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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.

As presented at SIGGRAPH/EUROGRAPHICS Graphics Hardware 2004
by Pradeep Sen on August 30, 2004