如何在matplotlib中找到两条绘制曲线之间的交点？

Question

我想找到两条曲线的交点。 例如下面。 可以有多个交点。 现在我通过找到x,y坐标之间的距离来找到交点。 但是，正如您在图中看到的那样，当交点介于（17-18 x 轴）之间时，这种方法有时无法给出准确的点。

我需要从曲线中获取所有点来解决这个问题。 有什么方法可以全部得到吗？

Answer 1

曲线只是一系列连接每个点的直线。 因此，如果要增加点数，只需在每对点之间进行线性外推即可：

x1,x2 = 17,20
y1,y2 = 1,5

N = 20
x_vals = np.linspace(x1,x2,N)
y_vals = y1+(x_vals-x1)*((y2-y1)/(x2-x1))

fig, ax = plt.subplots()
ax.plot([x1,x2],[y1,y2],'k-')
ax.plot(x_vals,y_vals, 'ro')

Answer 2

这是我的方法。 我首先创建了两条测试曲线，仅使用 12 个样本点，只是为了说明这个概念。 创建具有采样点的阵列后，曲线的精确方程将丢失。

然后，搜索两条曲线之间的交点。 通过逐点遍历数组，并检查一条曲线何时从另一条曲线从另一条曲线向下移动到另一条曲线上方（或反向），可以通过求解线性方程来计算交点。

然后绘制交点以直观地检查结果。

import numpy as np
from matplotlib import pyplot as plt

N = 12
t = np.linspace(0, 50, N)
curve1 = np.sin(t*.08+1.4)*np.random.uniform(0.5, 0.9) + 1
curve2 = -np.cos(t*.07+.1)*np.random.uniform(0.7, 1.0) + 1
# note that from now on, we don't have the exact formula of the curves, as we didn't save the random numbers
# we only have the points correspondent to the given t values

fig, ax = plt.subplots()
ax.plot(t, curve1,'b-')
ax.plot(t, curve1,'bo')
ax.plot(t, curve2,'r-')
ax.plot(t, curve2,'ro')

intersections = []
prev_dif = 0
t0, prev_c1, prev_c2 = None, None, None
for t1, c1, c2 in zip(t, curve1, curve2):
    new_dif = c2 - c1
    if np.abs(new_dif) < 1e-12: # found an exact zero, this is very unprobable
        intersections.append((t1, c1))
    elif new_dif * prev_dif < 0:  # the function changed signs between this point and the previous
        # do a linear interpolation to find the t between t0 and t1 where the curves would be equal
        # this is the intersection between the line [(t0, prev_c1), (t1, c1)] and the line [(t0, prev_c2), (t1, c2)]
        # because of the sign change, we know that there is an intersection between t0 and t1
        denom = prev_dif - new_dif
        intersections.append(((-new_dif*t0  + prev_dif*t1) / denom, (c1*prev_c2 - c2*prev_c1) / denom))
    t0, prev_c1, prev_c2, prev_dif = t1, c1, c2, new_dif
print(intersections)

ax.plot(*zip(*intersections), 'go', alpha=0.7, ms=10)
plt.show()