spline interpolation

其實我唔係好明咩叫做spline interpolation.
我有search過但係網上寫既defition寫好難明
可唔可以簡單explain一下最好with example
（唔好係咁copy=.=)


1). Let xi = {0,1,2} be grid points and S1=x^3 part of a spline interpolation.

a). Let fi = {0, 1,6} and S2= 2 - 6x - 6x^2 - x^3
Is {S1, S2} a spline interpolation? if it is state its type and boundary conditions.

b). Let fi = {0, 1,3} and S2= 5 - 15x - 15x^2 - 4x^3
Is {S1, S2} a spline interpolation? if it is state its type and boundary conditions.