import math

import numpy as np

"""
Minimal Enclosing Parallelogram

area, v1, v2, v3, v4 = mep(convex_polygon)

convex_polygon - array of points. Each point is a array [x, y] (1d array of 2 elements)
points should be presented in clockwise order.

the algorithm used is described in the following paper:
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.53.9659&rep=rep1&type=pdf
"""


def distance(p1, p2, p):
    return abs(((p2[1] - p1[1]) * p[0] - (p2[0] - p1[0]) * p[1] + p2[0] * p1[1] - p2[1] * p1[0]) /
               math.sqrt((p2[1] - p1[1]) ** 2 + (p2[0] - p1[0]) ** 2))


def antipodal_pairs(convex_polygon):
    l = []
    n = len(convex_polygon)
    p1, p2 = convex_polygon[0], convex_polygon[1]

    t, d_max = None, 0
    for p in range(1, n):
        d = distance(p1, p2, convex_polygon[p])
        if d > d_max:
            t, d_max = p, d
    l.append(t)

    for p in range(1, n):
        p1, p2 = convex_polygon[p % n], convex_polygon[(p + 1) % n]
        _p, _pp = convex_polygon[t % n], convex_polygon[(t + 1) % n]
        while distance(p1, p2, _pp) > distance(p1, p2, _p):
            t = (t + 1) % n
            _p, _pp = convex_polygon[t % n], convex_polygon[(t + 1) % n]
        l.append(t)

    return l


# returns score, area, points from top-left, clockwise , favouring low area
def mep(convex_polygon):
    def compute_parallelogram(convex_polygon, l, z1, z2):
        def parallel_vector(a, b, c):
            v0 = [c[0] - a[0], c[1] - a[1]]
            v1 = [b[0] - c[0], b[1] - c[1]]
            return [c[0] - v0[0] - v1[0], c[1] - v0[1] - v1[1]]

        # finds intersection between lines, given 2 points on each line.
        # (x1, y1), (x2, y2) on 1st line, (x3, y3), (x4, y4) on 2nd line.
        def line_intersection(x1, y1, x2, y2, x3, y3, x4, y4):
            px = ((x1 * y2 - y1 * x2) * (x3 - x4) - (x1 - x2) * (x3 * y4 - y3 * x4)) / (
                    (x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4))
            py = ((x1 * y2 - y1 * x2) * (y3 - y4) - (y1 - y2) * (x3 * y4 - y3 * x4)) / (
                    (x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4))
            return px, py

        # from each antipodal point, draw a parallel vector,
        # so ap1->ap2 is parallel to p1->p2
        #    aq1->aq2 is parallel to q1->q2
        p1, p2 = convex_polygon[z1 % n], convex_polygon[(z1 + 1) % n]
        q1, q2 = convex_polygon[z2 % n], convex_polygon[(z2 + 1) % n]
        ap1, aq1 = convex_polygon[l[z1 % n]], convex_polygon[l[z2 % n]]
        ap2, aq2 = parallel_vector(p1, p2, ap1), parallel_vector(q1, q2, aq1)

        a = line_intersection(p1[0], p1[1], p2[0], p2[1], q1[0], q1[1], q2[0], q2[1])
        b = line_intersection(p1[0], p1[1], p2[0], p2[1], aq1[0], aq1[1], aq2[0], aq2[1])
        d = line_intersection(ap1[0], ap1[1], ap2[0], ap2[1], q1[0], q1[1], q2[0], q2[1])
        c = line_intersection(ap1[0], ap1[1], ap2[0], ap2[1], aq1[0], aq1[1], aq2[0], aq2[1])

        s = distance(a, b, c) * math.sqrt((b[0] - a[0]) ** 2 + (b[1] - a[1]) ** 2)
        return s, a, b, c, d

    z1, z2 = 0, 0
    n = len(convex_polygon)

    # for each edge, find antipodal vertice for it (step 1 in paper).
    l = antipodal_pairs(convex_polygon)

    so, ao, bo, co, do, z1o, z2o = 100000000000, None, None, None, None, None, None

    # step 2 in paper.
    for z1 in range(0, n):
        if z1 >= z2:
            z2 = z1 + 1
        p1, p2 = convex_polygon[z1 % n], convex_polygon[(z1 + 1) % n]
        a, b, c = convex_polygon[z2 % n], convex_polygon[(z2 + 1) % n], convex_polygon[l[z2 % n]]
        if distance(p1, p2, a) >= distance(p1, p2, b):
            continue

        while distance(p1, p2, c) > distance(p1, p2, b):
            z2 += 1
            a, b, c = convex_polygon[z2 % n], convex_polygon[(z2 + 1) % n], convex_polygon[l[z2 % n]]

        st, at, bt, ct, dt = compute_parallelogram(convex_polygon, l, z1, z2)

        if st < so:
            so, ao, bo, co, do, z1o, z2o = st, at, bt, ct, dt, z1, z2

    return so, ao, bo, co, do, z1o, z2o


def sort_rectangle(poly):
    # sort the four coordinates of the polygon, points in is_poly should be sorted clockwise
    # First find the lowest point
    p_lowest = np.argmax(poly[:, 1])
    if np.count_nonzero(poly[:, 1] == poly[p_lowest, 1]) == 2:
        # - if the bottom line is parallel to x-axis, then p0 must be the upper-left corner
        p0_index = np.argmin(np.sum(poly, axis=1))
        p1_index = (p0_index + 1) % 4
        p2_index = (p0_index + 2) % 4
        p3_index = (p0_index + 3) % 4
        return poly[[p0_index, p1_index, p2_index, p3_index]], 0.
    else:
        #- find the point that sits right to the lowest point
        p_lowest_right = (p_lowest - 1) % 4
        p_lowest_left = (p_lowest + 1) % 4
        angle = np.arctan(
            -(poly[p_lowest][1] - poly[p_lowest_right][1]) / (poly[p_lowest][0] - poly[p_lowest_right][0]))
        # assert angle > 0
        # if angle <= 0:
        #     print(angle, is_poly[p_lowest], is_poly[p_lowest_right])
        if angle / np.pi * 180 > 45:
            #p2 - this point is p2
            p2_index = p_lowest
            p1_index = (p2_index - 1) % 4
            p0_index = (p2_index - 2) % 4
            p3_index = (p2_index + 1) % 4
            return poly[[p0_index, p1_index, p2_index, p3_index]], -(np.pi / 2 - angle)
        else:
            #p3 - this point is p3
            p3_index = p_lowest
            p0_index = (p3_index + 1) % 4
            p1_index = (p3_index + 2) % 4
            p2_index = (p3_index + 3) % 4
            return poly[[p0_index, p1_index, p2_index, p3_index]], angle
