有没有办法在matplotlib中找到两条线图的交点？
考虑以下代码：
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='^')
我尝试参考Python - matplotlib: find intersection of lineplots，但该方法似乎太复杂了 - 它涉及到像分段多项式插值这样的高级数学概念，虽然可以从文档中理解 API 的用途，但并不真正了解 Piecewise polynomial 解决方案背后的概念。如果有人能够提供更简单的解决方案或解释分段多项式解决方案的原理，那会很有帮助。
这里有一个丑陋的解决方案（改进版本在底部）。绘制图表后，我们知道两条线图在(6, 7)范围内交叉。
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()
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()
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from scipy.spatial import cKDTree
from scipy import interpolate
fig = plt.figure()
ax = fig.add_axes([0, 0, 1, 1], projection='3d')
ax.axis('off')
def upsample_coords(coord_list):
# s is smoothness, set to zero
# k is degree of the spline. setting to 1 for linear spline
tck, u = interpolate.splprep(coord_list, k=1, s=0.0)
upsampled_coords = interpolate.splev(np.linspace(0, 1, 100), tck)
return upsampled_coords
# target line
x_targ = [1, 2, 3, 4, 5, 6, 7, 8]
y_targ = [20, 100, 50, 120, 55, 240, 50, 25]
z_targ = [20, 100, 50, 120, 55, 240, 50, 25]
targ_upsampled = upsample_coords([x_targ, y_targ, z_targ])
targ_coords = np.column_stack(targ_upsampled)
# KD-tree for nearest neighbor search
targ_kdtree = cKDTree(targ_coords)
# line two
x2 = [3,4,5,6,7,8,9]
y2 = [25,35,14,67,88,44,120]
z2 = [25,35,14,67,88,44,120]
l2_upsampled = upsample_coords([x2, y2, z2])
l2_coords = np.column_stack(l2_upsampled)
# plot both lines
ax.plot(x_targ, y_targ, z_targ, color='black', linewidth=0.5)
ax.plot(x2, y2, z2, color='darkgreen', linewidth=0.5)
# find intersections
for i in range(len(l2_coords)):
if i == 0: # skip first, there is no previous point
continue
distance, close_index = targ_kdtree.query(l2_coords[i], distance_upper_bound=.5)
# strangely, points infinitely far away are somehow within the upper bound
if np.isinf(distance):
continue
# plot ground truth that was activated
_x, _y, _z = targ_kdtree.data[close_index]
ax.scatter(_x, _y, _z, 'gx')
_x2, _y2, _z2 = l2_coords[i]
ax.scatter(_x2, _y2, _z2, 'rx') # Plot the cross point
plt.show()