Test if a point is inside a triangle

point_inside_triangle.py

import numpy as np

def point_inside_triangle(p, a, b, c):
    '''
    Check whether point p is inside the triangle of (a,b,c).
    '''
    return same_side(p, a, b, c) \
        and same_side(p, b, a, c) \
        and same_side(p, c, a, b)

def same_side(p1, p2, x, y):
    '''
    Check if p1 and p2 stay within the same side of halves of plane divided by x and y.
    
           p1
          /
         /
        x ____________ y
         \
          p2
    '''
    cp1 = cross_product(y-x, p1-x)
    cp2 = cross_product(y-x, p2-x)
    return dot_product(cp1, cp2) >= 0

def vector(*args):
    return np.array(args)

def dot_product(x, y):
    return np.dot(x, y)

def cross_product(x, y):
    return np.cross(x, y)

if __name__ == '__main__':
    a = vector(1,1)
    b = vector(3,2)
    c = vector(2,4)
    points = ( vector(*x) for x in ( (2,2), (2,3), (1,1), (2,4), (3,2), (1,3), (3,4)) )
    print [ point_inside_triangle(p, a, b, c) for p in points ]