Graphics Reference
In-Depth Information
der time. This requires recomputing the BRDF textures, which slows the process
substantially. Nonetheless, the computation is still relatively fast.
BRDF textures and PRT.
BRDF textures can be used in precomputed radi-
ance transfer. As described earlier in this chapter, the key element to PRT is
the construction of transfer matrices that convert SH coefficients (light vector)
of the incident light to SH coefficients of the outgoing light. Transfer matrices
can be constructed to account for various effects, including self-shadowing, inter-
reflection, and subsurface scattering. How a BRDF texture is incorporated into a
transfer matrix depends on the particular effect the matrix handles.
The simplest case is self-shadowing, which accounts for occlusion of the inci-
dent light before it hits the object surface. In this case, the incident radiance
L
)
in the reflection integral (Equation (10.4)) is the occluded incident radiance. Mul-
tiplying the environment map light vector by the self-shadowing transfer matrix
produces the locally occluded environment map light vector. This is then used in
place of the original light vector in the BRDF texture rendering. In other words,
accounting for self-shadowing amounts to multiplying the constructed incident
light vector by the transfer matrix.
In contrast, BRDF textures are more difficult to incorporate into PRT involv-
ing interreflection, because the interreflection depends on the particular BRDF.
The surface BRDF therefore has to be included in the simulation step, which
means that it cannot be changed dynamically at render time. Multiple sample
points on the surface of the object are used to compute the transfer matrix during
the simulation, and each point has its own local coordinate system. Therefore
it is more efficient to perform the SH expansion in a common global coordinate
system.
The composition of the BRDF texture, the rotation matrix, and the transfer
matrix can (theoretically) be applied to any surface with any reflection character-
istics. However, both the BRDF texture approach and the original PRT approach
assumed low-frequency lighting and reflection. For the reasons described above,
the practical application of spherical harmonics in representing more general sur-
face reflection is considered rather limited. Recent research, e.g., [Sloan 06,Lehti-
nen 07], has proposed the use of other bases such as wavelets (described in Sec-
tion 10.2.4).
(
s
BRDF Matrices.
As described above, a separate SH expansion of the weighted
and clipped BRDF
b
is needed to apply the dot product formula (Equa-
tion (10.8)) to evaluate the reflection integral of Equation (10.4) for each viewing
vector
(
s
,
v
)
v
. The BRDF texture method uses a set of fixed sample vectors
v
,and
stores the SH coefficients
b
i
(
v
)
for each
i
in a texture. In general,
b
i
(
v
)
for a given
