…rations in
the blur shader.
Linear filtering allows us to evaluate the formula
k₀c₀ + k₁c₁ (Formula 1)
where c₀ and c₁ are the colors of adjacent texels and k₀ and k₁ are arbitrary
factors (in this case, the results of evaluating the Gaussian function) with a
single lookup. Linear filtering evaluates the following expression for some t
between 0 and 1:
lerp(c₀, c₁, t)
It can be shown algebraically that Formula 1 is equivalent to:
⎛ k₁ ⎞
(k₀ + k₁)lerp⎜c₀, c₁, ───────⎟
⎝ k₀ + k₁⎠
Which can be readily evaluated by letting `t = k₁/(k₀ + k₁)` and performing a
texture lookup.