Inverse distance weighting

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Inverse distance weighting (IDW) is a simple method for curve fitting, a process of assigning values to unknown points by using values from known points. A simple IDW weighting factor is

$w(d)=\frac{1}{d^p}$ ,

where $w (d)$ is the weighting factor applied to a known value, $d$ is the distance from the known value to the unknown value, and $p$ is a user-selected power factor. Here weight decreases as distance increases from the interpolated points. Greater values of $p$ assign greater influence to values closest to the interpolated point. The most common value of $p$ is 2.

A general form of interpolating a value using IDW is

$Z=\frac{\sum_{i=1}^N \frac{Z_i}{d_i^p}}{\sum_{i=1}^N \frac{1}{d_i^p}}$