[This is actually my project report for my Numerical Analysis course this semester]
* Cubic Spline Algorithm application in Typeface Design
As known Cubic Spline is usually the best choice in computer graphics applications, which have 2nd order continuity. If Typeface Design ([Knuth 1979] – this guy again !), each dimension (X & Y) should be applied with a Cubic Spline algorithm. Then, the curve nodes will be [Xi, Yi].
My work is as: 
* Polynomial & Chebyshev & Cubic Spline Interpolation
The target function: f(x) = (1 + 6 * x ^ 2) ^ –1 (A typical Runge Function)
Polynomial Interpolation (Newton Form)
Ck = (Yk - Pk-1(xk)) / (Xk - X0)(Xk - X1)..(Xk - Xk-1) is used to calculate coefficiences;
u = u (X - Xi) + Ci (Horner Method) is used to compute the final results.
The Runge Phenomena is really obvious … this is why Polynomial is a bad choice for a wide range of interpolation.
Chebyshev:
Xi = cos[(i - 1) * PI / 20] (1 <= i <= 21)
Cubic Spline Interpolation:
Much better isn’t it : )