def bell(t0):
    A =  -2
    B =   3
    t = t0
    m =  1
    if(t0< (-1)):
        return -1
    if(t0>1):
        return 1
    if t0<0:
	t=(-t0)
    ts = t*t
    return (A*t*ts + B*ts)

#input    0 <= t0 <= 2
#outputs [0:1] smoothed inverted bell curve
def invbell(t0):
    t=t0-1
    return (bell(t)-1)

#input    0 <= t0 <= 2
#outputs  [0:1] smoothed positive bell curve
def pbell(t0):
    t=t0-1
    return (1-bell(t))

#bell2
#input    0 <= t0 <= 4
#input    0 <= t0 <= 2 then 
#outputs [0:1] smoothed positive bell curve
#input    2 <= t0 <= 4
#outputs [0 : -1] smoothed inverted bell curve
def bell2(t0):
    if (t0<=2):
	return pbell(t0)
    return invbell(t0-2)

#bell4
#input t0 is positive integer t0 mod 4 is used
#input    0 <= t0 <= 2 then 
#outputs [0:1] smoothed positive bell curve
#input    2 <= t0 <= 4
#outputs [0 : -1] smoothed inverted bell curve
def bell4(t0):
    t = t0 % 4
    return bell2(t)

#cycles between the minimum and maximum of the range
#starts at the median when t=0
def range(t0, min, max):
    t = t0 % 4
    f = bell2(t)
    d = max - min
    m = d/2.0
    median = min + m
    return median+f*m