from visual import *

p0 = [0,0]
p1 = [10,0]
v0 = [0,20]
v1 = [0,-10]

def A(t):
    return (t-1)**2*(2*t+1)

def B(t):
    return -t**2*(2*t-3)

def C(t):
    return t*(1-t)**2

def D(t):
    return t**2*(t-1)

def Hermite(p0,p1,v0,v1):
    points(pos = [p0, p1])
    arrow(pos=p0, axis=v0, shaftwidth=0.01)
    arrow(pos=p1, axis=v1, shaftwidth=0.01)
    t = arange(0,1.01, 0.01)
    At, Bt, Ct, Dt = A(t), B(t), C(t), D(t)
    curve(x = At*p0[0]+Bt*p1[0]+Ct*v0[0]+Dt*v1[0],y = At*p0[1]+Bt*p1[1]+Ct*v0[1]+Dt*v1[1],radius = 0.1, color=color.red)

Hermite(p0,p1,v0,v1)