symmetric cubic spline

Hi, guys

anyone can tell me what is symmetric cubic spline which is used in multi-block LBM?
where can I find reference about the kind of spline?


this is a good tutorial

by the way I think you will get this equation

f(2.5) = 1/16 f(1) + 9/16 f(2) + 9/16 f(3)  1/16 f(4)

|     |     |     |     |     |     |      fine mesh
|     |     |     |     |     |     | 
|           |           |           |
|           |           |           |      coarse mesh



It is very kind of you for giving me the material and the heuristic diagram.

In your opinion, the symmetric cubic spline is nothing but a special knots distribution. Do I understand your intention exactly?

yes you can say that

but the exat definition is:

Cubic splines are a popular choice for curve fitting for ease of data interpolation, integration, differentiation,
and they are normally very smooth

The key characteristics of cubic spline interpolation are:
1. The curves pass through all specified data points
2. 1st derivative continuity at interior points
3. 2nd derivative continuity at interior points
4. boundary conditions specified at the free ends