ewhac@well.UUCP (Leo 'Bols Ewhac' Schwab) (12/03/88)
[ #include <witty_saying.h> ]
I was doing a few gedanken experiments with raytracing, and came up
with a few questions. Realize that I've never written a raytracer.
Suppose I have an object, a light source, and a flat surface set up
as a perfect mirror. Suppose further that I have a thing between the object
and light source preventing direct illumination of the object. Suppose
further still that the "mirror" is set up to reflect the light from the
light source to the object. Question: Will the object be illuminated?
Does it depend on whose software I'm using?
Suppose I have a flat surface, a light source, and an object in the
shape of a convex lens above the surface under the light. Suppose further
that the object is set up to be perfectly clear, and refracts light like
glass. Question: Will the light beneath the lens object be intensely
focused on the surface below, just like a real lens?
The point of the above two questions is to find out if, in general,
raytracers handle illumination from light bounced off of or refracted
through other objects.
Finally, has anyone come up with a raytracer whose refraction model
takes into account the varying indicies of refraction of different light
frequencies? In other words, can I find a raytracer that, when looking
through a prism obliquely at a light source, will show me a rainbow?
Something tells me that all three questions are rather hard.
_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_
Leo L. Schwab -- The Guy in The Cape INET: well!ewhac@ucbvax.Berkeley.EDU
\_ -_ Recumbent Bikes: UUCP: pacbell > !{well,unicom}!ewhac
O----^o The Only Way To Fly. hplabs / (pronounced "AE-wack")
"Work FOR? I don't work FOR anybody! I'm just having fun." -- The Doctorranjit@eniac.seas.upenn.edu (Ranjit Bhatnagar) (12/04/88)
Leo Schwab (ewhac@well.uucp) writes: > I was doing a few gedanken experiments with raytracing, and came up >with a few questions. Realize that I've never written a raytracer. Well, I've never written one either, so ignore everything I say. > >[Will a mirror shine reflected light on other objects?] >Does it depend on whose software I'm using? It depends on the software - most ray tracers do NOT model reflected light, because of the tremendous increase in complexity. The standard shadow model casts a ray from the object's surface to each light source, to see if there's an object in the way. To test for reflected light, you have to cast rays in EVERY DIRECTION, just in case there's a mirror in that direction that might be reflecting light on this part of the object surface. Even if you optimize it to cast rays only at known mirrors, you still need to cast an infinite number towards each mirror. A nice application of stochastic techniques is to cast a moderate number of rays in RANDOM directions, hoping that they will hit a mirror if there's one to hit. If the jitter is done well, then the effect will not be bad. Radiosity models take a completely different approach to this problem. See e.g. "A Radiosity Solution for Complex Environments" - Cohen and Greenberg, SIGGRAPH 85, or "A Radiosity Method for Non-Diffuse Environments" - Immel and Cohen, SIGGRAPH 86. These guys don't discuss mirrors, but you can sort of see how the radiosity method could handle them. Radiosity worries about the general problem of light reflected off of surfaces in the environment - in the real world, light doesn't just come straight from the bulb! > > Suppose I have a flat surface, a light source, and an object in the >shape of a convex lens above the surface under the light. Suppose further >that the object is set up to be perfectly clear, and refracts light like >glass. Question: Will the light beneath the lens object be intensely >focused on the surface below, just like a real lens? Answer is the same as above - it could be done by casting zillions of rays, but it's computationally expensive. Stochastic sampling can certainly help, though. > > Finally, has anyone come up with a raytracer whose refraction model >takes into account the varying indicies of refraction of different light >frequencies? In other words, can I find a raytracer that, when looking >through a prism obliquely at a light source, will show me a rainbow? > This is even nastier than the first two problems, because very few rendering systems really model light like it is in the real world. We don't usually think about it, because the RGB approximation LOOKS the same to us as real light, but if you wanted to get rainbows, you would have to take into account that visible light is a continuum of wavelengths that can be mixed arbitrarily. In the graphics world, the sun is really a red sun, a green sun, and a blue sun that happen to occupy the same position - if you were to look at it through a simulated prism, you would get not a rainbow, but a red spot, a green spot, and a blue spot. I think work has been done in rendering that models the entire visible spectrum instead of the RGB approximation - you can imagine that that would be really nasty, because every color vector, instead of being described by three numbers, would be described by a continuum (perhaps approximated as 500 numbers or something like that). So, while wavelength-based refraction could be modeled by extending current refraction techniques, nobody does it because it would reveal the artificiality of the RGB approximation. Come to think of it, it's even worse than that! You don't know the color of a ray until it has "cashed out" completely - all its descendants have been resolved. But you can't resolve the ray until you know its color, because the color will affect its trajectory! Based on this, I would say that frequency-based refraction is VERY difficult using eye-based ray-tracing. I expect one would cast a sort of "average" ray, based on a single color, and then use relaxation techniques to bend and twist the ray based on its color, and change its color based on the trajectory, until it reaches a stable state. Unfortunately, in any reasonable complex scene, there's probably no numerical technique that could reliably find the resultant ray even from a very well-chosen "guess", because of all the discontinuities and nonlinearities involved. The other two problems are soluble, though, and stochastic (also called "distributed") ray tracing is really neat way to get good approximations to that and other fun problems (it turns out to be applicable to simulation of motion blur, out-of-focus cameras, lens depth of field, fuzzy reflections (like in a formica tabletop), and all kinds of amazing stuff). A nice introduction is "Stochastic Sampling in Computer Graphics" - Rob Cook, in ACM Transactions on Graphics, v5#1, Jan 86. - Ranjit "Trespassers w" ranjit@eniac.seas.upenn.edu mailrus!eecae!netnews!eniac!... -- I'm not a drug enforcement agent, but I play one for TV -- Giant SDI lasers burn 1,000 points of light in Willie Horton - Dave Barry
cnsy@vax5.CIT.CORNELL.EDU (12/05/88)
>>[Will a mirror shine reflected light on other objects?] >>Does it depend on whose software I'm using? > >Radiosity models take a completely different approach to this problem. >See e.g. "A Radiosity Solution for Complex Environments" - Cohen and >Greenberg, SIGGRAPH 85, or "A Radiosity Method for Non-Diffuse Environments" >- Immel and Cohen, SIGGRAPH 86. These guys don't discuss mirrors, One radiosity article that does show the effect of mirrors is in the SIGGRAPH 87 Proceedings, "A Two-Pass Solution to the Rendering Equation: A Synthesis of Ray Tracing and Radiosity Methods" by Wallace, Cohen & Greenberg. See page 319, image 10c. The "mirror world" technique as it applies to radiosity is touched upon on page 315. For detailed info, get Holly Rushmeier's thesis (reference 21 of the article). I believe she may have an article about this topic somewhere soon (TOG, maybe?). Eric Haines, 3D/Eye Inc, ...!hplabs!hpfcla!hpfcrs!eye!erich
chris@spock (Chris Ott) (12/06/88)
ewhac@well.UUCP (Leo 'Bols Ewhac' Schwab) writes: > I was doing a few gedanken experiments with raytracing, and came up > with a few questions. Realize that I've never written a raytracer. I'm writing a ray tracer right now and have some experience. > Suppose I have an object, a light source, and a flat surface set up > as a perfect mirror. Suppose further that I have a thing between the object > and light source preventing direct illumination of the object. Suppose > further still that the "mirror" is set up to reflect the light from the > light source to the object. Question: Will the object be illuminated? > Does it depend on whose software I'm using? Software that does true ray tracing would definitely illuminate the object. For example, the ray could be sent from the eye through a specific pixel on the screen to the object, bounce off the object into the mirror, and finally, off the mirror into a light source. Then, given the color of the object and the light source, the pixel's color can be computed. At least mine works this way. The way my code looks, it seems as if this would be intrinsically part of ray tracing, i.e. I didn't have to make a special case for mirrors. > Suppose I have a flat surface, a light source, and an object in the > shape of a convex lens above the surface under the light. Suppose further > that the object is set up to be perfectly clear, and refracts light like > glass. Question: Will the light beneath the lens object be intensely > focused on the surface below, just like a real lens? Again, true ray tracing would definitely produce this result. Then ranjit@eniac.seas.upenn.edu (Ranjit Bhatnagar) writes: # It depends on the software - most ray tracers do NOT model reflected light, # because of the tremendous increase in complexity. The standard shadow # model casts a ray from the object's surface to each light source, to # see if there's an object in the way. To test for reflected light, # you have to cast rays in EVERY DIRECTION, just in case there's a mirror # in that direction that might be reflecting light on this part of # the object surface. Even if you optimize it to cast rays only # at known mirrors, you still need to cast an infinite number towards # each mirror. # # A nice application of stochastic techniques is to cast a moderate # number of rays in RANDOM directions, hoping that they will hit a mirror # if there's one to hit. If the jitter is done well, then the effect # will not be bad. This does not sound correct to me. My understanding is that the only rays we are interested in are the ones that the eye can see, so we just need to cast a ray (more than one, if we want some reasonable anti-aliasing) from the eye-point through each pixel. At least that's the way I did it and it gives very realistic results. Any comments? > The point of the above two questions is to find out if, in general, > raytracers handle illumination from light bounced off of or refracted > through other objects. Yes. > Finally, has anyone come up with a raytracer whose refraction model > takes into account the varying indicies of refraction of different light > frequencies? In other words, can I find a raytracer that, when looking > through a prism obliquely at a light source, will show me a rainbow? This could be tough. The red, green, and blue components of monitors only simulate the full color spectrum. On a computer, yellow is a mixture of red and green. In real life, yellow is yellow. You'd have to cast a large number of rays and use a large amount of computer time to simulate a full color spectrum. (Ranjit pointed this out in his article and went into much greater detail). > Something tells me that all three questions are rather hard. Nah. They were easy. > Leo L. Schwab # - Ranjit Chris Ott ------------------------------------------------------------------------------- Chris Ott Computational Fluid Mechanics Lab Just say "Whoa!!" and University of Arizona vote for Randee!! Internet: chris@spock.ame.arizona.edu UUCP: {allegra,cmcl2,hao!noao}!arizona!amethyst!spock!chris -------------------------------------------------------------------------------
markv@uoregon.uoregon.edu (Mark VandeWettering) (12/06/88)
In article <859@amethyst.ma.arizona.edu> chris@spock.ame.arizona.edu (Chris Ott) writes: }ewhac@well.UUCP (Leo 'Bols Ewhac' Schwab) writes: }> I was doing a few gedanken experiments with raytracing, and came up }> with a few questions. Realize that I've never written a raytracer. } I'm writing a ray tracer right now and have some experience. }> Suppose I have an object, a light source, and a flat surface set up }> as a perfect mirror. Suppose further that I have a thing between the object }> and light source preventing direct illumination of the object. Suppose }> further still that the "mirror" is set up to reflect the light from the }> light source to the object. Question: Will the object be illuminated? }> Does it depend on whose software I'm using? The question is actually trickier than you might believe. Even diffusely reflecting objects reflect light, hence at every point on the surface of an object, the illumination is a function of its own radiosity and the radiosity of every patch visible AFTER ANY NUMBER OF BOUNCES. Hence, there is not a great way of knowing when to quit tracing rays. For instance, you hit a triangle. You need to find the amount of light energy reaching that triangle from EVERY direction, not just the direction of the reflected ray. Techniques of MonteCarlo integration, distributed ray tracing, and radiosity all attempt to deal with this fundamental problem. } Software that does true ray tracing would definitely illuminate the }object. For example, the ray could be sent from the eye through a specific }pixel on the screen to the object, bounce off the object into the mirror, }and finally, off the mirror into a light source. Then, given the color of }the object and the light source, the pixel's color can be computed. At }least mine works this way. The way my code looks, it seems as if this }would be intrinsically part of ray tracing, i.e. I didn't have to make }a special case for mirrors. Solving the general problems of "light bleeding" or diffuse interreflections is very difficult and a current research topic. Consider the problem rephrased another way. Given a description of the objects, surfaces and lights in a scene, you are trying to determine what your light would see by observing the scene. Unfortunately, we can't model the path of every photon in the scene. We use the fact that we are only interested in the miniscule portion of light rays in the scene that actually "hit" your eye. To reconstruct the interplay of light from the eye position seems to be the goal of current state of raytracing research. }# It depends on the software - most ray tracers do NOT model reflected light, }# because of the tremendous increase in complexity. The standard shadow }# model casts a ray from the object's surface to each light source, to }# see if there's an object in the way. To test for reflected light, }# you have to cast rays in EVERY DIRECTION, just in case there's a mirror }# in that direction that might be reflecting light on this part of }# the object surface. Even if you optimize it to cast rays only }# at known mirrors, you still need to cast an infinite number towards }# each mirror. }# }# A nice application of stochastic techniques is to cast a moderate }# number of rays in RANDOM directions, hoping that they will hit a mirror }# if there's one to hit. If the jitter is done well, then the effect }# will not be bad. } This does not sound correct to me. My understanding is that the only }rays we are interested in are the ones that the eye can see, so we just }need to cast a ray (more than one, if we want some reasonable anti-aliasing) }from the eye-point through each pixel. At least that's the way I did it }and it gives very realistic results. Any comments? } Unfortunately, it is correct. Consider the problems associated with diffuse inter-reflections that I mentioned above. The light shone back to the eye is not merely based on light from a small number of directions, but from and infinite number of directions. }> The point of the above two questions is to find out if, in general, }> raytracers handle illumination from light bounced off of or refracted }> through other objects. } Yes. No. Kajiya's "Rendering Equation" produced some of the effects that you want however, and better computational methods should result in the kind of images that you desire. }> Finally, has anyone come up with a raytracer whose refraction model }> takes into account the varying indicies of refraction of different light }> frequencies? In other words, can I find a raytracer that, when looking }> through a prism obliquely at a light source, will show me a rainbow? } } This could be tough. The red, green, and blue components of monitors }only simulate the full color spectrum. On a computer, yellow is a mixture }of red and green. In real life, yellow is yellow. You'd have to cast a }large number of rays and use a large amount of computer time to simulate }a full color spectrum. (Ranjit pointed this out in his article and went }into much greater detail). Actually, this problem seems the easiest. We merely have to trace rays of differing frequency (perhaps randomly sampled) and use Fresnel's equation to determine refraction characteristics. If you are trying to model phase effects like diffraction, you will probably have a much more difficult time. Mark VandeWettering
po0o+@andrew.cmu.edu (Paul Andrew Olbrich) (12/07/88)
Hi folks. This is in reply to some of the recent ray tracing discussion. > I'm writing a ray tracer right now and have some experience. I've already written a ray tracer. And I'm a freshman at CMU! (I love this stuff!) > The question is actually trickier than you might believe. Even > diffusely reflecting objects reflect light, hence at every point on the > surface of an object, the illumination is a function of its own > radiosity and the radiosity of every patch visible AFTER ANY NUMBER OF > BOUNCES. Hence, there is not a great way of knowing when to quit > tracing rays. For instance, you hit a triangle. You need to find the > amount of light energy reaching that triangle from EVERY direction, not > just the direction of the reflected ray. Techniques of MonteCarlo > integration, distributed ray tracing, and radiosity all attempt to deal > with this fundamental problem. I just wanted to bring up a small point on this. Basically what's being said here is that every object that you're dealing with reflects light to some degree. This is extremely clear when you realize that if all of the objects did not reflect light, then no light would radiate from them at all, and you wouldn't be able to see them! This, of course, would be a severe bummer! --- Drew Olbrich po0o+@andrew.cmu.edu "You cannot depend on your eyes when your imagination is out of focus." -- Mark Twain "I wouldn't trust him any farther than I could spit a rat." -- Zaphod Beeblebrox
skinner@saturn.ucsc.edu (Robert Skinner) (12/07/88)
In article <859@amethyst.ma.arizona.edu> chris@spock.ame.arizona.edu (Chris Ott) writes: > >ewhac@well.UUCP (Leo 'Bols Ewhac' Schwab) writes: >> I was doing a few gedanken experiments with raytracing, and came up >> with a few questions. Realize that I've never written a raytracer. > > I'm writing a ray tracer right now and have some experience. I haven't written a ray tracer, but I've talked to people that have >> [in summary, Leo asks:] >> does ray tracing produce secondary illumination, i.e. does the light >> bouncing off of a mirror illuminate an object? > > Software that does true ray tracing would definitely illuminate the >object. For example, the ray could be sent from the eye through a specific >pixel on the screen to the object, bounce off the object into the mirror, >and finally, off the mirror into a light source. Then, given the color of >the object and the light source, the pixel's color can be computed. At >least mine works this way. The way my code looks, it seems as if this >would be intrinsically part of ray tracing, i.e. I didn't have to make >a special case for mirrors. Say you've got one sphere, one light source, and 40 mirrors, but only one miror reflects the light source onto the sphere. How do you know which mirror contributes light without casting test rays towards the mirrors? And how many rays do you cast before you give up? The mirror may be large, and the light only comes from one small part of it. This also goes for secondary illumination from non-mirrors (all objects reflect, except a black body). Imagine two surfaces that face each other, one is directly illuminated but the second is not. The second surface should be illuminated from the first one. If you have an algorithm that can do this naturally without using rays to search for the illuminant, then you should publish. I'm sure it would be accepted by SIGGRAPH. Jim Kajiya is the only one I'm aware of that has published anything about ray tracing that can handle secondary illumination, and this is how he does it. (He said he had to use HUGE lights to get it to work.) > >> Suppose I have a flat surface, a light source, and an object in the >> shape of a convex lens above the surface under the light. Suppose further >> that the object is set up to be perfectly clear, and refracts light like >> glass. Question: Will the light beneath the lens object be intensely >> focused on the surface below, just like a real lens? > > Again, true ray tracing would definitely produce this result. You can't get this without the secondary illumination you are asking for above. > >Then ranjit@eniac.seas.upenn.edu (Ranjit Bhatnagar) writes: > ># ... most ray tracers do NOT model reflected light, ># ... you have to cast rays in EVERY DIRECTION, .. ># ># A nice application of stochastic techniques is to cast a moderate ># number of rays in RANDOM directions, hoping that they will hit a mirror ># if there's one to hit. If the jitter is done well, then the effect ># will not be bad. > > This does not sound correct to me. My understanding is that the only >rays we are interested in are the ones that the eye can see, so we just >need to cast a ray (more than one, if we want some reasonable anti-aliasing) >from the eye-point through each pixel. At least that's the way I did it >and it gives very realistic results. Any comments? I agree with Ranjit. You are right as far as primary rays are concerned, but once you hit an object, what do you know about how it is illuminated? You know the positions of the lights, no sweat there. You know the positions of mirrors that may reflect light onto this object, but you don't know what part of the mirror really does it. Take the example above of the light being focused onto the object (a caustic). The light is intensified at the caustic, so you must take into account that the light is being reflected from many places on the mirror onto one spot on the surface. (Many of your test rays bounced off of the mirror and hit the light). A short distance away from the caustic, there is no extra illumination. (All of the test rays bounced off of the mirror and MISSED the light). > >> The point of the above two questions is to find out if, in general, >> raytracers handle illumination from light bounced off of or refracted >> through other objects. > > Yes. No > >> Finally, has anyone come up with a raytracer whose refraction model >> takes into account the varying indicies of refraction of different light >> frequencies? In other words, can I find a raytracer that, when looking >> through a prism obliquely at a light source, will show me a rainbow? > > This could be tough. ... This is the easy part. Rob Cook wrote a paper on stochastic sampling the screen pixel positions for antialiasing, the position of finite width light sources for shadow penumbras, object positions in time for motion blur, and aperture position for depth of field. So all you have to do is sample the frequency of light. You fire say 16 rays per pixel anyway to do antialiasing, and assign each one a color (frequency). When the ray is refracted through an object, take into account the index of refraction and apply Snell's law. A student here did that and it worked fine. He simulated rainbows and diffraction effects through prisms. What he couldn't do is to shine a light through a prism and cast a spectrum on a surface. But the sectrum is just a special case of a caustic, so if you do secondary illumination it will work. (Spencer Thomas (U. Utah, or is it U. Mich. now?) also implemented the same sort of thing at about the same time. (Oh yeah? Well I thought about doing it a year before that :^)... sure) > >> Something tells me that all three questions are rather hard. > >Nah. They were easy. Please show us how the first two are easy. Sorry if I sound overly cynical, but I don't see how it falls out naturally without sending out test rays to search for secondary illumination. If you really can do this, by all means let us know. The world anxiously awaits. Robert Skinner skinner@saturn.ucsc.edu -- ---- this is a test
jevans@cpsc.ucalgary.ca (David Jevans) (12/08/88)
In article <3324@uoregon.uoregon.edu<, markv@uoregon.uoregon.edu (Mark VandeWettering) writes:
< }< Finally, has anyone come up with a raytracer whose refraction model
< }< takes into account the varying indicies of refraction of different light
< }< frequencies? In other words, can I find a raytracer that, when looking
< }< through a prism obliquely at a light source, will show me a rainbow?
< }
< } This could be tough. The red, green, and blue components of monitors
< }only simulate the full color spectrum. On a computer, yellow is a mixture
< }of red and green. In real life, yellow is yellow. You'd have to cast a
< }large number of rays and use a large amount of computer time to simulate
< }a full color spectrum. (Ranjit pointed this out in his article and went
< }into much greater detail).
<
< Actually, this problem seems the easiest. We merely have to trace rays
< of differing frequency (perhaps randomly sampled) and use Fresnel's
< equation to determine refraction characteristics. If you are trying to
< model phase effects like diffraction, you will probably have a much more
< difficult time.
This has already been done by a number of people. One paper by
T. L. Kunii describes a renderer called "Gemstone Fire" or something.
It models refraction as you suggest to get realistic looking gems.
Sorry, but I can't recall where (or if) it has been published. I have
also read several (as yet) unpublished papers which do the same thing in
pretty much the same way.
David Jevans, U of Calgary Computer Science, Calgary AB T2N 1N4 Canada
uucp: ...{ubc-cs,utai,alberta}!calgary!jevanscoifman@yale.UUCP (Ronald Coifman) (12/16/88)
In article <5647@saturn.ucsc.edu> skinner@saturn.ucsc.edu (Robert Skinner) writes: >>> Finally, has anyone come up with a raytracer whose refraction model >>> takes into account the varying indicies of refraction of different light >>> frequencies? In other words, can I find a raytracer that, when looking >>> through a prism obliquely at a light source, will show me a rainbow? >> >> This could be tough. ... > >This is the easy part... >You fire say 16 rays per pixel anyway to do >antialiasing, and assign each one a color (frequency). When the ray >is refracted through an object, take into account the index of >refraction and apply Snell's law. A student here did that >and it worked fine. He simulated rainbows and diffraction effects >through prisms. > > (Spencer Thomas (U. Utah, or is it U. Mich. now?) also implemented >the same sort of thing at about the same time. Yep, I got a Masters degree for doing that (I was the student Rob is refer- ring to). The problem in modelling dispersion is to integrate the primary sample, over the visible frequencies of light. Using the Monte Carlo integra- tion techniques of Cook on the visible spectrum yields a nice, fairly simple solution, albeit at the cost of supersampling at ~10-20 rays per pixel, where dispersive sampling is required. Thomas used a different approach. He adpatively subdivided the spectrum based on the angle of spread of the dispersed ray, given the range of frequen- cies it represents. This can be more efficient, but can also have unlimited growth in the number of samples. Credit Spencer Thomas; he was first. As at least one person has pointed out, perhaps the most interesting aspect of this problem is that of representing the spectrum on an RGB monitor. That's an open problem; I'd be really interested in hearing about any solutions that people have come up with. (No, the obvious CIE to RGB conversion doesn't work worth a damn.) My solution(s) can be found in "A Realistic Model of Refraction for Computer Graphics", F. Kenton Musgrave, Modelling and Simulation on Microcomputers 1988 conference proceedings, Soc. for Computer Simulation, Feb. 1988, in my UC Santa Cruz Masters thesis of the same title, and (hopefully) in an upcoming paper "Prisms and Rainbows: a Dispersion Model for Computer Graphics" at the Graphics Interface conference this summer. (I can e-mail troff sources for these papers to interested parties, but you'll not get the neat-o pictures.) For a look at an image of a physical model of the rainbow, built on the dispersion model, see the upcoming Jan. IEEE CG&A "About the Cover" article. Ken Musgrave -- _____________________________________________________________________ Ken Musgrave arpanet: musgrave@yale.edu Yale U. Math Dept. Box 2155 Yale Station Primary Operating Principle: New Haven, CT 06520 Deus ex machina