# Use atan2 instead of acos to calc angle; atan2(x,y) of the point we potentially want to add
import random
from collections import namedtuple
import matplotlib.pyplot as plt
from math import atan2, degrees, tau, pi, acos, sqrt

Point = namedtuple('Point', 'x y')
Vector = namedtuple('Vector', 'x y')


def gen_point():
    a = random.uniform(1, 5)
    b = random.uniform(1, 5)

    x_i = random.uniform(1, 5)
    p_i = Point(x_i, a * x_i + b)

    return p_i


def calc_angle(v: Vector, upside_down=False) -> float:
    return (90 - degrees(atan2(v.y, v.x)) - 180*upside_down) % 360


def calc_vector(p1: Point, p2: Point) -> Vector:
    return Vector((p2.x - p1.x), (p2.y - p1.y))


def display(points, hull):
    x = [point.x for point in points]
    y = [point.y for point in points]

    h_x = [point.x for point in hull]
    h_y = [point.y for point in hull]

    plt.plot(h_x, h_y, 'ro-')

    plt.scatter(x, y)
    plt.show()


def rapper(points: set):
    min_pt = min(points)
    max_pt = max(points)
    hull = [min_pt]
    upside_down = False

    while True:
        hull.append(min(points - {hull[-1]},
                        key=lambda p: calc_angle(calc_vector(hull[-1], p), upside_down)))
        if hull[-1].x == max_pt.x:
            upside_down = True
        display(points, hull)
        if hull[-1] == min_pt:
            break

    return hull


points = {gen_point() for _ in range(30)}
hull = rapper(points)