pigmented colorants: dependence on media and time - Cornell ...

have been developed since the 1970s and are built into graphics hardware today.
While these models are adequate in simulating some materials, they are typically
unable to capture the subtle effects that distinguish most materials. As a result,
more sophisticated models have been developed over the years to simulate light
reflections.
4.2.1 Subsurface scattering theory
When the flow of light hits an object, the energy is partly transmitted or absorbed
into the material and partly scattered back into the environment. The amount
scattered light and its directional distribution depend on the material’s surface
properties. In Chapter 2, it was noted that the bidirectional reflectance distribution
function (BRDF) describes a material’s response to incoming light as it is reflected
toward a viewer. The BRDF fo is defined as the exitant radiance in a direction
per incident radiance from a direction per unit projected solid angle. That is,
The reflected radiance Lo in direction ωo is then
Lo(ωo) =
95
fo(ωi, ωo) = Lo
/µ(Ωi) (4.1)
H 2
Li
fo(ωi, ωo)Li(ωi)dµ(ωi) (4.2)
However, the BRDF is only an approximation to the more general bidirectional
subsurface scattering distribution function (BSSRDF). In the case of the BRDF, it
is assumed that light striking a surface location is reflected at that same location.
While this may be the case for many materials (as in metals), light arriving at
the surface of most materials enters and then scatters inside before leaving at a