Graphics Reference
In-Depth Information
Environment
map
Pixels
P
L
Figure 7.5
The solid angle Δω of a group of pixels in the environment map as seen from a point
p
.
working toward the dimmest (this is where the hierarchy comes in). The number
of samples in each layer is proportional to the value of
Γ
in each layer, where
L
and
come from summing the value and solid angle
(
Figure 7.5
)
of all the pixels in
the component (Equation 7.1). The collection of all these pixels is regarded as a
set of point samples, and the goal is to cluster them into a collection of representa-
tive samples. The authors employ an algorithm known as the Hochbaum-Shmoys
clustering algorithm, which uses a “farthest-first” approach. The first sample is
chosen to be the brightest pixel in the region. Then the next choice is the point in
the region farthest from this first sample. At each iteration, the next sample point
is the point farthest away from all the samples chosen so far; i.e., the next sample
is the point in the region having the largest minimum distance from all the other
chosen samples.
Figure 7.6(b) shows the resulting set of samples and the corresponding strata
for a component of the brightest layer. The strata for points near the edge of
the component are clipped by the component boundary for clarity; they really
extend further outward. The stratification process continues with the next layer
(
Figure7.6(c)
). The sample points in the higher layer remain the same. The new
sample points continue to be chosen using Hochbaum-Shmoys algorithm as if
nothing changed. The only difference is that fewer samples per area are chosen at
this layer, which results in a coarser sampling density. The process then continues
with the next lower layer, and stops when the lowest layer has been stratified
(
Figure 7.6(d)
)
. The sampling density is thus finest at the brightest parts of the
environment map, and becomes progressively coarser as the brightness decreases.
Figure 7.7(a) contains rendering of a simple scene illuminated by the HDR en-
vironment map captured in an environment with highly nonuniform illumination
and a number of bright illumination sources The multiple shadows in the image
are cast by these various light sources and are basically correct, even though they
look a bit strange out of context. Figure 7.7(b) shows close-ups of the rectangular
areas in the scene in part (a). The images in the left column were rendered using
Δω
