Algorithm from Wiki

Input: set of coordinates C, with |C| = n+1

Output: set splines which is composed of n 5-tuples.

Create new array a of size n + 1 and for i = 0 ,..., n set a_i = y_i

Create new arrays b and d each of size n.

Create new array h of size n and for i = 0 ,..., n-1 set h_i = x_i+1 - x_i

Create new array α of size n and for i = 1 ,..., n-1 set α_i = (3 / h[i] x (a_i+1 - a_i)) - (3 / h_i-1 x (a_i - a_i-1)).

Create new arrays c, l, μ, and z each of size n+1

Set l₀ = 1, u₀ = z₀ = 0

For i = 1 ,..., n-1

• Set l_i = 2 x( x_i+1-x_i-1) - h_i-1 x u_i-1.
• Set u_i = h_i/l_i.
• Set z_i = (α_i-1 - (h_i-1 x z_i-1)) / l_i
• Set l_n = 1; z_n = c_n = 0

For j = n-1 , n-2 ,..., 0

• Set c_j = z_j - u_j x c_j+1
• Set b_j = ((a_j+1 - a_j) / h_j) - (h_j x (c_j+1 + 2 x c_j) / 3)
• Set d_j = (c_j+1 - c_j) / (3 x h_j)

Create new set Splines and call it output_set. Populate it with n splines S.

For i = 0 ,..., n-1

• Set Si,a = ai
• Set Si,b = bi
• Set Si,c = ci
• Set Si,d = di
• Set Si,x = xi

Output output_set