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24.1. Particle Tracing for Lambertian Scenes 625
An alternative method to radiosity is to use a statistical simulation approach by
randomly following light “particles” from the luminaire though the environment.
This is a type of particle tracing. There are many algorithms that use some form
of particle tracing; we will discuss a form of particle tracing that deposits light
in the textures on triangles. First, we review some basic radiometric relations.
The radiance L of a Lambertian surface with area A is directly proportional to the
incident power per unit area:
L =
Φ
πA
, (24.1)
where Φ is the outgoing power from the surface. Note that in this discussion, all
radiometric quantities are either spectral or RGB depending on the implementa-
tion. If the surface has emitted power Φ
e
, incident power Φ
i
,andreflectance R,
then this equation becomes
L =
Φ
e
+ RΦ
i
πA
.
If we are given a model with Φ
e
and R specified for each triangle, we can proceed
luminaire by luminaire, firing power in the form of particles from each luminaire.
We associate a texture map with each triangle to store accumulated radiance, with
all texels initialized to
L =
Φ
e
πA
.
If a given triangle has area A and n
t
texels, and it is hit by a particle carrying
power φ, then the radiance of that texel is incremented by
ΔL =
n
t
φ
πA
.
Once a particle hits a surface, we increment the radiance of the texel it hits, prob-
abilistically decide whether to reflect the particle, and if we reflect it we choose a
direction and adjust its power.
Note that we want the particle to terminate at some point. For each surface we
can assign a reflection probability p to each surface interaction. A natural choice
would be to let p = R as it is with light in nature. The particle would then scatter
around the environment not losing or gaining any energy until it is absorbed.
This approach works well when the particles carry a single wavelength (Walter et
al., 1997). However, when a spectrum or RGB triple is carried by the ray as is
often implemented (Jensen, 2001), there is no single R and some compromise for
the value of p should be chosen. The power φ
for reflected particles should be
adjusted to account for the possible extinction of the particles:
φ
=
Rφ
p