Graphics Reference
In-Depth Information
Most of this is a straightforward simulation of the process of light bouncing
around in a scene. If, for a moment, we ignore wavelength dependence, then the
absorption step can be explained, just as we saw in path tracing, as follows: When
a photon hits a surface that scatters 30% of the arriving light, we could produce a
scattered photon with its power multiplied by a factor of 0.3, or we could produce
a scattered photon will full power, but only 30% of the time, an approach called
Russian roulette.
Over the long term, as many photons arrive at this point and get
scattered, the total outgoing power is the same, but there's an important difference
between the two strategies: In the second, at least for a scene that is not dependent
on wavelength, the power of a photon never changes. This means that all samples
stored in the photon map have the same power. This makes the radiance-estimation
step work better in general, although the statistical reasons for that are beyond
the scope of this topic. The code, in saying “reflect a full-strength photon with a
probability determined by the scattering probability,” is applying Russian roulette.
Because the scattering is wavelength-dependent, the final update to
Φ
i
(
)
scales the power in each band in proportion to that band's scattering probability.
Notice that if the surface is white (i.e., reflectance is the same across all bands),
then
Φ(
λ
)
is unchanged. By contrast, if we're using RGB and the surface is pure
red, then the average scattering probability is 1
λ
/
3; the red component of the pho-
1
ton power is multiplied by
3
=
3, while the green and blue components are set
1
/
to zero.
Inline Exercise 31.12:
What happens to the power of a photon if the surface
is a uniform 30% gray, so it reflects 30% of the light at each wavelength?
The actual implementation of light emission and of scattering (particularly for
reflectance models that have a diffuse, a glossy, and a specular part, for instance)
requires some care; we discuss these further in Chapter 32.
The second part of photon mapping is radiance estimation at points visible
from the eye, determined, for instance, by tracing rays from the eye
E
into the
scene. Before performing any radiance estimation, however, we balance the
k
-d
tree. Then for each visible point
P
, with normal
n
,welet
v
o
=
S
(
E
−
P
)
, and
compute the radiance.
m
2
sr.
L
represents the radiance scattered toward the eye.
2. Find the
K
photons nearest to
P
in the photon map, by searching for a
radius
r
within which there are
K
photons.
3. For each photon
ph
=(
Q
,
1. Set
L
=
0W
/
v
i
,
Φ
i
)
, update
L
using
L
←
L
+
f
s
(
P
,
v
i
,
v
o
)Φ
i
κ
(
Q
−
P
)
,
(31.100)
P
)=
1
π
r
2
is called the estimator
kernel.
This assign-
ment is wavelength-dependent (i.e., if we use three different wavelength
bands, Equation 31.100 represents three assignments, one for each of R,
G, and B).
It's easy to see that this computation is an approximation of the integral
where
κ
(
Q
−
f
s
(
P
,
v
i
over the positive hemisphere at
P
: The arriving radiance
at nearby points is used as a proxy for the arriving radiance at
P
in the integral. Of
course, light arriving at some point
Q
that's
near P
from direction
v
i
,
v
o
)
v
i
·
n
d
v
i
may have
originated at a fairly nearby light source. If so, then the arriving direction at
Q
will
be different from that at
P
(see Figure 31.28).
