Question

I have posted a part of my code below. Newton() function calls Bezier() function. The Bezier() function has a list from where I get p0 and p3. What I am trying to do is, in 1st iteration the program should take the first and second items from the plist as p0 and p3. Then in 2nd iteration, p0 and p3 are the second and third items and so on. With each iteration, the p0 and p3 values should change. It’s like the new p0 is the old p3. I could not put this in the code properly. Thank you.

import math

w = 1.0

def Newton(poly):
    """ Returns a root of the polynomial"""
    x = 0.5  # initial guess value
    counter = 0
    epsilon = 0.000000000001
    poly_diff = poly_differentiate(poly)

    while True:
        x_n = x - (float(poly_substitute(poly, x)) / float(poly_substitute(poly_diff, x)))
        counter += 1
        if abs(x_n - x) < epsilon :
            break
        x = x_n
        print "\tIteration " , counter , " : ", x_n

    print "u: ", x_n
    Bezier(x_n)

def Bezier(x_n) :
    """ Calculating sampling points using rational bezier curve equation"""
    u = x_n
    plist = [0.5, 0.1, 0.4, 0.35, 0.8, 0.6, 1.0, 0.2, 0.7, 0.9] # list of parameter values of the phonemes

    for i in range(len(plist) - 1) :
        p0 = plist[i]
        p3 = plist[i + 1] 
        p1 = p0
        p2 = p3
        print p0, p3   
        p_u = math.pow(1 - u, 3) * p0 + 3 * u * math.pow(1 - u, 2) * p1 \
            + 3 * (1 - u) * math.pow(u, 2) * p2 + math.pow(u, 3) * p3
        p_u = p_u * w
        d = math.pow(1 - u, 3) * w + 3 * u * w * math.pow(1 - u, 2) + 3 * (1 - u) * w * math.pow(u, 2) + math.pow(u, 3) * w
        p_u = p_u / d

    print "p(u): ", p_u
    return plist

if __name__ == "__main__" :

Answer 1

Change the top of your Bezier function to look like

def Bezier(x_n, p0, p3) :
    """ Calculating sampling points using rational bezier curve equation"""
    u = x_n
    p1 = p0
    p2 = p3

getting rid of that loop and the plist completely.

Then, in your time function (from my answer to your previous question getting a boundary of an item from another list), change it to look like:

def time() :
    tlist = [0.0, 0.12, 0.16, 0.2, 0.31, 0.34, 0.38, 0.46, 0.51] # list of start time for the phonemes
    plist = [0.5, 0.1, 0.4, 0.35, 0.8, 0.6, 1.0, 0.2, 0.7, 0.9] # list of parameter values of the phonemes

    total_frames = math.floor(tlist[-1] / 0.04)
    t_u = 0.0
    i = 0
    while i < len(tlist) - 1:
        # if the number is in the range
        # do the calculations and move to the next number
        if t_u > tlist[i] and t_u < tlist[i + 1] :
            print "\n The t_u value:", t_u, 'is between',
            print "start:", tlist[i], " and end: ", tlist[i+1]
            poly = poly_coeff(tlist[i], tlist[i + 1], t_u)
            Newton(poly, plist[i], plist[i+1])
            t_u = t_u + 0.04 # regular time interval

        # if the number is at the lower boundary of the range no need of calculation as u = 0
        elif t_u == tlist[i] :
            print "\n The t_u value:", t_u, 'is on the boundary of',
            print "start:", tlist[i], " and end: ", tlist[i+1]
            print "u : 0"
            Bezier(0, plist[i], plist[i+1])
            t_u = t_u + 0.04 # regular time interval

        # if the number is at the upper boundary of the range no need of calculation as u = 1
        elif t_u == tlist[i + 1] :
            print "\n The t_u value:", t_u, 'is on the boundary of',
            print "start:", tlist[i], " and end: ", tlist[i+1]
            print " u : 1"
            Bezier(1, plist[i], plist[i+1])
            t_u = t_u + 0.04 # regular time interval

        # if the number isn't in the range, move to the next range
        else :
            i += 1

The only changes are putting the plist there and passing the plist values to Newton and Bezier.

The only changes to you Newton function are to change the first line to

def Newton(poly, p0, p3):

and the last line to

    Bezier(x_n, p0, p3)