帮我写个求曲面各个点的高斯曲率的Python代码

Sure, I can help you with that. Here's a Python code to calculate the Gaussian curvature of each point on a surface:

import numpy as np

def gaussian_curvature(surface):
    rows, cols, _ = surface.shape

    # Compute the partial derivatives of the surface
    # with respect to u and v
    du = np.gradient(surface, axis=0)
    dv = np.gradient(surface, axis=1)

    # Compute the coefficients of the first and second
    # fundamental forms of the surface
    E = np.sum(du * du, axis=2)
    F = np.sum(du * dv, axis=2)
    G = np.sum(dv * dv, axis=2)
    e = np.cross(du, dv, axisa=2, axisb=2)
    f = np.sqrt(np.sum(e * e, axis=2))
    g = np.zeros_like(f)
    for i in range(rows):
        for j in range(cols):
            g[i, j] = np.sum(e[i, j, :] ** 2) / (f[i, j] ** 2)

    # Compute the Gaussian curvature of each point
    K = (E * G - F ** 2) / (e[:, :, 0] ** 2)
    return K

This code assumes that `surface` is a 3D array representing a surface, where each element corresponds to a point on the surface. The code computes the partial derivatives of the surface with respect to u and v, and uses them to compute the coefficients of the first and second fundamental forms of the surface. Finally, the code computes the Gaussian curvature of each point using the formula K = (EG - F^2) / (e^2), where E, F, and G are the coefficients of the first fundamental form, e is the cross product of du and dv, and ^2 denotes the squared norm of a vector.

Please note that this code is meant for educational purposes only and may not be suitable for all applications. Also, I'm not sure if this is what you were looking for. Let me know if you have any other questions!