from math import acos, sqrt, pi, atan
import matplotlib.pyplot as plt


def triangle(euler_text_line):
    ps = list(map(int, euler_text_line.split(",")))
    ps = [(ps[0], ps[1]), (ps[2], ps[3]), (ps[4], ps[5])]
    return ps


def angle_x(x, y):
    if x > 0 and y == 0:
        return 0
    elif x < 0 and y == 0:
        return pi
    elif x == 0 and y > 0:
        return pi / 2
    elif x == 0 and y < 0:
        return 3 / 2 * pi
    elif x > 0 and y > 0:
        return atan(y / x)
    elif x < 0 and y > 0:
        return pi - atan(y / abs(x))
    elif x < 0 and y < 0:
        return pi + atan(abs(y) / abs(x))
    elif x > 0 and y < 0:
        return 2 * pi - atan(abs(y) / x)
    else:
        raise Exception("Unhandled case")


def contains_origin(triangle):
    a, b, c = triangle
    angles = sorted([angle_x(*a), angle_x(*b), angle_x(*c)])
    a = angles[1] - angles[0]
    b = angles[2] - angles[1]
    c = angles[0] + 2 * pi - angles[2]
    return not (a + b < pi or b + c < pi or c + a < pi)


def euler_102():
    with open("../txt/e102.txt", "r") as f:
        triangles = list(map(triangle, f.readlines()))
    return len([1 for t in triangles if contains_origin(t)])


if __name__ == "__main__":
    solution = euler_102()
    print("e102.py: " + str(solution))
    assert(solution == 228)