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)