What it calculates

Bilinear interpolation is an extension on linear interpolation. Linear interpolation uses two points to interpolate in one dimension where bilinear interpolation uses 4 points to interpolate in two dimensions. We always interpolate for a point (the point to be interpolated P_tbi), so regardless if the output is a scalar, regular or irregular grid; the output is reduced to points for which a value is calculated individually. In the case of scalar values, this reduction means using it's X and Y coordinates from the associated location. For regular or irregular grids, the X and Y coordinates of each cell center is used. The input can only be a regular grid. 

This leaves us with a collection of P_tbi's and an input grid. First the 4 surrounding cell centers (P_s) for the P_tbi are selected from input grid.

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Now the values of these 4 points are used to calculate the interpolated value as shown below (first interpolate twice on the X axis, then from the resulting points once on the Y axis).

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Some exceptions:

• If the P_tbi has the same location as one of the P_s's, the resulting value for P_tbi will be that of the P_s.
• If the P_tbi is on a horizontal or vertical line between 2 P_s's, the resulting value for P_tbi will be a linear interpolation between those two P_s's.
• If there are less then 4 surrounding points (when for example the P_tbi is outside the input grid), there will be no resulting value for P_tbi

_Schema

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Overruling coordinate attributes

It is possible to configure overruling X and Y attributes, which will overrule the X and Y coordinates use for the interpolation.

<transformation id="bilinear">
   <interpolationSpatial>
      <bilinear>
         <inputVariable>
            <timeSeriesSet>
               <moduleInstanceId>SpatialInterpolationBilinearOverrulingCoordinatesTest</moduleInstanceId>
               <valueType>grid</valueType>
               <parameterId>T.historical</parameterId>
               <locationId>gridLocation3</locationId>
               <timeSeriesType>external historical</timeSeriesType>
               <timeStep unit="day"/>
               <relativeViewPeriod unit="day" start="0" end="10"/>
               <readWriteMode>add originals</readWriteMode>
            </timeSeriesSet>
         </inputVariable>
         <overrulingXAttribute>overrulingX</overrulingXAttribute>
         <overrulingYAttribute>overrulingY</overrulingYAttribute>
         <outputVariable>
            <timeSeriesSet>
               <moduleInstanceId>SpatialInterpolationBilinearOverrulingCoordinatesTest</moduleInstanceId>
               <valueType>scalar</valueType>
               <parameterId>T.historical</parameterId>
               <locationId>polygonLocation2</locationId>
               <timeSeriesType>external historical</timeSeriesType>
               <timeStep unit="day"/>
               <relativeViewPeriod unit="day" start="0" end="10"/>
               <readWriteMode>add originals</readWriteMode>
            </timeSeriesSet>
         </outputVariable>
      </bilinear>
   </interpolationSpatial>
</transformation>