check if point belongs to polygon

inner_points.py

# coding: utf-8
import cmath
import unittest
from itertools import chain


def eq_to_zero(x, eps=1e-7):
    return abs(x) < eps


def degree(c_0, *cs):
    """

    см. http://ru.wikipedia.org/wiki/Теорема_Жордана,
    часть про описание внутренности как множества точек,
    у которых степень относительно кривой равна +- 1.

    """
    cs = iter(cs)

    deg = 0
    initial_num = cs.next()
    prev_vector = initial_num - c_0
    for cur_num in chain(cs, iter([initial_num])):
        cur_vector = cur_num - c_0
        if eq_to_zero(cur_vector):
            deg += 0
            continue

        deg += cmath.phase(prev_vector / cur_vector)
        prev_vector = cur_vector

    return deg


def is_inner(point, closed_polyline):
    deg = degree(complex(*point), *map(lambda t: complex(*t), closed_polyline))
    return not eq_to_zero(deg)


class UnitsIntersectionTestCase(unittest.TestCase):
    def test_degree(self):
        self.assertTrue(is_inner([0.5, 0.5], [[0, 0], [1, 0], [0, 1], [0, 0]]))
        self.assertTrue(is_inner([0, 0], [[1, 0], [1, 1], [-1, 1], [-1, -1], [1, -1], [1, 0]]))

        self.assertFalse(is_inner([-1, -1], [[0, 0], [1, 0], [0, 1], [0, 0]]))


if __name__ == '__main__':
    unittest.main()