三次hermite曲线python代码

以下是三次Hermite曲线的Python代码示例：

import numpy as np
import matplotlib.pyplot as plt

def hermite_cubic(x0, y0, m0, x1, y1, m1, t):
    h00 = (1 + 2*t) * (1 - t)**2
    h10 = t * (1 - t)**2
    h01 = t**2 * (3 - 2*t)
    h11 = t**2 * (t - 1)
  
    x = h00*x0 + h10*m0 + h01*x1 + h11*m1
    y = h00*y0 + h10*m0 + h01*y1 + h11*m1
  
    return x, y

# sample data
x0, y0 = 0, 0
m0 = 1
x1, y1 = 5, 5
m1 = -1

# generate points along the Hermite curve
N = 100
t_values = np.linspace(0, 1, N)
points = [hermite_cubic(x0, y0, m0, x1, y1, m1, t) for t in t_values]

# plot the curve and control points
fig, ax = plt.subplots()
ax.plot(*zip(*points), label='Hermite curve')
ax.scatter([x0, x1], [y0, y1], label='Control points')
ax.legend()
plt.show()

此代码生成了一个三次Hermite曲线，使用了两个控制点和它们在每个点处的导数。曲线在控制点之间平滑地移动，并在每个点处具有正确的切线方向。