Graphics Reference
In-Depth Information
This says that aside from light reaching the eye directly from luminaires (the first
e
term), we can instead apply the transport operator once to the luminaires (
T
e
)
to get a new set of luminaires which we can then render using the series solution
(
I
+
T
+
...
). This is the key idea in an approach called virtual point lights [Kel97]:
The initial transport of the luminaires is performed by something very similar to
photon tracing, except that instead of recording the field radiance at the intersec-
tion point, we record the resultant surface radiance after scattering. This surface
radiance becomes one of the virtual point lights (or, in image-space photon map-
ping, the bounce map).
If, following Arvo, we further decompose
T
into the product
KG
, where
G
transports surface radiance at each point to field radiance at another, and
K
scatters
field radiance at a point into surface radiance there, then we can consider breaking
a term off the series solution in a slightly different way:
T
)
−
1
e
=(
I
+
T
+
T
2
+
(
I
−
...
)
e
,
(31.104)
=
e
+(
T
+
T
2
+
...
)
T
e
,
(31.105)
=
e
+(
I
+
T
+
...
)
KG
e
, and
(31.106)
=
e
+((
I
+
T
+
...
)
K
)(
G
e
)
.
(31.107)
In this form, we transport the radiance from the luminaires to become field radi-
ance at the other surfaces in the scene (
G
e
). Subsequent processing involves trac-
ing rays from the eye to various depths, and then scattering (the
K
term) the field
radiance we find at intersection points. This can be regarded as a primitive form
of photon mapping, in which the photon map contains only one-bounce photons.
Doubtless other factorizations of the series solution can lead to further algo-
rithms as well.
This chapter has merely given a broad view of some topics in rendering, focus-
ing attention on Monte Carlo methods because of our belief that these are likely to
remain dominant for some time. To paraphrase Michael Spivak [Spi79b], we've
introduced you to much of the foundational material, and “beyond all this lies a
vast porridge of literature, and [we are] not glutton[s] enough to pick out all the
raisins.”
If you want to know more about the physical and mathematical basis of ren-
dering, and especially Monte Carlo methods, we recommend Veach's disserta-
tion [Vea97] as an education in itself. For those for whom the assumptions that
lie at the foundation of rendering are important, Arvo's dissertation [Arv95]
is an excellent starting point, particularly for the operator-theoretic point of
view. Both, however, involve considerable mathematics. The SIGGRAPH course
notes [JAF
+
01] give a slightly less demanding transition.
On the other hand, if efficient approximations to the ideal interest you, then
Real Time Rendering
[AMHH08] is an excellent reference.
For modern implementations of Monte Carlo methods,
Phyiscally Based Ren-
dering
by Pharr and Humphreys [PH10] is detailed and comprehensive.
Most important, the best place to start is with current research in the field.
Research in rendering is featured at almost every graphics conference. The Euro-
graphics Symposium on Rendering deserves special mention, however, as its long-
term focus on rendering has made it a particularly fertile ground for new ideas. We
suggest that you grab a paper, start reading and chasing references, and be both
open-minded and skeptical at all times.
