The interpolation function we want to perform is shown here as
f(x,y), and is simply barycentric interpolation. It is also the
result you would get if you fit a plane through the three corner
points to try to determine the value of the point to shade.
Please note that we have to be careful about clamping the result
when it extends beyond the B,C,D triangle and we discuss that in
the paper. So how do we implement this function? We note that we
have two linear interpolators available to us through the
bilinear interpolation function g(x,y). The first is the linear
interpolation between C and B, which we get if we simply plug in
the x-coordinate into g(x,y) and zero out the y input. The
second is the linear interpolation between C and D that can be
computed if we keep the y-coordinate of the bilinear
interpolation function and zero out the x input. Now we note
that if we add these two functions, we get an expression that is
very similar to what we want, except that it has an extra "C"
term. Thus, we can subtract