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

distance zr beneath the surface. The second one, the negative virtual light source
is located above the surface at a distance zv = zr +4AD.
Figure 4.2: An incoming ray is transformed into a dipole source for the
diffusion approximation. Adapted from [JMLH01]
Using this approximation, the diffuse reflectance at point xo due to illumination
at point xi is
where
Rd(xi,xo) = α
zr(1 + σsr)
4π
e−σsr
s3 r
zr = 1
σ ′ t
and zv = zr +4AD
+ zv(1 + σsv) e−σsv
s3
v
sr = xr − xo , with xr = xi − zr · Ni
sv = xv − xo , with xv = xi − zv · Ni
A = 1+Fdr
1 − Fdr
Fdr = 1.440
η 2
D = 1
3σ ′ t
0.710
+
η +0.668+0.0636η
and σ = 3σaσ ′ t
101
(4.8)