xi1 = [x[i] for i in index]
xi0 = [x[i - 1] for i in index]
yi1 = [y[i] for i in index]
yi0 = [y[i - 1] for i in index]
zi1 = [z[i] for i in index]
zi0 = [z[i - 1] for i in index]
hi1 = [xi1[i] - xi0[i] for i in range(len(xi1))]

f0 = []
for i in range(len(zi0)):
    value = zi0[i] / (6 * hi1[i]) * (xi1[i] - x0[i])**3 + \
            zi1[i] / (6 * hi1[i]) * (x0[i] - xi0[i])**3 + \
            (yi1[i] / hi1[i] - zi1[i] * hi1[i] / 6) * (x0[i] - xi0[i]) + \
            (yi0[i] / hi1[i] - zi0[i] * hi1[i] / 6) * (xi1[i] - x0[i])
    f0.append(value)