# Use atan2 instead of acos to calc angle; atan2(x,y) of the point we potentially want to add
from math import acos, sqrt

from util import Vector, Point, gen_point, display


def calc_angle(v1: Vector, v2: Vector) -> float:
    dot = (v1.x * v2.x) + (v1.y * v2.y)
    len_1 = sqrt(v1.x**2 + v1.y**2)
    len_2 = sqrt(v2.x**2 + v2.y**2)

    tmp = dot / (len_1 * len_2)

    return acos(round(tmp, 6))


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


def rapper(points: set):
    min_pt = min(points)
    hull = [min_pt]
    comp_vec = Vector(0, 1)
    while True:
        hull.append(min(points - {hull[-1]},
                        key=lambda p: calc_angle(comp_vec,
                                                 calc_vector(hull[-1], p))))
        comp_vec = calc_vector(hull[-2], hull[-1])

        if hull[-1] == min_pt:
            return hull


if __name__ == '__main__':
    points = {gen_point() for _ in range(30)}
    hull = rapper(points)