[comp.graphics] Point nature of ray tracing?

webber@athos.rutgers.edu (Bob Webber) (01/07/89)

In article <364@pte.UUCP>, kiy@pte.UUCP (Kevin Young) writes:
> seen mentioned (or obviously missed :-).  This discussion seems to
> assume that light and sound are identical in property.  From what I
> remember from high school physics, light is made up of discrete particles.
> Sound is the propogation of wave energy through a medium.  I know light
> particles may be thought of as both waves AND particles but it seems as
> though ray tracing is particle oriented.  The difference to me (and I
> certainly would like to hear arguments) is that as a sound wave propogates,
> each molecule transfers a part of its energy to severeral other molecules.
> The original molecule never actually makes it to the destination, only
> its energy.  This seems to constrast the ray approach in which the ray 
> continues, uninhibited, until it is absorbed or leaves the frame.
> 
> Comments?

I have not looked into the physics of sound enough to comment on the 
applicability of ray tracing to acoustics beyond the observation that
people are doing it.  What I want to address is the comment that ray
tracing is somehow related to a particle-ness or a wave-ness of light.

If one were running what is called a forward ray tracer that tracked
``rays'' from light sources, one might be able to push the notion that
it was a particle simulation.  However, ray tracing is generally done
by ``tracing'' rays backward from the viewer.  These rays really have
nothing to do with whether light is particle or wave or what not, but
are simply a way of sampling the light model.  The model of light that
is being used is actually wrapped up in the equations used to determine
how the intensity transfers and accumulates as the path determined by
a particular tracking of a particular ray moves from surface to surface 
branching out in tree like formation.  

Of course, for some models of light, this sampling approach will be
more effective at getting a reasonable estimate than with other
models.  When using the Torrance-Sparrow equations for light transfer
at surfaces, one actually is appealing to a statistical model of
particles bouncing off of a randomly perturbed collection of
microfacets (hence the value for the ray actually represents some
collective statistical behavior of a large collection of particles
rather than an individual particle), when using the later work of Cook
and Torrance you are appealing to an essentially wave model of what is
going on, and the reflectance curve of Phong's model is essentially a
quantum mechanics phenomena.  [cf, Roger's Procedural Elements for
Computer Graphics, McGrawHill, 1985 for explanations plus pointers to
the literature relevant to these models.]

The simplest ray tracing techniques assume that the light energy
``recieved'' by a particular ray off a particular surface can be best
estimated by looking at the contribution to that portion of the
surface from a ray coming directly from each light source, and the
results of sending out another sample in the direction of reflection
(and/or refraction).  More complicated approaches try to improve this
estimate by sending out multiple rays in a stochastic sampling (e.g.,
Distributed Ray Tracing by Cook, Porter, and Carpenter, SIGGRAPH'84)
or by trying to evaluate the sample over an area instead of at just
a point (e.g., Beam Tracing Polygonal Objects by Heckbert and Hanrahan
and Ray Tracing with Cones by Amanatides, both in SIGGRAPH'84 as
well).  This later approach of evaluating the sample over an area
has been applied to sound tracing as cited in an earlier message, 
from an optical ray tracing point of view, their main interest is that
they handle the aliasing problem that arises from sampling using the 
straightforward approach.

There is also another approach to optical modelling called radiosity
(e.g., Modeling the Interaction of Light between Diffuse Surfaces by
Goral, Torrance, Greenberg, and Battaile also introduced at SIGGRAPH'84).
This approach trys to solve for the light flow by setting up a collection
of linear simultaneous equations whose solutions correspond to the
amount of light being emitted from different portions of the scene.
From 1984 onward, SIGGRAPH proceedings have chronicled the further
developement and intertwining of these techniques.  Also of interest
is The Rendering Equation by Kajiya (Siggraph'86), which presents
these various techniques as attempts to solve a particular integral
equation, which he calls the Rendering Equation, and then discusses
other techniques available for solving such integral equations.  My
understanding is that these sorts of integral equations are sufficiently
general that they apply to acoustics and a rather wide range of other
physical phenomena.

Well, you know what they say
          All integral equations look alike to me.

----- BOB (webber@athos.rutgers.edu ; rutgers!athos.rutgers.edu!webber)