
Nearest neighbor

Bilinear

Bicubic
In numerical analysis, multivariate interpolation is interpolation on functions of more than one variable (multivariate functions); when the variates are spatial coordinates, it is also known as spatial interpolation.
The function to be interpolated is known at given points and the interpolation problem consists of yielding values at arbitrary points .
Multivariate interpolation is particularly important in geostatistics, where it is used to create a digital elevation model from a set of points on the Earth's surface (for example, spot heights in a topographic survey or depths in a hydrographic survey).
For function values known on a regular grid (having predetermined, not necessarily uniform, spacing), the following methods are available.
Bitmap resampling is the application of 2D multivariate interpolation in image processing.
Three of the methods applied on the same dataset, from 25 values located at the black dots. The colours represent the interpolated values.
See also Padua points, for polynomial interpolation in two variables.
See also bitmap resampling.
CatmullRom splines can be easily generalized to any number of dimensions. The cubic Hermite spline article will remind you that for some 4vector which is a function of x alone, where is the value at of the function to be interpolated. Rewrite this approximation as
This formula can be directly generalized to N dimensions:^{[1]}
Note that similar generalizations can be made for other types of spline interpolations, including Hermite splines. In regards to efficiency, the general formula can in fact be computed as a composition of successive type operations for any type of tensor product splines, as explained in the tricubic interpolation article. However, the fact remains that if there are terms in the 1dimensional like summation, then there will be terms in the dimensional summation.
Schemes defined for scattered data on an irregular grid are more general. They should all work on a regular grid, typically reducing to another known method.
Gridding is the process of converting irregularly spaced data to a regular grid (gridded data).