Graphics Reference
In-Depth Information
→
/2
0
1
0
3
0
0
3
5
7
2
θ
4
P
12
13
10
θ
10
6
17
40
20
φ
8
13
27
21
11
0
0
φ
2
π
Figure 2.8
Importance sampling deliberately spreads out samples according to some known distribu-
tion. Stratifying the hemisphere and sampling more points in sections of known importance
is one example (right).
(in spherical coordinates), and an approximate incoming radiance for each patch
has been precomputed. Sampling is then done separately in each patch, with the
number of samples proportional to the precomputed value in the patch. Impor-
tance sampling the BRDF further improves the sampling quality.
2.3.6 Interpolation and Irradiance Caching
Monte Carlo methods assume that obtaining each sample is computationally in-
expensive. In ray and path tracing, the cost of firing a ray or tracing a path is
relatively small, but is significant nonetheless. Running times can be improved
if some of the samples can be obtained by interpolating existing values at nearby
sample points rather than by tracing new rays. If most sample values are inter-
polated rather than traced, the improvement can be significant. Interpolation is
well suited to situations where the lighting changes gradually, such as diffuse in-
terreflection, but fails to reproduce fine details such as highly specular reflection
and sharp shadows. This is one motivation for separating diffuse indirect lighting
from specular reflections. The diffuse contribution normally requires integration
over the entire hemisphere, but relatively few samples are needed. More samples
can be dedicated to the specular reflection by sampling according to the specular
part of the BRDF.
Interpolation of irradiance (more properly, radiant exitance) across surfaces
was applied in the radiosity method from the beginning: interpolating the con-
stant radiosity between patches is one way of performing the final reconstruction
step. Radiosity interpolation is straightforward, although it becomes more dif-
ficult when the objects have geometrically complicated surfaces or the subdivi-
sion has complicated geometry. The values and the arrangement of the patches
are fixed at the time of reconstruction, and the patches are typically arranged in
