quadratic polynomial to quadratic bezier

gistfile1.py

from math import factorial

def nchoosek(n, k):
    return factorial(n) / (factorial(k) * factorial(n - k))

class point(tuple):
    def __add__(self, other):
        return point(ps + po for ps, po in zip(self, other))

    def __mul__(self, scalar):
        return point(scalar * p for p in self)

    def __rmul__(self, scalar):
        return self * scalar

class origin(point):
    def __add__(self, other):
        return other

    def __mul__(self, scalar):
        return self

class bezier(tuple):
    def __call__(self, t):
        n = len(self) - 1
        return sum((nchoosek(n, i) * pow(1 - t, n - i) * pow(t, i) * p
                    for i, p in enumerate(self)), origin())

class quadratic(tuple):
    def __call__(self, x):
        return sum(an * pow(x, n) for n, an in enumerate(self))

    def bezier(self, xi, dx):
        c, b, a = self
        return bezier((point((xi, self(xi))),
                       point((xi + dx / 2., a * xi**2 + b * (xi + dx / 2.) + c)),
                       point((xi + dx, self(xi + dx)))))