Interpolation problem

find a function which passes through (or close to) the given set of discrete points:
univariate - curve:  y = f(x)
bivariate - surface: z = f(x,y)
trivariate - volume: w = f(x,y,z)
quadvariate - dynamic volume: w = f(x,y,z,t)
The problem does not have a unique solution and the character and properties of the interpolation function f(r) depend on additional conditions (statistical, geometrical:smoothnes, locality, physical: minimum energy, etc.)