Linear Interpolation of Attenuation

Consider the case when we interpolate the attenuation linearly, as is done in much of the volume rendering literature [63,64,86,92,102,104,105]. That is, $\tau (t) = {\tau }_{\,\mathrm{b}}(1-t) + {\tau }_{\,\mathrm{f}}t$. This section discusses solutions for $\zeta$ and $\Psi$ and provides means of computing them when the attenuation is linear.