点云主曲率及高斯曲率Python代码

以下是计算点云主曲率和高斯曲率的Python代码：

import numpy as np
from sklearn.neighbors import KDTree

def compute_curvature(points):
    """
    计算点云主曲率和高斯曲率
    :param points: Nx3的点云数组
    :return: 主曲率和高斯曲率
    """
    k = 10  # 设置K值
    tree = KDTree(points)
    N = points.shape[0]
    curvatures = np.zeros((N, 2))

    for i in range(N):
        indices = tree.query(points[i], k=k, return_distance=False)[0]
        neighbors = points[indices, :]

        # 计算协方差矩阵
        centroid = np.mean(neighbors, axis=0)
        deviation = neighbors - centroid
        covariance = np.matmul(deviation.T, deviation) / k

        # 计算特征值和特征向量
        w, v = np.linalg.eig(covariance)

        # 计算主曲率和高斯曲率
        curvatures[i, 0] = np.max(w)
        curvatures[i, 1] = np.prod(w)

    return curvatures

使用时，只需要将点云数据作为参数传入即可：

points = np.loadtxt('point_cloud.xyz')
curvatures = compute_curvature(points)

其中，`points` 是一个 Nx3 的点云数组，`curvatures` 是一个 Nx2 的数组，第一列是主曲率，第二列是高斯曲率。