In univariate interpolation, an interpolant is a function 
which agrees with a particular function 
at a set of known points 
and which is used to compute values for
at points 
, 
.
Modulo a change of notation, the above definition translates verbatim to multivariate interpolation models as well.
Generally speaking, the properties required of the interpolant are the most fundamental designations between various interpolation models. For example, the main difference between the linear and spline interpolation models is that the interpolant of the prior is required merely to be piecewise linear whereas spline interpolants are assumed to be piecewise polynomial and globally smooth.
