python - 找到在matplotlib中绘制的两条线图的交点

Question

有没有办法在 matplotlib 中找到两个折线图的交点？

考虑代码

import numpy as np
import matplotlib.pyplot as plt


fig = plt.figure()


ax = fig.add_subplot(111)

ax.plot([1,2,3,4,5,6,7,8],[20,100,50,120,55,240,50,25],color='lightblue',linewidth=3)
ax.plot([3,4,5,6,7,8,9], [25,35,14,67,88,44,120], color='darkgreen', marker='^')

我试着引用 Python - matplotlib: find intersection of lineplots ，但该方法似乎过于复杂 - 它涉及高级数学概念，如分段多项式插值，可以从文档中理解 API 在做什么，但并没有真正理解它背后的概念，如果有人可以提供更简单的解决方案或解释什么在分段多项式求解中进行，这将有很大帮助。

Answer 1

这是一个丑陋的解决方案(改进版本在底部)。绘图后，我们知道两个折线图在(6, 7)

范围内交叉

现在，我们用下面的源代码绘制这个交叉点，

import numpy as np
import matplotlib.pyplot as plt

fig = plt.figure()
ax = fig.add_subplot(111)

x1 = [1,2,3,4,5,6,7,8]
y1 = [20,100,50,120,55,240,50,25]
x2 = [3,4,5,6,7,8,9]
y2 = [25,35,14,67,88,44,120]

ax.plot(x1, y1, color='lightblue',linewidth=3)
ax.plot(x2, y2, color='darkgreen', marker='^')


# Plot the cross point

x3 = np.linspace(6, 7, 1000)        # (6, 7) intersection range
y1_new = np.linspace(240, 50, 1000) # (6, 7) corresponding to (240, 50) in y1
y2_new = np.linspace(67, 88, 1000)  # (6, 7) corresponding to (67, 88) in y2

idx = np.argwhere(np.isclose(y1_new, y2_new, atol=0.1)).reshape(-1)
ax.plot(x3[idx], y2_new[idx], 'ro')

plt.show()

---

最终用户不会乐意手动输入交叉范围。这是每两个片段循环一次的改进版本，但它可能会消耗时间。

import numpy as np
import matplotlib.pyplot as plt

fig = plt.figure()
ax = fig.add_subplot(111)

x1 = [1,2,3,4,5,6,7,8]
y1 = [20,100,50,120,55,240,50,25]
x2 = [3,4,5,6,7,8,9]
y2 = [25,35,14,67,88,44,120]

ax.plot(x1, y1, color='lightblue',linewidth=3)
ax.plot(x2, y2, color='darkgreen', marker='^')

# Get the common range, from `max(x1[0], x2[0])` to `min(x1[-1], x2[-1])`   
x_begin = max(x1[0], x2[0])     # 3
x_end = min(x1[-1], x2[-1])     # 8

points1 = [t for t in zip(x1, y1) if x_begin<=t[0]<=x_end]  # [(3, 50), (4, 120), (5, 55), (6, 240), (7, 50), (8, 25)]
points2 = [t for t in zip(x2, y2) if x_begin<=t[0]<=x_end]  # [(3, 25), (4, 35), (5, 14), (6, 67), (7, 88), (8, 44)]

idx = 0
nrof_points = len(points1)
while idx < nrof_points-1:
    # Iterate over two line segments
    y_min = min(points1[idx][1], points1[idx+1][1]) 
    y_max = max(points1[idx+1][1], points2[idx+1][1]) 

    x3 = np.linspace(points1[idx][0], points1[idx+1][0], 1000)      # e.g., (6, 7) intersection range
    y1_new = np.linspace(points1[idx][1], points1[idx+1][1], 1000)  # e.g., (6, 7) corresponding to (240, 50) in y1
    y2_new = np.linspace(points2[idx][1], points2[idx+1][1], 1000)  # e.g., (6, 7) corresponding to (67, 88) in y2

    tmp_idx = np.argwhere(np.isclose(y1_new, y2_new, atol=0.1)).reshape(-1)
    if tmp_idx:
        ax.plot(x3[tmp_idx], y2_new[tmp_idx], 'ro')                 # Plot the cross point

    idx += 1

plt.show()