问假设我们知道一个多边形的顶点，并想得到它的半空间表示A*x <= b

EN

"""How to compute the halfspace representation of a convex polytope.

The polytope is given in vertex representation,
and this script shows how to convert the vertex representation
to a halfspace representation.
"""
import numpy as np
import polytope

vertices = np.array([[2, -2], [2, 2], [-10, 2], [-10, -2]])
poly = polytope.qhull(vertices)  # convex hull
    # `poly` is an instance of the class `polytope.polytope.Polytope`,
    # which is for representing convex polytopes.
    # Nonconvex polytopes can be represented too,
    # using the class `polytope.polytope.Region`.
print('Halfspace representation of convex polytope:')
print('matrix `A`:')
print(poly.A)
print('vector `b`:')
print(poly.b)
# print(poly)  # another way of printing
    # a polytope's halfspace representation

"""Showing that the question's halfspace representations are the same polytope.

Any polytope has infinitely many minimal halfspace representations.
The representations below happen to be minimal, and equal up to scaling and
permutation of rows of `A` and elements of `b`.
"""
import numpy as np
import polytope

# halfspace representation computed using `polytope`
# from the vertex representation given in the question
vertices = np.array([[2, -2], [2, 2], [-10, 2], [-10, -2]])
poly = polytope.qhull(vertices)
# first halfspace representation given in the question
A = np.array([
    [-0.00000000e+00, -1.00000000e+00],
    [-1.00000000e+00, -0.00000000e+00],
    [4.93432455e-17, 1.00000000e+00],
    [1.00000000e+00, -0.00000000e+00]])
b = np.array([2., 10., 2., 2.])
question_poly_1 = polytope.Polytope(A, b)
# second halfspace representation given in the question
A = np.array([
    [0.0, -0.4472],
    [0.4472, -0.0000],
    [0.0, 0.4472],
    [-0.0995, -0.0000]])
b = np.array([0.8944, 0.8944, 0.8944, 0.9950])
question_poly_2 = polytope.Polytope(A, b)
# check that all the above halfspace representations
# represent the same polytope
assert poly == question_poly_1, (poly, question_poly_1)
assert poly == question_poly_2, (poly, question_poly_2)

pip install polytope