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shows up here. Single scattering requires integration over the refracted rays and
it has a different distribution than multiple scattering. For the multiple scattering
integral, a dipole model is constructed for each sample point: the positive and
negative virtual sources are placed directly below and above the sample point,
respectively, with the flux of each computed according to the actual illumination.
In the case of an area source, sample points can be taken concurrently over the
light source. Because the value of R d (
falls off exponentially, it is more efficient
to concentrate the samples near the evaluation point x o and spread them out more
as the distance from x o increases ( Figure 4.9(b) ) .
The dipole model is derived and verified assuming the geometry of a plane
surface and infinitely deep material. Object geometry in CG scenes is seldom this
simple. The authors therefore had to devise a way of applying the dipole model
to geometrically more complicated objects. Their method works by constructing
the dipole as usual, but places the positive source so that it is always at least
1
r
)
/ σ t below each surface point. This ensures that d r is bounded away from zero;
otherwise, the value of R d could get arbitrarily large. The model breaks down if
the object is thinner than 1
/ σ t .
Images of a glass of milk rendered with a BSSRDF model using measured
parameters for skim and whole milk are shown in Figure 4.10(b) and (c), respec-
tively. The image in Figure 4.10(a) is rendered using a BRDF model derived from
the dipole model. The BSSRDF model adds a lot: the BRDF image looks more
like a glass of paint. Figure 4.11(a) shows an image of a human face model ren-
dered with the BRDF model; Figure 4.11(b) shows the same model rendered with
the BSSRDF using the measured parameters for human skin.
The dipole BSSRDF model developed by Jensen et al. fits naturally into a ray-
tracing renderer using the method described in the paper. The multiple scattering
component is computed only from surface samples; the only need for ray tracing
comes from sending shadow rays to the light, and shadowing can be handled
(a) (b) (c)
Figure 4.10 Rendered milk, using: (a) a BRDF approximation to the dipole model; (b) and (c) the
dipole-based BSSRDF with measured parameters for skimmed and whole milk, respec-
tively. (From [Jensen et al. 01b] c
2001 ACM, Inc. Included here by permission.)
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