

The one corner case is also straightforward. Here we need to assign the
value at A to the entire blue region.
To do this, we need to make sure that for any of the points
in the blue region we plug in the
correct coordinates to the bilinear interpolation function to
get the value of A. In this case, we need to plug in (1,0), which
are the coordinates of A. This is because our cells have local
coordinate frame of unit length with the origin at the C corner.
