在三维空间中，Alpha Shapes算法可以用于计算形状的几何体积和表面积。但是，当生成Alpha Shapes之后，我们可能需要进行一些进一步的操作，例如计算表面积、体积或提取边界。

为了计算Alpha Shapes的体积和表面积，可以使用scipy库中的ConvexHull包。以下是一个实例，假设我们有一组数据点，我们可以使用Alpha Shapes来描述这些点形成的3D形状，并计算它的表面积和体积。

import numpy as np
from scipy.spatial import Delaunay

# Generate random data points
points = np.random.rand(10, 3)

# Use Delaunay triangulation to generate simplices
tri = Delaunay(points)

# Use ConvexHull to calculate surface area and volume
from scipy.spatial import ConvexHull

hull = ConvexHull(points)

# Calculate surface area and volume
surface_area = hull.area
volume = hull.volume

另一种常见的操作是提取Alpha Shapes的边界或曲线。为了做到这一点，我们可以使用scikit-image库中的marching_cubes_lewiner函数。

from skimage import measure

# Define the Alpha Shapes function
def alpha_shape_3d(points, alpha):
    """Compute the alpha shape (concave hull) of a set of 3D points."""
    from scipy.spatial import Delaunay
    tetra = Delaunay(points)
    # Find the tetrahedrons that satisfy the circumsphere criterion
    # (https://en.wikipedia.org/wiki/Circumscribed_sphere#Tetrahedron)
    # i.e. those tetrahedrons whose circumsphere radius is less than alpha
    tetra = tetra.points[tetra.simplices[np.where(tetra.in_radius < alpha)]]
    # We can then use the marching_cubes_lewiner function to extract the surface mesh
    # and the Dual Contour