Graphics Reference
In-Depth Information
trace them through the scene. We say “representative” because real images are
formed by trillions of photons, yet graphics applications can typically estimate the
image very well from only a few million photons, so each graphics photon rep-
resents many real ones. Today's computers and rendering algorithms can execute
a simulation in this model for rendering images in a few minutes. The emission
itself isn't particularly expensive. Instead, the later steps of the tracing consume
most of the processing time because each representative photon must be handled
individually, and the interaction of millions of photons with millions or billions of
polygons can be complicated.
To render even faster, we can simplify the emission model so that an aggregate
of photons along a light ray can be considered by the later light transport steps.
This is a common approximation for real-time rendering. The simplified models
tend to fix the origin for all photons from an emitter at a single point. Doing so
allows algorithms to amortize the cost of processing light rays from an emitter
over the large number of light rays that share a single origin. As we said earlier,
it is common practice to consider a small number of frequencies, to simplify the
spectral representation, and to treat photons in the aggregate by measuring the
average rate of energy emitted at each of those frequencies. Three frequencies
loosely corresponding to “red,” “green,” and “blue” are almost always chosen to
represent the visible spectrum, where each represents a weighted sum of the spec-
tral values over an interval of the true spectrum, but is treated during simulation as
a point sample, say, at the center of the interval. For an example of a more refined
model, Pharr and Humphreys [PH10] describe a renderer with a nice abstraction
of spectral curves.
In computer graphics, light transport is almost always modeled by (steady-state)
ray optics on uncollimated, unpolarized light. This substantially simplifies the
simulation by neglecting phase and polarization. In this model, photons propagate
along straight lines through empty space. They do not interfere with one another,
and their energy contribution simply sums. Under this simplification and with a
discrete set of frequency samples, a geometric ray and a radiance vector (indicat-
ing radiance in the red, green, and blue portions of the spectrum) are sufficient to
represent a stream of photons.
In more sophisticated models of light, some physicists model the phase of pho-
tons. Such photons can interfere with one another in certain conditions, giving
rise to phenomena such as Newton rings. But Newton rings and other small-
scale diffraction events rarely occur at noticeable levels in common experience,
so we generally ignore them in graphics.
We'll see in Chapter 27 that ignoring photon interference and polarization to
simplify the representation of light energy is what forces us to complicate our rep-
resentation of matter. For example, glossy and perfect reflection arises from the
interference of nearly parallel streams of photons. This interference does not arise
under ray optics, so we must introduce specific terms (such as Fresnel terms) to
materials to model the same phenomena. One could use a richer model of light
and a simpler model of a surface to produce the same image. However, a simple
