问在python中，如何检查四个元组点是否形成正方形、矩形、平行四边形或菱形？

EN

import numpy as np

def quadrilateral2(*args):
    if len(args) != 4:
        return 'Not a quadrilateral'
    args = np.array(args)
    vectors = np.array([args[i-1]-j for i, j in enumerate(args)])
    unique_vectors = np.unique(np.round(np.abs(vectors), 6), axis=0) #Round to avoid numerical errors: can change the number of digits to round to
    if len(unique_vectors) != 2:
        return 'Not a square, rectangle, rhombus or parallelogram'
    norms = [np.linalg.norm(i) for i in vectors]
    norm_vectors = [i/j for i, j in zip(vectors, norms)]
    unique_norms = set(round(i, 6) for i in norms) # Again, round for numerical errors
    angles = [np.arccos(np.dot(norm_vectors[i-1], j)) for i, j in enumerate(norm_vectors)]

    if all(i == np.pi/2 for i in angles):
        if len(unique_norms) == 1:
            return 'Square'
        if len(unique_norms) == 2:
            return 'Rectangle'
    
    elif len(set(round(i, 6) for i in angles)) == 2: #Again, round for numerical errors
        if len(unique_norms) == 1:
            return 'Rhombus'
        if len(unique_norms) == 2:
            return 'Parallelogram'
    else:
        return 'Not a square, rectangle, rhombus or parallelogram'

square = [(2, 2), (2, 4), (4,4), (4, 2)]
rectangle = [(2, 2), (2,8), (4, 8), (4, 2)]
rhombus = [(0, 0), (np.sqrt(8), 0), (2+np.sqrt(8), 2), (2, 2)]
parallelogram = [(2,2), (5, 2), (6,4), (3,4)]
print(quadrilateral2(*square))
print(quadrilateral2(*rectangle))
print(quadrilateral2(*rhombus))
print(quadrilateral2(*parallelogram))
print(quadrilateral2(*[[2, -3], [6, 5], [-2, 1], [-6, -7]]))
print(quadrilateral2(*[(0, 0), (0, -5), (3,2.5), (3, -2.5)]))
print(quadrilateral2(*[(0, 2), (0, -2), (-1,0), (1, 0)]))

Square
Rectangle
Rhombus
Parallelogram
Rhombus
Not a square, rectangle, rhombus or parallelogram
Not a square, rectangle, rhombus or parallelogram

import itertools
import numpy as np


def quadrilateral(*args):
    tol = 1e-4
    if not len(args) == 4:
        return 'Not a quadrilateral'
    #Calculate all permutations of the coordinates
    permutations = np.array(list(itertools.permutations(args, r=2)))
    #Calculate all distances
    distances = np.array(list(np.sqrt(sum((i[0]-i[1])**2)) for i in permutations))
    #Choose unique distances within a tolerance tol
    distances = distances[~(np.triu(np.abs(distances[:,None] - distances) <= tol,1)).any(0)]
    #Calculate all absolute angles
    angles = np.array(list(abs(np.arctan2(*(i[0]-i[1])[::-1])) for i in permutations))
    #Choose unique angles within a tolerance tol
    angles = sorted(angles[~(np.triu(np.abs(angles[:,None] - angles) <= tol,1)).any(0)])
    if len(distances) == 2 and all(np.pi*i/4 == j for i, j in enumerate(angles)):
            return "It's a square"
    elif len(distances) == 3:
        if len(angles) == 5:
            return "It's a rectangle"
        elif len(angles) == 8:
            return "It's a rhombus"
        else:
            return 'Not a square, rectangle, rhombus or parallelogram'
    elif len(distances) == 4 and len(angles) == 8:
        return "It's a parallelogram"
    else:
        return 'Not a square, rectangle, rhombus or parallelogram'

square = [(2, 2), (2, 4), (4,2), (4, 4)]
rectangle = [(2, 2), (4, 2), (2,8), (4, 8)]
rhombus = [(0, 0), (2, 2), (np.sqrt(8), 0), (2+np.sqrt(8), 2)]
parallelogram = [(2,2), (3,4), (5, 2), (6,4)]
print(quadrilateral(*square))
print(quadrilateral(*rectangle))
print(quadrilateral(*rhombus))
print(quadrilateral(*parallelogram))

It's a square
It's a rectangle
It's a rhombus
It's a parallelogram