如何找到两个凸包的交集？

我有两个凸包。让我们假设它们被给出为scipy.spatial.ConvexHulls

import numpy as np


points1 = np.random.rand((10, 3))
points2 = np.random.rand((10, 3))

hull1 = ConvexHull(points1)
hull2 = ConvexHull(points2)

我想要凸包是这两个凸包的交集，但找不到内置方法来执行此操作。

我认为这可以通过使用手动完成scipy.spatial.HalfspaceIntersection通过使用由以下定义的半空格hull1切断hull2，但仍然遇到困难，并且不敢相信这还没有在某个地方实现。

请注意，如果不使用 scipy，我不介意。

我会尝试pycddlib https://pypi.org/project/pycddlib/，实现了多面体的双重描述。多面体的双重描述是：

• V-描述：通过顶点描述
• H-描述：线性不等式系统的描述（“H”代表“超平面”）

您可能有两个凸多面体的顶点。转换为 H 描述，然后组合两个线性不等式组，然后转换为 V 表示。

这是一个例子。

import numpy as np
import pyvista as pv
import cdd as pcdd
from scipy.spatial import ConvexHull

# take one cube
cube1 = pv.Cube()
# take the same cube but translate it 
cube2 = pv.Cube() 
cube2.translate((0.5, 0.5, 0.5))

# plot 
pltr = pv.Plotter(window_size=[512,512])
pltr.add_mesh(cube1)
pltr.add_mesh(cube2)
pltr.show()

# I don't know why, but there are duplicates in the PyVista cubes;
# here are the vertices of each cube, without duplicates
pts1 = cube1.points[0:8, :]
pts2 = cube2.points[0:8, :]

# make the V-representation of the first cube; you have to prepend
# with a column of ones
v1 = np.column_stack((np.ones(8), pts1))
mat = pcdd.Matrix(v1, number_type='fraction') # use fractions if possible
mat.rep_type = pcdd.RepType.GENERATOR
poly1 = pcdd.Polyhedron(mat)

# make the V-representation of the second cube; you have to prepend
# with a column of ones
v2 = np.column_stack((np.ones(8), pts2))
mat = pcdd.Matrix(v2, number_type='fraction')
mat.rep_type = pcdd.RepType.GENERATOR
poly2 = pcdd.Polyhedron(mat)

# H-representation of the first cube
h1 = poly1.get_inequalities()

# H-representation of the second cube
h2 = poly2.get_inequalities()

# join the two sets of linear inequalities; this will give the intersection
hintersection = np.vstack((h1, h2))

# make the V-representation of the intersection
mat = pcdd.Matrix(hintersection, number_type='fraction')
mat.rep_type = pcdd.RepType.INEQUALITY
polyintersection = pcdd.Polyhedron(mat)

# get the vertices; they are given in a matrix prepended by a column of ones
vintersection = polyintersection.get_generators()

# get rid of the column of ones
ptsintersection = np.array([
    vintersection[i][1:4] for i in range(8)    
])

# these are the vertices of the intersection; it remains to take
# the convex hull
ConvexHull(ptsintersection)