Triangle and Point class for Project Euler

from __future__ import print_function, division
"""See Project Euler Problem 102 (http://projecteuler.net/index.php?section=problems&id=102) for the problem definition,
shortly we must determine which triangles contain the origin point.

Algorith used:

If a point P is inside triangle ABC, then

Area PAB+Area PBC +Area PAC=Area ABC

notice that if P is on the edge of AB, BC, or CA, the above hold. But effectively, one of the area PAB, PBC, PAC is 0 (so just make sure you check that).

if P is outside, the above equality does NOT hold...

How to determine area? you have two options:
1) Heron's theorem, involves sqrt, slower
2) the more perferred way is the cross products (or effectively, the half of absolute value of (sum of the down products minus the sum of up products))

for example, if A=(x1,y1) B=(x2,y2), C=(x3,y3)
Area= abs(x1*y2+x2*y3+x3*y1-x1*y3-x3*y2-x2*y1)/2

also you might want to be careful about floating point errors... instead of checking for strict inequality,
check for abs(b-a)<eps, where eps can be a small value, such as 1e-12 (0.000000000001)

Source:
http://compsci.ca/v3/viewtopic.php?t=6034"""
from  collections import namedtuple
Point = namedtuple('Point', 'x y')

origin = Point(0,0)
eps = 1e-12

class Triangle(object):
    def __init__(self, a = None, b = None, c = None, string = ""):
        if string:
            self.from_string(string)
        else:
            self.a = a
            self.b = b
            self.c = c

    def area(self):
        return abs(self.a.x * self.b.y +
                    self.b.x * self.c.y +
                    self.c.x * self.a.y -
                    self.a.x * self.c.y -
                    self.c.x * self.b.y -
                    self.b.x * self.a.y) / 2.0

    def is_inside(self, point):
        triangles = (Triangle(point, self.a, self.b), Triangle(point, self.b, self.c), Triangle(point, self.a, self.c))
#         print  sum(t.area() for t in triangles) , self.area()
        return abs(sum(t.area() for t in triangles) - self.area()) < eps

    def from_string(self, point_string):
        coords = map(float, point_string.strip().split(','))
        self.a, self.b, self.c  = Point(*coords[:2]), Point(*coords[2:4]),Point(*coords[4:])

    def __repr__(self):
        return 'Triangle({self.a}, {self.b}, {self.c})'.format(self = self)
    __str__ = __repr__

test = "Triangle(Point(x=-340, y=495), Point(x=-153, y=-910), Point(x=835, y=-947))"
assert repr(eval(test)) == test

print('Solution for Euler problem 102 is {0}'.format(sum(tri.is_inside(origin)
                                                for tri in (Triangle(string=line)
                                                for line in open('triangles.txt')))) )
# debug lines
# :#(Triangle(Point(-340,495),Point(-153,-910),Point(835,-947)), Triangle(Point(-175,41), Point(-421,-714), Point(574,-645))):
#     print('Origin inside %s: %s' % (tri, tri.is_inside(origin)))
#print( Triangle(Point(-340,495),Point(-153,-910),Point(835,-947)))
#print(str(Triangle(Point(-340,495),Point(-153,-910),Point(835,-947))))