Graphics Reference
In-Depth Information
The interpolated sample value at point
P
is computed as a weighted average
of the nearby usable sample points:
)=
i
∈
s
w
i
(
P
)
E
i
(
P
)
i
∈
s
w
i
(
P
)
(
P
E
(2.11)
where
1
w
i
(
P
)=
1
(2.12)
||
P
−
P
i
||
−
N
(
P
)
·
N
(
P
i
)
+
R
i
is the relative weight of sample point
i
(and implicitly depends on the surface
normal
N
at
P
).
The weighting function given in Equation (2.12) comes from the light-dark
sphere, and is therefore an estimate of the maximum change in irradiance in the
region. In 1992, Ward and Paul Heckbert presented a more precise approxima-
tion to the change in irradiance called the
irradiance gradient
that comes from
interpreting the incident radiation over the hemisphere [Ward and Heckbert 92].
This irradiance gradient produces a better weighting function for the surrounding
sample points and thereby results in a better irradiance approximation.
In the late 1980s radiosity was the most popular global illumination method,
but the versatility of ray-tracing methods coupled with improvements in computer
processor speeds made MCRT increasingly attractive. Irradiance caching was
originally invented with the goal of fast MCRT in mind. However, it should be
noted that the use of caching and interpolation has become widespread in modern
computer graphics outside of ray tracing, particularly in real-time applications
and graphics hardware.
2.4 Photon Mapping
2.4.1 Foundations of Photon Mapping
The technique known as
photon mapping
was first introduced by Henrik Wann
Jensen in 1996 [Jensen 96]. One of the original goals was to improve the ren-
dering of focused light effects, such as the moving patterns of light seen at the
bottom of a pool on a sunny day, or the bright pattern created on a table from light
transmitted through a glass of wine. These effects are known as
caustics
.They
are caused by a lensing effect, where light is concentrated by refraction through
curved surfaces. The term “caustic” comes from optics: when enough radiant
power is focused on a small area, it can literally burn like a caustic substance.
