Rectangular or bi-linear interpolation

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Rectangular or bi-linear interpolation

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With a reasonably dense and uniform arrangement of data points (or with a grid image file) a number of simple and fast interpolation procedures can be performed. A common procedure for non-uniform data involves dividing the area around a grid point to be interpolated with a segmented circle enclosing a number of neighboring data points. The nearest data point in each of four segments or sectors of the circle is then selected and a 4-sided polygon defined connecting these points. This polygon can be used to define a weighted average for the grid point, either directly (e.g. using simple inverse distance weighting) or indirectly by assigning an adjusted value to each of the 4 grid cells that surround the sample point and taking the average of these. In either case a square or rectangle is determined which again may be used to assign a linearly interpolated value to the central grid point. The cell-based version of this procedure is widely used in image processing, including re-scaling/resampling operations.