使用python，写出alpha shape算法对二维点云进行边界提取

好的，下面是使用Python实现alpha shape算法对二维点云进行边界提取的代码：

from scipy.spatial import Delaunay
import numpy as np
from matplotlib import pyplot as plt

def alpha_shape(points, alpha):
    """
    Compute the alpha shape (concave hull) of a set of points.
    """
    # Delaunay triangulation
    tri = Delaunay(points)

    # Filter triangles by alpha value
    edges = set()
    edge_points = []
    for j, tri in enumerate(tri.simplices):
        # Calculate circumcenter and radius of circumcircle
        x, y = np.mean(points[tri], axis=0)
        r = np.sqrt((points[tri[0]][0] - x)**2 + (points[tri[0]][1] - y)**2)

        # Check if triangle is within alpha value
        if r < alpha:
            for i in range(3):
                edge = (tri[i], tri[(i+1)%3])
                if edge not in edges and (edge[1], edge[0]) not in edges:
                    edges.add(edge)
                    edge_points.append(points[tri[i]])
                    edge_points.append(points[tri[(i+1)%3]])

    # Compute boundary vertices and edges
    boundary_vertices = set()
    boundary_edges = []
    for i, point in enumerate(points):
        for edge in edges:
            if i in edge:
                boundary_vertices.add(i)
                boundary_edges.append(edge)

    # Plot alpha shape
    plt.triplot(points[:,0], points[:,1], tri.simplices.copy())
    plt.plot(edge_points[:,0], edge_points[:,1], 'r.')
    plt.plot(points[list(boundary_vertices),0], points[list(boundary_vertices),1], 'b.')
    plt.show()

    return boundary_vertices, boundary_edges

在这个代码中，我们使用了`scipy.spatial`库中的`Delaunay`函数来进行Delaunay三角剖分，然后根据alpha值筛选出在范围内的三角形，并提取出边界。

下面是一个使用示例：

# Generate random points
points = np.random.rand(30, 2)

# Compute alpha shape
alpha = 0.3
boundary_vertices, boundary_edges = alpha_shape(points, alpha)

# Print boundary vertices and edges
print("Boundary vertices:", boundary_vertices)
print("Boundary edges:", boundary_edges)

这个例子中，我们先生成了30个随机点，然后使用`alpha_shape`函数计算alpha shape，并输出边界点和边。