function for dividing quadrangle into two triangles that create it regardless of initial points order

quadrangle to triangles

import math

def matrix_det(mat):  # mat - matrix
    det, k_1, k_2 = 0, 1, 1
    for i in range(3):
        for j in range(3):
            k_1 *= mat[(i + j) % 3][j % 3]
            k_2 *= mat[-((i + j) % 3)][-(j % 3)]
        det += k_1 - k_2
    return det

def subtract_vectors(a,b):
    return tuple([bi - ai for ai, bi in zip(a, b)])

def add_vectors(a,b):
    return tuple([bi + ai for ai, bi in zip(a, b)])

def vector_len(vec):
    return math.sqrt(sum(i**2 for i in vec))

def dot_product(v1,v2):
    return sum(v1_i*v2_i for v1_i,v2_i in zip(v1,v2))

def vectors_angle(v1,v2):
    return math.acos(dot_product(v1,v2)/(vector_len(v1)*vector_len(v2)))

def middle_vector(v):
    angles, v = [], set(v)
    for vector in v:
        angles.append([vectors_angle(*v.difference({vector})), vector])
    return max(angles)[1]

def coplanarity(v): # v - vectors
    return matrix_det(v) == 0

def quad_to_triang(a,*points):
    if len(points) != 3:
        raise ValueError
    v=[]
    for point in points:
        v.append(subtract_vectors(a,point))

    if not coplanarity(v):
        raise ValueError

    c = add_vectors(middle_vector(v), a)
    v.remove(middle_vector(v))
    b = add_vectors(v[0], a)
    d = add_vectors(v[1], a)
    return (a, c, b,
            a, c, d)

# test
# = [ x,  y,  z]
a = [ 1,  5,  0]
b = [ 5,  4,  0]
c = [ 1,  2,  0]
d = [ 4,  1,  0]
print(quad_to_triang(a,b,c,d))