Glow Parameter

When deriving the volume rendering integral in Section 1.1, I parameterized the emission of light within the volume as the luminance, $L(s)$, which has units per area of visible surface. The actual intensity of light, therefore, varies with respect to the density of particles. Other literature (such as [104]) instead defines the emission of light within the volume with a glow parameter, $g(s)$, that varies the light intensity independent of the particle density. We can express the relationship between luminance and glow as

$$g(s) = L(s) \tau (s)$$ (4)

Modifying the volume rendering integral (Equation 1.2) to use the glow term is a simple matter of substitution.

$${ I(D) = I_0 e^{-\int_0^D \tau (t) dt} + { \int_0^D g(s) e^{-\int_s^D \tau (t) dt} ds } }$$ (5)

Equations 1.2 and 1.5 are equivalent and the choice between them is mostly a matter of preference. In this dissertation, I usually choose Equation 1.2 with the luminance term. When defining volume lighting parameters it is far more natural for the light emission to fluctuate with the particle density.

Changing the particle density independent of the glow can lead to unexpected visual results. Raising the particle density without raising the glow leads to a dark, sooty-looking volume. Lowering the particle density without lowering the glow results in an overly bright volume, often saturating the color channels of the display device. However, when we parameterize the color by luminance rather than glow, the color of the volume will appear constant as the particle density is varied.

The only real advantage of using the glow parameter is to allow volumes to emit light without attenuating a significant amount of light. This can happen in a hot, tenuous gas such as in a neon sign. This situation is difficult to model with luminance because as the attenuation goes to zero the luminance must go to infinity, but the glow can remain at a finite value. However, this is a rather simple special case to solve (and I do it in Section 1.3.2).