bezier.py

def make_bezier(xys):
    # xys should be a sequence of 2-tuples (Bezier control points)
    n=len(xys)
    combinations=pascal_row(n-1)
    def bezier(ts):
        # This uses the generalized formula for bezier curves
        # http://en.wikipedia.org/wiki/B%C3%A9zier_curve#Generalization
        result=[]
        for t in ts:
            tpowers=(t**i for i in range(n))
            upowers=reversed([(1-t)**i for i in range(n)])
            coefs=[c*a*b for c,a,b in zip(combinations,tpowers,upowers)]
            result.append(
                tuple(sum([coef*p for coef,p in zip(coefs,ps)]) for ps in zip(*xys)))
        return result
    return bezier

def pascal_row(n):
    # This returns the nth row of Pascal's Triangle
    result=[1]
    x,numerator=1,n
    for denominator in range(1,n//2+1):
        # print(numerator,denominator,x)
        x*=numerator
        x/=denominator
        result.append(x)
        numerator-=1
    if n&1==0:
        # n is even
        result.extend(reversed(result[:-1]))
    else:
        result.extend(reversed(result)) 
    return result