Graphics Reference
In-Depth Information
Of course, the process of actually computing the elements of the transfer ma-
trix is a major task in itself. Not only does it require evaluation of the double inte-
gral of Equation (10.6) for each
i
and
j
, it requires simulation of multiple bounces
if interreflection is to be considered. This is in fact a scaled down global illumi-
nation problem, and it can be simulated, for example, with a form of Monte Carlo
path tracing. The simulation has to be done at each point on the surface where an
outgoing light vector is to be computed. This involves significant computation,
because for most surfaces, a fairly dense set of surface sample points is required.
However, the cost of the simulation precomputation is less of a concern than the
run-time evaluation. Once the transfer matrices are computed, the radiance trans-
fer computation is just a matrix multiplication, hence the name “precomputed
radiance transfer.”
10.1.3 Transfer Matrices and Simulation
At a particular sample point on the surface, the transfer matrix can be computed
as a sum of the effects of direct lighting and indirect interreflection. A first pass,
called a
shadow pass
, is applied to evaluate the integral of Equation (10.6) by
sampling over the hemisphere or sphere of directions. The only ray tracing re-
quired is the casting of shadow rays, and this is only necessary to determine
the value of the visibility function. Figure 10.5 illustrates what is involved in
the shadow pass. In practice, the results of the shadow rays are stored and used
for other passes. The shadow pass constructs the direct lighting transfer matrix,
and can be described as “pass zero.” The shadow pass is applied to each sample
point.
Ray from
environment map
→
Normal
n
p
c
b
d
a
→
→
Shadow ray
s
d
Shadow ray
s
d
Figure 10.5
The shadow pass in precomputation.
