import math

ZERO = (0, 0)

def dot(x1, y1, x2, y2):
    return (x1 * x2) + (y1 * y2)

def length(x, y):
    return math.sqrt((x * x) + (y * y))

def normalize(x, y):
    _len = length(x, y)
    return x / _len, y / _len

def scale(x, y, factor):
    return x * factor, y * factor

def add(x1, y1, x2, y2):
    return x1 + x2, y1 + y2

def sub(x1, y1, x2, y2):
    return x1 - x2, y1 - y2

def vmin(x1, y1, x2, y2):
    return min(x1, x2), min(y1, y2)

def vmax(x1, y1, x2, y2):
    return max(x1, x2), max(y1, y2)