Function Bezier Curve

study("Function Bezier Curve", overlay=true)
useHA = input(false, title='Use Heikken Ashi Candles')
useAltTF = input(true, title='Use Alt Timeframe')
tf = input('D', title='Alt Timeframe')
zigzag() =>
    _isUp = close >= open
    _isDown = close <= open
    _direction = _isUp[1] and _isDown ? -1 : _isDown[1] and _isUp ? 1 : nz(_direction[1])
    _zigzag = _isUp[1] and _isDown and _direction[1] != -1 ? highest(2) : _isDown[1] and _isUp and _direction[1] != 1 ? lowest(2) : na

_ticker = useHA ? heikenashi(tickerid) : tickerid
sz = useAltTF ? (change(time(tf)) != 0 ? security(_ticker, tf, zigzag()) : na) : zigzag()

plot(sz, title='zigzag', color=black, linewidth=2)


pb = valuewhen(sz, sz, 2) 
pc = valuewhen(sz, sz, 1) 
pd = valuewhen(sz, sz, 0)
tb = valuewhen(sz, n, 2) 
tc = valuewhen(sz, n, 1) 
td = valuewhen(sz, n, 0)

//  ||  Function for drawing Bezier Curves:
//  ||  y = price scale
//  ||  (percentage of time, start point, start control point, end control point, end point)
f_CalculateBezierPoint(_percent, _p0_y, _p1_y, _p2_y, _p3_y)=>
    _u = 1 - _percent
    _tt = pow(_percent, 2)
    _uu = _u * _u
    _uuu = _uu * _u
    _ttt = _tt * _percent
    _p_y1 = _uuu * _p0_y //first term
    _p_y2 = _p_y1 + 3 * _uu * _percent * _p1_y //second term
    _p_y3 = _p_y2 + 3 * _u * _tt * _p2_y //third term
    _p_y4 = _p_y3 + _ttt * _p3_y //fourth term
    _return = _p_y4

//  Input Variables:
perc = (n-td)/(td-tc)
p0_start = pd
p0_control = pd > pc ? pd+(pd-pc) : pd-(pd-pc)
p1_control = pd > pc ? pc+(pd-pc)*-2 : pc-(pd-pc)*2
p1_end = pc
//  Output Variables:
lin_y = f_CalculateBezierPoint(perc, p0_start, p0_control, p1_control, p1_end)
lin_y0 = lin_y - (pd-pc)*0.618
lin_y1 = lin_y + (pd-pc)*0.618
//  Output:
p0 = plot(change(pd)!=0?na:lin_y, style=linebr, color=navy)
p1 = plot(change(pd)!=0?na:lin_y0, style=linebr, color=navy)
p2 = plot(change(pd)!=0?na:lin_y1, style=linebr, color=navy)
fill(p0, p1, color=black, transp=25)
fill(p0, p2, color=black, transp=50)