spline.py

class Point:
    def __init__(self,x,y):
        self.x = float(x)
        self.y = float(y)


def Spline(points):
    N   = len(points)-1
    w   =     [(points[i+1].x-points[i].x)      for i in range(N  )]
    h   =     [(points[i+1].y-points[i].y)/w[i] for i in range(N  )]
    ftt = [0]+[3*(h[i+1]-h[i])/(w[i+1]+w[i])    for i in range(N-1)]+[0]
    A   =     [(ftt[i+1]-ftt[i])/(6*w[i])       for i in range(N  )]
    B   =     [ftt[i]/2                         for i in range(N  )]
    C   =     [h[i]-w[i]*(ftt[i+1]+2*ftt[i])/6  for i in range(N  )]
    D   =     [points[i].y                      for i in range(N  )]
    return A,B,C,D


def PrintSpline(points,A,B,C,D):
    for i in range(len(points)-1):
        func = str(points[i].x)+' <= x <= '+str(points[i+1].x)+' : f(x) = '
        components = []
        if A[i]:
            components.append(str(A[i])+'(x-'+str(points[i].x)+')^3')
        if B[i]:
            components.append(str(B[i])+'(x-'+str(points[i].x)+')^2')
        if C[i]:
            components.append(str(C[i])+'(x-'+str(points[i].x)+')')
        if D[i]:
            components.append(str(D[i]))
        if components:
            func += components[0]
            for i in range (1,len(components)):
                if components[i][0] == '-':
                    func += ' - '+components[i][1:]
                else:
                    func += ' + '+components[i]
            print func
        else:
            print func+'0'


# Usage Example
points = [Point(x,y) for x,y in [(1,0),(2,1),(3,0),(4,1),(5,0)]]
A,B,C,D = Spline(points)
PrintSpline(points,A,B,C,D)