Spatial interpolation

In numerical analysis, multivariate interpolation or spatial interpolation is interpolation on functions of more than one variable.

The function to be interpolated is known at given points ${\displaystyle (x_{i},y_{i},z_{i},\dots )}$ and the interpolation problem consist of yielding values at arbitrary points ${\displaystyle (x,y,z,\dots )}$.

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.

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