The atmospheric model uses a Reduced Gaussian Octahedral grid (which is triangular in nature).   Interpolation of NWP model values to and from the MIR grid uses a triangular interpolation technique which:  

Fig3.3.1: The Reduced Gaussian grid is triangular in nature.  The interpolation uses the three corner points (black points) closest to the selected location (red point) and takes a weighted average based upon the proximity of the point to the to vertices to arrive at the interpolated value.  

In deriving a value for point P the weighting factor apportioned to each point A,B,C is equal to the area of the diametrically opposite triangle. Therefore the weighting for:

A special case then arises when Point P lies on the line directly between two points. (see diagram).

The weighting factor apportioned to each point is by linear interpolation.  Therefore the weighting for: