If ncp is zero, linear interpolation is used in the triangles bounded by data points. Cubic interpolation is done if partial derivatives are used. If extrap is FALSE, z-values for points outside the convex hull are returned as NA. No extrapolation can be performed if ncp is zero.
interp
(Package: akima) :
Gridded Bivariate Interpolation for Irregular Data
These functions implement bivariate interpolation onto a grid for irregularly spaced input data. Bilinear or bicubic spline interpolation is applied using different versions of algorithms from Akima.