沿地形曲面进行贝塞尔曲线

下面是一个使用Python和NumPy库实现沿地形曲面进行贝塞尔曲线的代码示例：

import numpy as np
import matplotlib.pyplot as plt

def bezier_curve(points, t):
    n = len(points) - 1
    result = np.zeros_like(points[0])
    for i in range(n + 1):
        result += scipy.special.comb(n, i) * (1 - t)**(n-i) * t**i * points[i]
    return result

def bezier_surface(points, m, n, t_u, t_v):
    u_curve = np.zeros((m, len(points[0])))
    for i in range(m):
        u_curve[i] = bezier_curve(points[i], t_u)
    
    v_curve = np.zeros_like(points[0][0])
    for i in range(n):
        column_points = [points[j][i] for j in range(m)]
        v_curve[i] = bezier_curve(column_points, t_v)
    
    return bezier_curve(v_curve, t_u)

# 示例数据
points = np.array([
    [[0, 0, 0], [1, 0, 2], [2, 0, 0], [3, 0, 1]],
    [[0, 1, 1], [1, 1, 3], [2, 1, 1], [3, 1, 2]],
    [[0, 2, 2], [1, 2, 4], [2, 2, 2], [3, 2, 3]],
    [[0, 3, 1], [1, 3, 3], [2, 3, 1], [3, 3, 2]]
])

# 对曲面进行采样
m, n = 50, 50  # 曲面的采样点数
t_u = np.linspace(0, 1, m)
t_v = np.linspace(0, 1, n)
surface = np.zeros((m, n, 3))
for i in range(m):
    for j in range(n):
        surface[i, j] = bezier_surface(points, 4, 4, t_u[i], t_v[j])

# 绘制曲面
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_surface(surface[:, :, 0], surface[:, :, 1], surface[:, :, 2])
plt.show()

上述代码定义了bezier_curve函数来计算贝塞尔曲线上的点，然后定义了bezier_surface函数来计算贝塞尔曲面上的点。最后，使用示例数据和参数对曲面进行采样，并使用Matplotlib库绘制出曲面。