# Gift wrapping algorithm
# https://en.wikipedia.org/wiki/Gift_wrapping_algorithm
# Date: 2021-11-16

import random
import matplotlib.pyplot as plt


def generate_points(n=100):
    X = []
    Y = []
    for _i in range(n):
        X.append(random.random())
        Y.append(random.random())
    plt.plot(X, Y, ".")
    return [(X[i], Y[i]) for i in range(n)]


def cross_product(u, v):
    x1, y1 = u
    x2, y2 = v
    return x1 * y2 - x2 * y1


def gift_wrapping(points):
    convex_hull = []
    x_sorted = sorted(points, key=lambda point: point[0])
    left_most = x_sorted[0]
    point_on_hull = left_most
    endpoint = None
    while endpoint != left_most:
        convex_hull.append(point_on_hull)
        endpoint = points[0]
        for point in points:
            cp = cross_product(
                (endpoint[0] - point_on_hull[0], endpoint[1] - point_on_hull[1]),
                (point[0] - point_on_hull[0], point[1] - point_on_hull[1]),
            )
            if endpoint == point_on_hull or cp < 0:
                endpoint = point
        point_on_hull = endpoint
    return convex_hull


def draw_points(points, with_edge=False):
    X, Y = [], []
    for p in points:
        X.append(p[0])
        Y.append(p[1])
    plt.plot(X, Y, "." if not with_edge else "")


pts = generate_points(50)

print(pts)
draw_points(pts)
hull = gift_wrapping(pts)
draw_points(hull + [hull[0]], True)
plt.show()