Graphics Reference
In-Depth Information
a “one-bounce” approximation, the outgoing radiance at all secondary points is
approximated by the direct illumination.
Path tracing
comes from a “depth first” version of this approach. One sample
direction is chosen from
x
, the ray to the point of origin
x
is traced, where another
sample direction is chosen and traced, and so on. The process stops when a light
source is reached.
BRDF bidirectionality assures that reverse of the collected path, from the light
through each surface bounce to
x
, is a valid light path.
1
The radiance coming into
x
along a given light path is the radiance from the light source multiplied by the
surface BRDF value at each bounce. The basic idea of computing GI by path
tracing is to sum the incoming radiance along all light paths.
Ray tracing in which the sample directions are chosen based on random num-
bers is called
Monte Carlo ray tracing
(MCRT);
Monte Carlo path tracing
(MCPT) is the extension to general light paths. The idea is similar to Whitted-
style ray tracing, in that rays are shot from the viewpoint into the environment.
The difference is that reflected rays are shot in all directions rather than just fol-
lowing the path of mirror reflection or refraction. Path tracing in general is a
straightforward and effective method for GI computation. It handles reflection
using any BRDF model, from purely diffuse surfaces to true mirror reflection,
as well as transmission and refraction, and even wavelength-dependent refrac-
tion (dispersion). Furthermore, it works well with complicated geometry. The
drawback is that a very large number of samples is usually necessary to achieve
accurate results: rendering an image of moderate complexity can require tracing
billions
of rays.
2.3.1 The Origin of Monte Carlo Methods
A
Monte Carlo method
is a general name applied to any numerical method that
relies on some kind of sampling based on randomnumbers.
2
Monte Carlo integra-
tion is a typical example. The integral of a function can be viewed as the average
value of the function times the measure of the domain of integration (e.g., its
length, area, or volume). Monte Carlo integration works by averaging many func-
tion values at random points in the domain. As more samples are included, the
computed average
×
the measure of the domain converges to the value of the in-
1
The feasibility of reversing light paths is sometimes called
Helmholtz reciprocity
. Path reversal
in general involves principles of
thermodynamics
; Eric Veach provides an extensive discussion of this
in his dissertation [Veach 97].
2
The term “Monte Carlo method” was coined by Los Alamos scientists, in reference to the famous
casino in Monte Carlo, Monaco. The connection to gambling is that outcomes of enough random
events, such as rolling dice or spinning a roulette wheel, eventually follows an expected distribution;
i.e., the house always wins.
