Multivariate interpolation

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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 (x_i, y_i, z_i, \dots) and the interpolation problem consist of yielding values at arbitrary points (x,y,z,\dots).

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[edit] Uniform grid

For function values known on a prescribed uniform grid, the following methods are available

[edit] 2 dimensions


Bitmap resampling is the application of 2D multivariate interpolation in image processing.

Three of the methods applied on the same dataset, from 16 values located at the black dots. The colours represent the interpolated values.

Nearest neighbor

Bilinear

Bicubic

See also Padua points, for polynomial interpolation in two variables.

[edit] 3 dimensions

See also bitmap resampling

[edit] Non-uniform grid

Schemes defined on a non-uniform grid should all work on a uniform grid, typically reducing to another known method.


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