [x_end, I1 + shift], [x_end, I1 - shift]])
ax.scatter(triangle[:, 0], triangle[:, 1], s=1, color='grey')

t1 = plt.Polygon(triangle[:3, :])
ax.add_patch(t1)

ax.fill_between(x[10:], y1[10:], y2[10:], facecolor='lime', clip_path=t1, zorder=2)
plt.show()

PS: Note that your formula y2 = a2 / (x - c2) divides by zero for the first value (0) of x. You might want to start x with a larger value, eg x = np.linspace(0.1, 100, 500) .

If you don't want to show the triangle, ax.add_patch() is still needed for the clipping to work as expected. You could make it invisible ( t1 = plt.Polygon(triangle[:3, :], color='none') or t1 = plt.Polygon(triangle[:3, :], visible=False) ).

As commented by @swatchai, if you just want a different line style, you could clip the plotted curves:

t1 = plt.Polygon(triangle[:3, :], visible=False)
ax.add_patch(t1)

#ax.fill_between(x[10:], y1[10:], y2[10:], facecolor='lime', clip_path=t1, zorder=2)
ax.plot(x[10:], y1[10:], 'w:', clip_path=t1)
ax.plot(x[10:], y2[10:], 'w:', clip_path=t1)