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In-Depth Information
the albedo value, the particle is sent in a random direction (with respect to the
phase function) a logarithmically random distance proportional to the inverse of
the scattering coefficient. Otherwise it is absorbed. The position, the radiance car-
ried by the photon, and the direction of travel are stored in the
volume photon map
at each
secondary
collision. Values from photons coming directly from the light
are not stored, because the photon map is only used to compute the in-scattering
from indirect light.
In the ray marching stage, during the in-scattering computation for a ray
marching segment, the volume photon map is queried by searching for a constant
number of photons near the center of the segment (
Figure 3.15
)
.
The desired number of photons are contained in a bounding sphere of radius
r
.
The in-scattered light from a photon is the product of the phase function and
the power carried by the photon, divided by the volume of the bounding sphere.
The direction
ω
of the photon is necessary to find the value of the phase function,
which is why photon directions are stored in the photon map. The radiance
L
s
,
the strength of the in-scattered light at point
x
, from
N
photons in the bounding
sphere of point
x
is therefore
1
σ
s
(
,
ω
,
ω
)
,
ω
)
ω
L
s
(
x
,
ω
)=
p
(
x
L
(
x
d
x
)
Ω
d
2
,
ω
)
dV
1
Φ
(
x
,
ω
,
ω
)
=
p
(
x
(
)
σ
x
s
Ω
i
=
1
p
x
,
ω
i
,
ω
ΔΦ
i
(
x
,
ω
i
)
N
1
σ
s
(
≈
x
)
4
3
π
r
3
,
ω
i
are the flux and incident direction, respectively, of photon
i
.
Using the volumetric photon map in place of direct integral sampling in ray
marching considerably improves efficiency for media having a large degree of
where
Φ
i
and
Bounding
sphere
L
s
r
x
Figure 3.15
In-scattering radiance estimation from a volume photon map works by averaging photons
limited to a bounding approximation sphere. (After [Jensen and Christensen 98].)
