*"Light Makes Right"*

August 26, 1992

Volume 5, Number 2

Compiled by

All contents are copyright (c) 1992, all rights reserved by the individual authors

Archive locations: anonymous FTP at
ftp://ftp-graphics.stanford.edu/pub/Graphics/RTNews/,

wuarchive.wustl.edu:/graphics/graphics/RTNews, and many others.

You may also want to check out the Ray Tracing News issue guide and the Mother of all Ray Tracing Pages.

- Introduction - SIGGRAPH roundtable, etc
- New People, New Addresses, etc
- BSP Traversal Errata, by Kelvin Sung
- The Art of Noise, by Steve Worley
- Ray Tracing Roundup, by Eric Haines
- Graphics Gems III Residency Mask errata, by Joe Cychosz
- Any Future for Efficiency Research?, by Eric Haines
- NuGrid Update, by Mike Gigante

- Spline Patch Ray Intersection Routines, by Sean Graves
- Xdart, from Mark Spychalla
- 4D Space Viewing Software, by Steve Hollasch
- BYU Modelling and Visualization Package - Free Demo, by Stacey D. Son
- New Radiosity Program Available, by Guy Moreillon
- Optics Lab Information, by Anthony Siegman
- Ray Tracing (or Casting) Applications, by Tom Wilson
- Goofy (?) Idea, Gary McTaggart
- Constant Time Ray Tracing, by Tom Wilson, Eric Haines, Brian Corrie, and Masataka Ohta
- VLSI for Ray Tracing, by Kenneth Cameron, George Kyriazis, Peter De Vijt, Jon Leech, Sam Uselton, Thierry Priol, and "Dega Dude"
- The Moon Revisited, by Tom Duff
- Soft Shadow Ideas, compiled by Derek Woolverton
- Book Announcement: Multiprocessor Methods for Computer Graphics Rendering, by Scott Whitman

As usual, SIGGRAPH was fun this year. Ray tracing is becoming fairly common, with many rendering packages having it available. The idea of saving each ray intersection tree at each pixel is spreading: Intergraph has had this for years, and now TDI has added it to their renderer (see Sequin & Smyrl, SIGGRAPH '89, for the basic technique). We'll undoubtedly see more of this in years to come, given that main memory is increasing much faster than screen resolution.

My favorite product was Fractal Painter, which is the most paint-like paint program I've seen yet. Nothing to do with ray tracing, but it was cool...

One interesting business has arisen in the past year or so: selling digitized models. Viewpoint Animation Engineering has a nice glossy catalog of models ranging from pterodactyls to spinal cords to eighteen wheelers (and I dare you to render a scene with all three). At the show they were giving out demo disks of Al Capone related datasets: a '32 Packard, a violin case, a tommygun, an antique lamp, and a cartoon Al. No normals per vertex (it's unclear if their other models have these or not) and no normal per polygon (most polygons were consistently one way, though I found a few were reversed - ugh). Prices listed are in the hundreds of $$$, but these seem fairly variable, partially depending on your use: one folder puts various vehicles at $300-$500 a piece, but another folder offered 20 vehicles for $395 total. You figure it out: call them at 1-800-DATASET. They also do custom digitizing, running around $1000 per model. Another company that sells 3D models (primarily architectural related items, geographic data, and people) and does digitizing is Acuris at 415-329-1920.

Graphics Gems III is out, and contains some nice tidbits on ray tracing and many other topics. I particularly like Ben Trumbore's gem for computing tight bounding volumes for quadrics and tori. There are some truly gem-like, sharp thoughts, like Andrew Woo's clever method of avoiding epsilon problems when using shadow maps. Plus lots of other great stuff. And at last, you can find out what the Gems III code on princeton.edu:/pub/Graphics/GraphicsGems/GemsIII actually does! Gems IV will be edited by Paul Heckbert, and is due out in two years. Academic Press would like to have one out every year, but the editors felt that this might lead to diminishing overall quality.

One of my recent discoveries in Graphics Gems II (reprinted in Gems III) is Steve Hollasch's set of macro routines for vector manipulation. They're easy to overlook, but quite compact and useful: two of them (Vec2Op and Vec3Op) replaced dozens of macros in our old vector manipulation macro library. Check them out! The Gems series is interesting in that there is a lot of knowledge crammed into each book, and it sometimes takes a little exploration to find (or stumble upon) some of the wonderful ideas and tricks therein.

Two nice things have been happening in ray tracing over the past year. One is that wuarchive.wustl.edu:/graphics/graphics has become a good collection site for various graphics information. It includes Radiance, a good chunk of the NCSA programs, many object databases, 31 megs of ray-tracing stuff and the milton.u.washington.edu virtual worlds archive. wuarchive recently got a new drive, which allowed the graphics archive to hop to over 300 megs. Write to George Kyriazis (kyriazis@rdrc.rpi.edu), who is maintaining the graphics area, if you see something that's old or missing.

The other trend is that Rayshade is becoming a testbed for other researchers' efficiency schemes. Erik Jansen (fwj@duticg.tudelft.nl) and Wim de Leeuw have made their BSP traversal code publicly available (see RTNv5n1), Mike Gigante plans on releasing his NuGrid code as soon as his research paper is accepted, and there is one researcher who has implemented Arvo & Kirk's 5D scheme using Rayshade as a base. This is a wonderful development, in that good code for various efficiency schemes for one ray tracer are becoming available and so can be used as the basis for meaningful timing tests. Such things as simulated annealing may become easier to explore, since a variety of interchangeable efficiency schemes will become commonly available.

To wrap it up, here is the first paragraph of the Acknowledgements of David Jevans' interesting Master's thesis (which uses nested grids for efficiency), "Adaptive Voxel Subdivision for Ray Tracing," Dept. of Computer Science, Univ. of Calgary, 1990:

As a young, overfunded graduate student, I would often pass idle hours drinking medicinal alcoholic concoctions, and firing shotgun blasts at pieces of paper nailed to the side of the university's orgone accumulator outhouse. Imagine my surprise when I discovered that the performance graphs of my ray tracing algorithms exactly matched the patterns blasted into those pellet ridden sheafs! Seeing this as a sign of divine acceptance, of some kind of grand conjunction of information, I collected my results into the volume of forbidden knowledge that you hold before you.

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Rob LaMoreaux 907 Wisconsin Ave. St. Joseph, MI 49085 (616)-982-3187 work (616)-983-1743 Home r.lamoreaux@mi04.zds.com Raytracing Interest: Creating pictures and eventually short animations

I'm using POV to create scenes, and would eventually like to create short animations. I try not to program much, but I have been thinking about a Visual basic front end to launch POV (depends on time (not much available), ambition and whether someone does it first). Interested in object files and object creation utilities (I'm too lazy and impatient to hand assemble things out of triangles). Some of the objects I am interested in are: Cars (especially racing), houses, landscaping, bicycles, sailboards, a sewing machine, and anything else interesting to look at.

# Abe Megahed - interested in issues of scene complexity, # global illumination, ray tracing data structs in animation # University of Wisconsin # 1413 Mound St # Madison, Wisconsin 53711 # (608) 256-6306

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(...) the recursive ray traversal algorithm introduced independently by Jansen (1986) is a different implementation of the same tree walking idea.

should be removed. The sentence on page 271 should be read as:

It is straightforward to implement the Recursive Ray Traversal Algorithm as proposed by Jansen(1986) and Arvo(1988) on a BSP tree.

I thought the date of the work (Jansen 1986 vs Arvo 1988) shows that Erik Jansen was the one who first introduced the algorithm. The fact that his work was referenced later than Arvo's in that Gem may cause confusion and thus may not reflect enough credit from Jansen's past work. This is a mistake and should be corrected.

[Note: Erik Jansen and Wim de Leeuw have made their BSP code for Rayshade publicly available. Write fwj@duticg.tudelft.nl for details. - EAH]

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Implementing this algorithm is really quite easy, but there are some small tweaks that can enhance the quality of the surface. Assuming you have a noise-generation function (a smooth 3D interpolator given a lattice of values and derivatives: Graphics Gems II has the code for a routine by Greg Ward to do just this) you will often want to make "fractal" noise by summing over many scales of the noise function. By decreasing the characteristic size of each scale as well of the amplitude of those summed scales, after about 5 or 6 scales you'll have a function that will have details on many different size ranges. This function (when expressed as a greyscale or even thresholded) has a cloudy appearance: there are blobs of diffuseness with soft, ragged edges.

How to use these noise fields to make textures is pretty straightforward: Perlin gives many examples and there was even an entire course at '92 SIGGRAPH. I've implemented nearly 50 textures that use fractal noise, and I've learned some tricks.

The biggest problem with the algorithm described above is that there are artifacts. You are interpolating over a cubic lattice, and you'll be able to SEE that lattice especially if you look at just one scale function. One trick I use to remove these artifacts is to make the fractal noise more isotropic by rotating each summed scale to a random orientation. Since the lattices of the different scales don't line up, the artifacts will at least be uncorrelated and a lot less noticeable. I do this by rotating each scale with a random, precomputed, rotation matrix. If you want to return derivatives (for bump mapping) you'll have to post-multiply the result from each scale with the appropriate inverse rotation matrix before you add them.

I made these matrices by generating random rotation matrices, and taking only those that point inside a single octant of a sphere. Since a 90 degree rotation (or 180 or 270) will still let the lattices match up, a single octant is the most rotation that is necessary. [Note that these are full 3D rotations, not 2D, but you know what I mean.] Keeping the rotations to this smaller angle lets you see that there are not two similar rotations for different scales. (Remember this is a one-time precompute: you can manually sort through about 10 of these and you're done.) To test what octant a rotation matrix maps to, just pump the vector (1 0 0) through the matrix and look for a vector with all positive components. You can generate the rotation matrices using the algorithm(s) in Graphics Gems III by Ken Shoemake and Jim Arvo.

This rotation trick is most useful when bump mapping, since the differentiation really exposes the lattice artifacts: there are sharp discontinuities of the second derivatives along the lattice lines. When you differentiate for bump mapping, these second derivatives become FIRST derivatives and are visible.

____

When you are summing the scales, each scale will have a size and amplitude which is a fixed ratio of the scale size and amplitude of the previous scale. The natural scale to use is 0.5, but DON'T USE THIS. Better to use 0.4857463537 or 0.527849474673 which will give you the same effective ratio. A ratio of exactly 0.5 will help the different scales "register" more effectively (the small scale repeats exactly twice on top of the larger scale,) so artifacts can appear periodically. By using the odd number, the periodicity is broken.

____

A couple of other tricks also makes more useful noise. MAKE A SPECIAL CASE. Half of the time when you use noise, it is on a flat surface, like woodgrain on a table top. If you make a 2D version of fractal noise, it will be over twice as fast as a 3D version (which basically computes two "layers" of noise and interpolates.) I have a special case that checks for the Y (vertical) component to be 0, and branches off into a special case subroutine. If you're clever, you can even make the 2D special case be a perfect subset of the 3D case: that is, the SIDES of the tabletop will call the 3D noise routine but they will mesh up with the 2D version which is called for the TOP of the table. [Easiest way to be clever: take your original code, globally replace the variable "Y" with 0, then have fun in Emacs removing all the terms that vanish. This guarantees that your special case will match up with your general 3D routine, but you won't have to think too hard about how to implement it.] Only one disadvantage to this technique: the rotation matrices (from the previous idea) will make even a flat tabletop have Y!=0. You can either change your rotation matrices to be only 2D (spins around the Y axis), live without the rotation enhancement, or live with the slower computation. Your call. My implementation let the user decide, with the default being NOT to use rotations.

____

Yet another trick. NORMALIZE your noise. Ideally, you want the fractal noise, no matter how many scales or what scale size or ratio you use, to return a value over the same range. This is easy to do: just divide the final sum by the square root of the sum of the squares of all the amplitudes of the scales. This makes it a lot nicer when you are tweaking textures: the relative amounts of colors or size of the bumps won't be affected when you change the scale or amplitude ratio or number of summed scales.

____

For user convenience, you might even want to make another type of normalization. One common use of the fractal noise value is to feed the value into a color spline. If a user sets the "levels" of the color spline, it can be VERY difficult for them to set the levels right in order to get the "coverage" they need. If they want to make white clouds on a mostly blue sky, what value does they choose for the threshold where white starts being added? I solved this problem by computing 25,000,000 values of noise and making a probability distribution (just a histogram.) By recording the different percentiles (5% of the noise values are under this number, 10% under this one.... 95% under this one..) I was able to get a PERCENTAGE mapping of the distribution. When a user wants the sky to be 90% blue, they say that the white color should be added starting at 0.90. The program maps this value 0.90 back into the corresponding noise value, and the user gets the 90% coverage they asked for. (I have noise that returns a value from -1 to 1, but most values are clustered around 0. 90% corresponds to a value of 1.442 in my implementation.) This convenience is no real computational load, but for the user, it makes using the texture a LOT more intuitive.

Using Perlin fractal noise is an art, but it is a very effective way to make complex surfaces. Good luck!

And for the curious, my textures are a commercial product, sorry, I can't give you the code. :-)

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The fabled POV v1.0 ray tracer (a.k.a. son of DKBtrace) is finally available, being released just before SIGGRAPH. It's available on alfred.ccs.carleton.ca [134.117.1.1]:pub/pov-ray, on the BBS 'You Can Call Me Ray' in North Chicago suburbs (708-358-5611), and on Compu$erve.

There is also a mailing list for POV and DKBtrace. To subscribe, send a mail
containing the body:
subscribe dkb-l

GIF and JPEG images of the SPD databases and some of my old thesis images are stored at ftp.ipl.rpi.edu [128.113.14.50] sigma/erich, nic.funet.fi (somewhere) and at gondwana.ecr.mu.oz.au [128.250.70.62] pub/images/haines.

Lee Butler is attempting to create a texture library at his FTP site. His interest is in 2 and 3 dimensional textures of materials suitable for surface texturing. He is mostly interested in photographic quality textures and bump-maps. He accepts data in most popular formats (TIFF, GIF, JPEG, etc), but may convert data in order to conserve disk space. He'd like a little descriptive text to go with any textures you send, i.e. just enough to identify what the subject matter is, what the image dimensions are, etc. Please make sure what you send is in the public domain (e.g. scanned in pictures from books are not allowed, including Brodatz's well-known "Textures" book, which is copyright). (contact Lee A. Butler (butler@BRL.MIL))

On hanauma.stanford.edu is a 720x360 array of elevation data, containing one ieee floating point number for every half degree longitude and latitude. [This is quite nice! - EAH] (from Ken Chin-Purcell (ken@msc.edu))

Some scanned in Brodatz textures are available from cicero.cs.umass.edu: /texture_temp. They are 512x512 grayscale. (from Julien Flack (julien@scs.leeds.ac.uk)).

Colby Kraybill has placed texture maps from Hans du Buf (dubuf@ltssun1.epfl.ch) on pioneer.unm.edu [129.24.9.217]: pub/texture_maps (from Colby Kraybill (opus@pioneer.unm.edu)) [these include aerial swatches, Brodatz textures, and synthetic swatches. - EAH]

The Chapel Hill Volume Rendering Test Datasets, Volumes I and II are available for FTP from omicron.cs.unc.edu in pub/softlab/CHVRTD. These include a 3D volume set for two heads, a brain, a knee, electron density maps for RNA and other molecules, etc.

T3DLIB (the TTDDD model conversion package) is now at version 34 and is at hubcap.clemson.edu [130.127.8.1]:pub/amiga/incoming/imagine/TTDDDLIB. There are 3D models in .../imagine/objects. The converter now supports DXF format output.

Version 4 of the collection of ray tracing abstracts is ready. I've put it in several ftp sites (wuarchive.wustl.edu:graphics/graphics/ray or maybe bib). To get it, do the following: get rtabs.11.91.shar.Z using binary mode, uncompress it, and then unshar it (sh rtabs.11.91.shar). Then read READ.ME. The abstracts (RTabs) can be converted to two forms: Latex (preferred) or troff -me. The filters I've included may help you write your own if you need something else. A second file (RTnew) contains just the added abstracts if you don't want to print the whole thing again. There are now 306 abstracts. (from Tom Wilson (wilson@cs.ucf.edu))

After listening in on the fast rotation / wireframe discussion in comp.graphics. I decided to release a simple 3D wireframe viewer that I wrote myself that runs under X11. It is available via anonymous ftp at castlab.engr.wisc.edu (128.104.52.10) and is found as /pub/x3d.1.1.tar.Z . MIFF files of rendered objects are on castlab in /pub/rendered_objs. More objects are on castlab in /pub/more_objs. (from Mark Spychalla (spy@castlab.engr.wisc.edu))

The shadow buffer algorithm is now implemented in the SIPP rendering library. Version 3.0 is available from isy.liu.se (130.236.1.3), pub/sipp/sipp-3.0.tar.Z

As part of Guy Moreillon's diploma project (Interactive Radiosity), he has
created a scene made out of objects in OFF format. It represents the inside
of a house, with one big room and a smaller one, stairs going up, a couple of
armchairs, a table, a kitchen chair, a fridge, and so on. He uploaded it on
gondwana.ecr.mu.oz.au as well as cs.uoregon.edu in the incoming directory
(file house.tar.Z). (from Guy Moreillon

fractint v17 will output a few raytrace formats (dkb/pvray, vivid, raw
triangle mesh) from the 3d mapping function. fraint17.exe will be on
wuarchive.wustl.edu. (from Tony Audas

There is an enhanced version of Rayshade available at weedeater.math.yale.edu: incoming/ray406enh2.tar.Z. It adds new blobbies, swept spheres, and all sorts of other things to the original (from Larry Coffin (lcoffin@clciris.chem.umr.edu))

An Amiga version of Rayshade 4.0.6 is up for FTP at ab20.larc.nasa.gov (/incoming/amiga/Rayshade) and at weedeater.math.yale.edu (/incoming/AmigaRayshade). Bug reports to me and I'll see who they originally belong to. If they're mine, I'll fix'em, eh? (by Colin DeWolfe, (dewolfe@ug.cs.dal.ca))

A distributed version of Craig Kolb's Rayshade 4.0 is available on ftp site princeton.edu as pub/Graphics/rayshade.4.0/etc/rayshade-rrlib.tar.Z It makes raytracing very much faster by dividing a frame or animation into squares, which are distributed on a unlimited number of servers. (from Wilfried Koch (bj030@aix370.rrz.uni-koeln.de)).

The "art" raytracer has undergone some changes and now includes the addition of heightfields (as output by programs such as fracland), some additional capabilities for rendering algebraic surfaces, several new textures, a couple of speed ups and the usual collection of bug fixes. Contributed scenes are available in pub/contrib/artscenes on gondwana and /graphics/graphics/echidna on wuarchive.wustl.edu. Anyone wishing to contribute can place files in incoming on gondwana. (from Eric H. Echidna (echidna@ecr.mu.oz.au)) [wuarchive.wustl.edu has this in graphics/graphics/echidna]

There are new versions of the RTrace ray-tracer (version 7.3.2) and the scene translator SCN2SFF (version 1.3) at asterix.inescn.pt [192.35.246.17] in directory pub/RTrace. Some bugs were fixed and new features added: - 3D text (fonts, orientation, spacing, etc - high quality) - CSG objects An MS-DOS version for use with DJGPP DOS extender (GO32) is in pub/RTrace/PC-386/rtrace.zip. The pub/RTrace directory has been reorganized. There are new subdirectories with new images (medical, molecular, etc), scene converters and other tools. [There have been further bug fixes and new features since then, but you get the idea - EAH] (from Antonio Costa (acc@basinger.inescn.pt))

Some more notes on reaction-diffusion textures (see last issue, this column): do a lint on Greg Turk's code before you run it, and you might also want to make sure your "random()" function works as he thinks it does (mine didn't - I changed to drand48()). Note that Witkin & Kass's equation #5 also has a typo: it should be C(t+ delta t) - C(t) on the left side of the equation. Also, Andrew Witkin says section 6.1's R function is a bit unstable. I haven't got it to work, but Greg Turk's code does pretty much the same thing in a different way.

Other new things (later in this issue) include spline patch ray intersection routines, 4D space viewing software, a distributed ray tracer, a free trial version of a modelling and visualization package from BYU, and a new radiosity program.

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Page 285 should read:

By updating the ray mask as it passes from cell to cell, a quick determination of whether an object within the cell needs to be intersected can be made by simply ANDing the residency mask of the object with the (not the complement of) residency mask for the ray.

The process goes something like this:

ray_mask = 0

foreach (cell the ray passes through) { foreach (object in the cell) { if (ray_mask & object_mask == 0) { compute the ray-object intersection } } update ray_mask marking for cell }

The important thing here is to mark the cell after it is processed.

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On one level, I tend to agree that efficiency is "solved": grids, octrees/BSP, and automatic bounding volume hierarchy are all in the same ballpark. However, Mike Gigante points out that raw speed is not the best qualification for a scheme. Yes, if you tweak grid placement and run it at a variety of resolutions, you'll usually find that scheme is very fast, possibly faster than any other scheme. The problem is that a typical user does not want to deal with efficiency tweaking at all, and so the best efficiency scheme may not be the fastest, but rather something near optimal that is automatic and will work in a wide range of environments without serious degradations in speed or memory usage.

As far as future research goes, I've yet to see much work on Jim Arvo's idea of simulated annealing applied to efficiency schemes (see the RTNews/RTNews1 file). His idea is that sometimes one scheme is significantly better than the others for a particular scene or part of an environment (see Kirk & Arvo's "Ray Tracing Kernel" paper from Ausgraph '88 for using multiple efficiency schemes). For a single 1280x1024 image it may not be worth doing much analysis to determine which is the best efficiency scheme, but if you're doing an animation or an extremely high resolution image it may be worth spending more time up front to save time later. Hybrid approaches may be the best overall solution, where objects or volumes have different efficiency schemes depending on predicted performance. There's an interesting paper:

H. K. Choi, C. M. Kyung, "PYSHA: a shadow-testing acceleration scheme for ray tracing", Computer-aided design, vol. 24, no. 2, Feb. 1992

which talks about deciding which efficiency scheme to use on the fly by having a cost function approximate which will be cheaper.

It seems that the way in which space is filled is the main determinant of which scheme is most efficient. Grids, for example, excel when the distribution of primitives is uniform. Being able to quickly characterize how space is filled could allow choosing the best efficiency scheme. Determining what the correlation between some distribution statistics and which scheme is fastest is probably trickier than characterizing the space itself. There is also the problem of platform independence and attempting to determine what "fastest" means in a general sense (minimizing the number of intersection tests is a good start, but the costs of each scheme needs to be factored in).

Some interesting work is being done on speeding up ray-tracing for animation by using temporal coherence. For example, Jevans paper in Graphics Interface '92:

%A David Jevans %T Object Space Temporal Coherence for Ray Tracing %J Proceedings of Graphics Interface '92 %I Canadian Information Processing Society %C Toronto, Ontario %D May 1992 %P 176-183

is one of the latest in this area of research.

Another topic of interest which has not been explored much is efficient ray-casting for non-rendering related tasks. Saul Youssef (see the ray tracing bibliography on the net) has researched shooting rays for high energy physics work, John Wallace and I wrote a paper about ray-casting for radiosity visibility testing, and there has been some work done for volume visualization ray tracing. The assumption has been that "what's good for ray tracing is good for everything else" and that the current popular efficiency schemes are sufficient. In our work on radiosity we have seen different sources of coherence which can be exploited in interesting ways. If someone is doing a mass-properties study of an object by casting rays the problem can be restructured to minimize ray-object testing that is not normally available to a ray tracer, since we know in advance where all the rays will be traveling.

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I was actually writing a paper (for SIGGRAPH) with the results as well as a better criteria for building the NUgrid (rather than the end of the bbox), when I worked out a technique for the totally automatic construction of NUgrids. That is right -- even tho' NUgrid was much much less sensitive than grids in the selection of the grid resolution, it now builds a close to optimal NUgrid automatically. In fact in many cases, the result is better than the best case performance in previous NUgrid versions. All this was absolute last minute stuff! Since we are so far away, the damn couriers wanted 4 working days to get it to pixar!!! I only came up with the method 3 days before the paper had top leave (as I was starting to write up the previous stuff!!!). I actually managed to crank all the code out and do a set of test cases. I had the courier waiting by while I pasted in the results!! Why do ideas come at awkward times?

I have spent the last couple of days cleaning up the paper and stuff, even tho' it won't get to the siggraph committee, I wanted to finish it off now while it was all fresh in my mind. I am disappointed that the copy I sent was fairly rough, but boy were the results good! I am now working on making the automatic method work even better.

I have included a couple of tables below.

BTW, we actually got the Octree stuff implemented also, it uses Samet's neighbour following stuff so traversal is very fast. NUgrid still whips it in most cases and is very competitive in the other cases. From these results, the uniform grid should be a dead duck.

BTW, I have tested over 60 datasets with each of the methods below, ranging from a few dozen polygons up to 880,000 independent phong triangles.

I plan to make all the code available after I know what is happening with the paper, if the results don't make up for the rather hurried nature of the paper, then I already have in my hands a very publishable newer version and I have no doubt it will get in somewhere.

Here are some results, all this was in rayshade, with

1) Uniform grid (as per vanilla rayshade) 2) NUgrid 1 (as described in Ausgraph 90 paper, but with ray counter and raybounds optimizations (which rayshade's uniform grid had)) 3) NUgrid 2 (as described in my paper submission - a different criteria for where to drop the dividing planes) 4) AutoNUgrid 5) Octree.

the first 3 were tested with resolution 4x4x4 -> 36x36x36 in increments of 2, AutoNUgrid had only 1 test config of course, Octree was tested with subdivision depth 2 (equiv to 4x4x4 grid/NUgrid) through to depth 10 (where we didn't run out of memory!!!).

Some of the bigger cases are still finishing their timings now, so within another week or so I can complete the tables. Even so, the trend is very clear from the plots I have done of all the tests. I am completing the test cases for completeness only.

Anyhow, here are the tables...

Best and worst case performance for SPD model Balls: | Grid | NUgrid 1 | NUgrid 2 | Auto | Octree Best | 1286.75 | 476.09 | 421.30 | 737.32 | 21695.24 Worst | 10510.54 | 2755.95 | 2895.47 | | 895.49 ... for SPD model Gears: | Grid | NUgrid 1 | NUgrid 2 | Auto | Octree Best | 1935.06 | 2225.37 | 2129.30 | 2475.14 | 1844.92 Worst | 25870.45 | 12116.60 | 7039.23 | | 68208.26 ... for SPD model Mount: | Grid | NUgrid 1 | NUgrid 2 | Auto | Octree Best | 505.69 | 455.84 | 436.91 | 512.24 | 451.99 Worst | 2059.52 | 1479.85 | 1326.74 | | 9281.84 ... for SPD model Rings: | Grid | NUgrid 1 | NUgrid 2 | Auto | Octree Best | 799.76 | 918.94 | 767.40 | 811.32 | 760.52 Worst | 4852.32 | 5376.37 | 4284.81 | | 13688.93 ... for SPD model Teapot: | Grid | NUgrid 1 | NUgrid 2 | Auto | Octree Best | 345.39 | 344.60 | 336.09 | 491.06 | 357.74 Worst | 3617.02 | 2492.49 | 2672.95 | | 17756.98 ... for SPD model Tetra: | Grid | NUgrid 1 | NUgrid 2 | Auto | Octree Best | 79.13 | 77.45 | 75.45 | 98.29 | 123.64 Worst | 348.72 | 242.01 | 245.11 | | 1699.55 ... for SPD model Tree: | Grid | NUgrid 1 | NUgrid 2 | Auto | Octree Best | 5013.27 | 667.20 | 502.07 | 833.47 | 565.85 Worst | 18763.96 | 5019.25 | 3670.67 | | 25418.44

======== USENET cullings follow ======================

I wrote some routines for raytracing patches. They are based on a paper by:

Levner G, Tassinari P, Marini D (1987) A simple method for ray tracing bicubic surfaces. In: Kunii TL (ed) "Theoretical Foundations of Computer Graphics and CAD", 1987, Springer, Tokyo, pp 805-814.

These routines can work with any bicubic patch such as a bezier, b-spline, cardinal, beta-spline, etc. These are the routines that are in the library:

* NewPatch - Allocates the patch data structures and returns a pointer. * DefPatch - Defines a patch, given a patch pointer. * IsectPatch - Intersects a ray and a patch. Returns u, v, t, pnt. * NormalPatch - Given a patch and a u, v position, returns the normal. * FreePatch - Deallocates a patch. * * Additionally, there is one useful routine not specific to patches: * BoxIntersect - Given a ray and a box, returns the intersection point.

These should give you the capability to raytrace a patch. I have used them successfully in a raytracing package I wrote. You can use them as is or use them as an example for your own code.

[these are in wuarchive in the ray subdirectory, spline-patch.tar.Z]

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DECstation SPARCstation NeXT HP Snake (710)

You MUST have one of the above machine types in order to run the program. I wrote the client and encourage anyone who wishes to modify the source and experiment with it. Abe Megahed wrote the raytrace engine and does not wish to release its source code; thus, source for the server will not be distributed.

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wire4 is a 4D wireframe package that takes geometry information from input files, and has such features as PostScript output, colored edges, depth-cued edges, real-time 3D and 4D rotations, and other little features. wire4 uses the GL interface, so it runs on most GL platforms and quite a few others that support the GL interface.

ray4 uses 4D raytracing to render hyperspheres, hypertetrahedra, hyperplanes, and hyperparallelepipeds. ray4 runs on any platform that supports C with floating-point arithmetic, but the current package only has the display program for SGI workstations. I have a display program for the Amiga, but it's not ready for release yet (I haven't yet uploaded it to work). In addition, Mark Craig has written a sunraster output file display program; I hope to release that soon also (let me know if you're interested). The software is available by ftp from ftp.kpc.com /pub/graphics/holl91, /pub/graphics/ray4, /pub/graphics/wire4.

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The Engineering Computer Graphics Laboratory at Brigham Young University is offering a 30-day demonstration of this new software. CQUEL.BYU will run on the following workstations under X-Windows: SGI 4D, DEC Station 3100/5000, HP9000 700/800 series, SUN4/Sparc Station, and IBM RS6000. Just send a tape or a $20 (US dollars) check to:

Engineering Computer Graphics Laboratory Brigham Young University 368 Clyde Building Provo, UT 84602 PHONE: 801-378-2812 E-Mail: cquel@byu.edu

Also, please specify your machine type and operating system.

Stacey D. Son 459 Clyde Building Operations Manager Provo, UT 84602 Brigham Young University Voice:(801)378-5950 FAX:(801)378-6586 College of Engineering & Technology Email: sson@ee.byu.edu

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Rad (as it is called) allows real-time walkthrough and interactive modification of the scene during computation. Textures are supported when hardware allows. The computation algorithm is based on progressive radiosity, and uses automatic patch subdivision to refine the solution.

There is one small catch though: Rad only runs on SGI Workstations. Sorry about that, but I wasn't gonna rewrite a whole GL for X11.

Rad is currently available on the following anonymous ftp sites: gondwana.ecr.mu.oz.au in pub/rad.tar.Z wuarchive.wustl.edu in pub/rad.tar.Z

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>i.e. for simulation of image formation through a user definable

>lens.

"Optics Lab", an educational program available for about $35 from

Intellimation Library for the Macintosh P. O. Box 1530 Santa Barbara CA 93116-1530

800-346-8355 805-968-8899 (fax)

is not a super-high-powered lens design program but might be adequate for your application. Includes a "lens cabinet" of user adjustable lenses, mirrors, and stops; click and drag to position elements on screen; use the mouse to launch individual rays or ray bundles, and see them propagate or bounce on screen.

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Image Synthesis (Rendering) Advertising Film Production Lighting Design Medical Imaging Molecular Modeling Relativity Acoustic Simulation Seismic Simulation Simulation and Training (flight/tank simulators, etc.)

____

Howard Lo (hlo@sgi.com) adds:

Antenna analysis Radar Cross Section analysis

____

Davyd Norris (daffy@vaxc.cc.monash.edu.au) adds:

Attenuation and Multiple Scattering corrections for Neutron Diffraction

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Eric Haines adds:

Monte Carlo simulation of particle interactions in High Energy Physics - Saul Youssef has a number of papers related to this topic.

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Steve Hollasch (hollasch@kpc.com) comments:

> Lighting Design

Raytracing is only of limited use in lighting design. It's good for casting shadows and dealing with reflections of light sources, but it fails for diffuse interreflection. For this reason, radiosity is usually a better approach for lighting design, since it propagates light more realistically than raytracing. The "best" approaches that I've seen attempt to marry the methods of ray tracing with radiosity.

> Medical Imaging

> Molecular Modeling

> Simulation and Training (flight/tank simulators, etc.)

In my opinion, these areas are NOT best met with ray tracing, since they are better implemented in a dynamic fashion. In fact, I don't believe I've _ever_ seen a simulator that uses a ray tracing method. If you've got one up your sleeve, we'd LOVE to see it. =^)

> Relativity

This is a very good one. Ray tracing has the advantage that of all other methods, it (IMHO) extends most easily to alternate geometries. This in fact is a good area to explore further. I used ray tracing to render 4D geometry for my thesis, and was surprised by how straight- forward the implementation was. Implementing the display of 4D objects with scanline (scanplane?) methods is anything but trivial, but raytracing 4D is delightfully simple.

Other possible areas include:

Rendering Translucent Densities (clouds, gasses, liquids, etc.)

Simple Optic Design (using the refractive capabilities of raytracing).

Mathematical Graphics Since it is often easier to just intersect a surface via implicit equations, rather than to tessellate some sort of representation of the object.

____

Iain Sinclair (axolotl@socs.uts.edu.au) comments:

Greg Ward's Radiance software does raytracing with diffuse interreflection, doesn't it? It all depends on what you're trying to light (or design).

Straight radiosity looks strange in some circumstances, or simply isn't suitable. As you say, combinatory approaches are probably best.

>In fact, I don't

>believe I've _ever_ seen a simulator that uses a ray tracing method. If

>you've got one up your sleeve, we'd LOVE to see it. =^)

There are real-time auditory simulators which use raytracing.

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Why not incorporate into the proprietary communication programs that are used for such online services as Prodigy a simple raytracer which can calculate a very small number of pixels/frame? First, when users first log on, you could upload a scene description to their computers. While they are online, you could send escape codes to them for viewpoint changes and object repositioning, and have them return the value of a pixel or a small group of pixels. The computers at the Prodigy-like company could shell out the scene information and collect the results to make for a very fast distributed raytracer. This is assuming that the time spent sending scene information is not too substantial.

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This is something that has been bugging me for a long time, but I'm glad I waited until now to bring it up. Whilst writing a paper and reading old issues of the RTNews (or is that RTOlds 8-), I was reminded of it.

Constant Time Ray Tracing: Theory OR Practice?

Two things I will refer to are:

OHT87 "Ray Coherence Theorem and Constant Time Ray Tracing Algorithm" Masataka Ohta and Mamoru Maekawa Computer Graphics 1987, Proc. of CGI '87, p. 303-314.

OHT90 "Algorithm Order Discussion" Masataka Ohta and Pete Shirley Ray Tracing News, Vol. 1, #4, 1990

You might also read the Intro. to Ray Tracing by Glassner, et al., for a summary of OHT87. I'm hoping Ohta may be reading, but I thought I would post it for all to read.

THEORY

In theory, is constant time ray tracing as in OHT87 possible? Sure. Given a sufficient 3D subdivision and a fine enough division of ray directions, each list in the structure will contain fewer than some constant number of objects. For a given ray, mapping the origin to the grid is constant time, mapping the ray direction to one of the subdirections is constant time, and intersecting the ray against a constant number of objects is constant time.

In theory, is constant time ray tracing on a 3D grid possible? Yes, given a very huge grid. Suppose the grid is so large that tracing a ray through it will result in less than a constant number of ray-object intersections, then yes, right? Wait! What about the traversal of the grid? Well, if the grid size is not a function of the number of objects, then the traversal time is constant. Well, this can't be done. Even if you scale the grid size as a function of the screen resolution, it can't be done. You can always make a scene that will cause some rays to cause a lot of intersections.

OHT87 - yes 3D grid - no

What does the OHT87 method do that the 3D grid doesn't? Perhaps the answer lies in the preprocessing. The ray tracing is constant time, but is the preprocessing? Of course not, but maybe that's still ok. I'll discuss that in the next part.

REALITY

How much preprocessing is allowed? SUPER-SILLY EXAMPLE: Preprocessing consists of computing all shade trees, and the ray tracing process consists of a table look up based on the primary ray! Talk about asking a lot! Well, the ray tracing sure is constant time, but the preprocessing isn't. Any technique that processes the objects to build a data structure, won't be constant time, of course. However, that still leaves the question of how much is allowed.

Consider this example: A scene consists of many parallel polygons that are parallel to the image plane (like a stack of paper). These aren't run of the mill 4-sided rectangles. They have holes in them. A lot of the holes line up with rays through the view plane and they are really small. Now, suppose we preprocess using the OHT87 algorithm. *I* think that no matter how many ray directions you allow, you might not be able to eliminate enough objects to make the list for that direction be smaller than a constant number. Remember, we're not talking theory here, you can't have billions of ray directions. There is some limit on the number of ray directions. I'm pretty sure this falls under the no-coherence clause 8-) (p. 308 - "Because the algorithm utilizes the coherence of the image, the efficiency of the algorithm heavily depends on the coherence of the image. If there is no coherence, no performance will be gained."). So ---> it's not constant time then!

FURTHER DISCUSSION

Now I'm not trying to shoot down the work done in OHT87. I don't know how it compares to other schemes in implementation either. The problem I have is one of terminology. Ray tracing has very little theory behind it. In the early 80's, it seemed most algorithms we're "hacked together implementations" done at the terminal (I hope that doesn't sound demeaning, since I don't mean it that way). Of late, research is turning toward some theory since most of the "good ideas" have been done already 8-): meaning we need to analyze what exists to see what's wrong with it. However, there is still little theory supporting the field. So "Constant Time..." is misleading since you can't really do it, and who wants to generate theoretical images.

A somewhat unrelated thought arises from a comment in OHT90: "My algorithm may consume possibly long and computationally complex pre-processing time to analyze a scene. But, the important fact is that the time for pre-processing is dependent only on the scene and not on the number of rays."

My first reaction is "GNNNAAARRRR?" The number of rays in a scene is bounded above by a constant: total number of pixels * maximum size of a ray tree (unless we assume an infinite ray tree -> unrealistic). Neither of these factors is a function of the number of objects. Preprocessing is dependent upon the scene and THAT is what is important. How much preprocessing of the scene is ok? My SUPER-SILLY EXAMPLE does too much preprocessing.

Suppose we make a super-general assumption that preprocessing time can be no greater than k% of the ray tracing time. Make k whatever you want, but in OHT87 preprocessing is O(f(N)) (i.e. some function of N) and tracing is O(1). So the preprocessing demands are too high using this k% assumption. Maybe it's a bad assumption, but it's the one I see in the literature.

Finally this leads me to another point, support of a claim via testing. Too often assumptions are made about the scene which are just too convenient. Not only in this case, but in many, a sphere is just too simple an object to support a proof. Again, I don't doubt the theory here (the proof itself is sufficient), I doubt the reality. In this case, the reality is supported by convenient scenes, which make it appear that the reality is sound (and thus constant time). What I'm getting at is, give me some really ugly objects, e.g. GEARS database.

Depending upon the response to this article, I might post another about assumptions for algorithm testing. If I get flamed badly or there are no followups, then I won't.

A little something to think about: No computer in the world, no matter what its word size, no matter its memory size, no matter what its architecture, can prevent overflow <--> no ray tracer in the world, no matter what the internal data structure, can perform in constant time (you just can't ignore preprocessing, as in the case of the SUPER-SILLY EXAMPLE).

I would like to reiterate that I am not claiming that the work in OHT87 is incorrect. I just think that a theoretical concept is misleading in a realistic research world. No mudslinging, and keep name-calling to four letter words 8-).

____

Eric Haines responds:

>REALITY

>

>How much preprocessing is allowed? SUPER-SILLY EXAMPLE: Preprocessing consists

>of computing all shade trees, and the ray tracing process consists of a table

>look up based on the primary ray!

I agree, "constant" time is a provocative, fun thing to say (and Ohta is not the first to say it, Kaplan's "Space-Tracing, A Constant Time Ray-Tracer" from SIGGRAPH 85 course notes is the first instance I know). If your efficiency scheme can, in theory, guarantee that given a ray, you know exactly which object is hit by just performing some simple (non-recursive) look-up, then you'll have constant time ray tracing. The problem with such "in theory" statements are that they can't be backed up in practice. Either the scheme takes an infinite amount of memory, or finding the actual object to intersect in the efficiency structure takes O(log n) time, or some other catch. So, getting "near constant time" is more interesting in practice.

Many people make use of this kind of thing for rays from the eye: do a hidden surface preprocess (which is much faster than ray tracing in most situations, and is constant with the number of objects) to find what is at each screen sample. This truly is "constant time" ray tracing because we know exactly where all the rays are going to go (through the pixels in the screen), so we can indeed store all these directions in a grid and easily walk through them to find what's visible. The look up time is constant, and there is at most one object at each pixel. The preprocess time is O(n) with the number of objects.

The intersections of rays from the eye then need just a look-up to get what's hit. Ohta & Maekawa, Arvo & Kirk's 5D idea, and my own shadow buffer try to further this directional preprocessing. Arvo & Kirk have a nice table comparing the three in their chapter of "An Intro to RT". From my own experience it's impossible to solve the problem of, given an arbitrary ray, doing an immediate look-up (i.e. we don't have to traverse a hierarchy to find our object, we just translate the ray information into a table index) combined with always having at most a single object on the list. By being willing to not have all three elements we can often come up with schemes that do the other two perfectly and the third fairly well.

Like the shadow buffer, Ohta creates grids containing candidate lists. The lists are not bounded in size, so the testing time is not a constant. In his defense, Ohta's scheme gives almost constant times for his sparse spheres case and near constant for his dense spheres case. It's impressive that it can do so well, and this was back in 1987. The cost is that you need a direction cube structure for _each_ object in the scene, which is costly in preprocessing time and memory.

>Consider this example: A scene consists of many parallel polygons that are

>parallel to the image plane (like a stack of paper). These aren't run of the

>mill 4-sided rectangles. They have holes in them. A lot of the holes line up

>with rays through the view plane and they are really small.

I agree, this case will make preprocessing schemes no longer constant. You can do LOTS of preprocessing to try to resolve the indeterminate areas, and you may have to get down to a ridiculous resolutions to attempt to resolve these, and you still will have places where things fall apart.

Another approach is to work from the objects themselves to split up 5D space and determine what object is visible for what set of positions and directions. I recall seeing some computational geometry paper on doing something like this, where you preprocess all 5D space into volumes, each of which is associated with one object. Aha, found it:

%A Marco Pellegrini %T Stabbing and Ray Shooting in 3 Dimensional Space %J Proceedings of the 6th Annual Symposium on Computational Geometry %I Berkeley, CA %D June 1990 %P 177-86

Since you were interested in theoretical papers, this is an interesting one to check out. To quote: "The result presented in this paper, although not yet practical because of the huge constants involved, is the first example of a ray shooting algorithm with a sublinear cost per ray, for any set of triangles and rays." He proves that given a ray one can determine in O(log n) worst case time which is the first triangle hit, with O(n^5) preprocessing (truly the record for preprocessing time). His results are interesting in that the best he claims is O(log n), not O(1), because he knows pathological cases can kill all the other schemes out there. His bias is towards worrying about the worst case performance, which most of the rest of us blithely ignore. What's interesting about his scheme is that he could maintain it's constant in intersection testing time (in fact, the constant is zero), since he never tests any rays against any triangles: the scene is entirely encoded in a structure, and he gets a ray and merely looks up what triangle (if any) is hit by that ray. It's accessing the structure and finding where the ray is in it that takes O(log n).

Another good pathological case is the shell database (Introduction of Ray Tracing News, volume 3, number 3). Try it on your favorite ray tracer sometime and see what happens: many overlapping spheres bring most ray tracers to their knees (mine included). Most efficiency schemes are good overall, but when a large number of the surfaces of complex objects overlap a given volume of space, preprocessing that space well is impossible or very costly. It would be interesting to see how Ohta's scheme works on the shell data, since it's entirely spheres. Ohta's ray tracer is at various FTP sites, though I haven't tried it out.

>Suppose we make a super-general assumption that preprocessing time can be no

>greater than k% of the ray tracing time. Make k whatever you want, but in

>OHT87 preprocessing is O(f(N)) (i.e. some function of N) and tracing is O(1).

>So the preprocessing demands are too high using this k% assumption. Maybe it's

>a bad assumption, but it's the one I see in the literature.

Good point - no matter what k% you assign, if tracing is really O(1) then you can never in theory fulfill the k% ratio, since the number of objects can be arbitrarily high. The "k%" is just a rule of thumb working assumption in the literature, not some theoretical limit that cannot be exceeded ("it'd be nice if the preprocessing time was some percentage less than the ray tracing time" is all "k%" is, after all).

What's interesting about preprocessing schemes is that once they're done you can reuse them. If you're making an animation of flying around a static scene, that's a heck of a lot of pixels to compute, which massively amortizes the cost of the one-time preprocess. Because of this I think we'll see more time spent preprocessing as the years go by (though if CPU speed increases faster than memory size, then it might not be possible to store the preprocess structures around for a large scene...).

>A little something to think about: No computer in the world, no matter what

>its word size, no matter its memory size, no matter what its architecture, can

>prevent overflow <--> no ray tracer in the world, no matter what the internal

>data structure, can perform in constant time (you just can't ignore

>preprocessing, as in the case of the SUPER-SILLY EXAMPLE).

Yep, "constant time" is an attention grabber, and saying "near constant time" would be a bit more realistic. If your efficiency structure has any hierarchy in it, then you're not constant. If you have a simple lookup structure like an evenly spaced grid or somesuch, you're constant time lookup, but short of infinite resolution you won't get a single object to test at _every_ spot in the structure.

Well, that was certainly long-winded! Anyway, I thought it was worth mentioning the Pellegrini paper, since it's pretty obscure and one of the few I've seen that really tries to tackle the theoretical aspects. Hopefully I didn't say anything too stupid here...

____

Brian Corrie responds:

>Suppose we make a super-general assumption that preprocessing time can be no

>greater than k% of the ray tracing time. Make k whatever you want, but in

>So the preprocessing demands are too high using this k% assumption. Maybe it's

>a bad assumption, but it's the one I see in the literature.

I have just run into an interesting result similar to this. I am working on a MIMD parallel machine made by Fujitsu, the AP1000. It has 128 processing nodes, each processor being a SPARC chip running at 25 MHz. Needless to say, this thing is fast. I have just gone through the process of parallelizing my Ray Tracer on this machine. Let me clarify that, I parallelized the rendering, NOT the preprocessing. I use Glassner's Space Subdivision acceleration technique. Guess what, in some cases, the preprocessing actually takes longer than the rendering on this architecture. Giving a demo just isn't too satisfying when the boss is looking over my shoulder saying:

Boss: "whats it doing now?" ME: "Oh, preprocessing." Boss: "Whats it doing now?" ME: "Still preprocessing.. ahhhh, now its rendering, oh there, its done."

This certainly doesn't fit the k% model that you state above. It always seemed that the preprocessing stage was insignificant compared to the rendering time, but it really isn't. You just need some strange circumstances or some serious thought to see that the preprocessing time can not be ignored.

____

Masataka Ohta responds:

>I would like to reiterate that I am not claiming that the work in OHT87 is

>incorrect. I just think that a theoretical concept is misleading in a

>realistic research world. No mudslinging, and keep name-calling to four letter

>words 8-).

Well, at the presentation of OHT87, I received silly questions from those who can not understand the difference between realtime and constant time.

But it is not my problem. Any paper is misleading to those who can not understand basic terminologies in it.

Constant timeness is a purely theoretical property. Remember it.

>THEORY

>OHT87 - yes

>3D grid - no

I agree. Note that implicit simplification is that multiplication, addition and address arithmetic are all O(1).

When I wrote OHT87, many (including me) believed 3D grid is O(log(N)) and some even claimed O(1) without knowing what O(1) means.

>REALITY

>Remember,

>we're not talking theory here, you can't have billions of ray directions.

>There is some limit on the number of ray directions.

It is pointless. Constant timeness is a purely theoretical property. Theoretically, you can have billions of ray directions. There is no limit on the number of ray directions.

>I'm pretty sure this

>falls under the no-coherence clause 8-)

No. Constant timeness of your case is covered by a sentence (p. 308) "It is worthwhile to note that nearly all images can be calculated in this very fast manner, if we can use unlimited pre-processing time and space".

>(p. 308 - "Because the algorithm

>utilizes the coherence of the image, the efficiency of the algorithm heavily

>depends on the coherence of the image. If there is no coherence, no

>performance will be gained."). So ---> it's not constant time then!

No, of course. What my no-coherence clause means is that with insufficient D (the number of directions) or M (the number of origins) it's not constant time.

With large enough D and M determined by the coherence of scene, it will be constant time again.

>FURTHER DISCUSSION

>A somewhat unrelated thought arises from a comment in OHT90: "My algorithm

>may consume possibly long and computationally complex pre-processing time to

>analyze a scene. But, the important fact is that the time for pre-processing

>is dependent only on the scene and not on the number of rays."

I said "analyze a scene", not "generate an image". OK?

>My first reaction is "GNNNAAARRRR?" The number of rays in a scene is bounded

>above by a constant: total number of pixels * maximum size of a ray tree

>(unless we assume an infinite ray tree -> unrealistic). Neither of these

>factors is a function of the number of objects.

You misunderstand basic terminologies.

An image have fixed number of pixels, but a scene itself has no resolution. A scene can be rendered into images with various resolutions and various quality.

The number of rays to generate an image depends on required resolution and quality (if you need antialiased but precise RGB value, you often must fire large number of rays within a pixel), and not limited by any constant.

>Too often assumptions are made about the scene which are just too convenient.

>Not only in this case, but in many, a sphere is just too simple an object to

>support a proof. Again, I don't doubt the theory here (the proof itself is

>sufficient), I doubt the reality.

I used spheres in measurement because it is most unfavourable to the ^^^^^^^^^^^^ implementation of my algorithm. If you use complex shapes, possible startup time for constant timeness might be masked. Implementation of my algorithm might have required large constant time comparable to ray bicubic patch intersection, which could have been masked if I used a scene with bicubic patches.

See Fig. 4 for unbelievably small overhead (nearly equals to the time for ray sphere intersection) of the implementation.

>In this case, the reality is supported by

>convenient scenes, which make it appear that the reality is sound (and thus

>constant time). What I'm getting at is, give me some really ugly objects,

>e.g. GEARS database.

Then, we can have beautiful but theoretically meaningless images.

What I want to show is constant time property. To do so, we must be able to control the number of objects in the scene up to several hundreds (or more, see Fig. 8).

____

and further comments from Masataka Ohta:

>This certainly doesn't fit the model that you state above. It always

>seemed that the preprocessing stage was insignificant compared to the

>rendering time, but it really isn't. You just need some strange circumstances

>or some serious thought to see that the preprocessing time can not be ignored.

When tracing state-of-the-art realistic scenes with state-of-the-art complex shading, anti-aliasing and so on, tracing and shading time become much much longer than when tracing sphere-only simply-shaded non-anti-aliased scenes.

Hints for serious thought:

1) the preprocessing time to achieve constant time property is constant once a scene is fixed.

2) the preprocessing time to achieve constant time property is less than or nearly equal to tracing time for sphere- only images in my paper.

3) the preprocessing time to achieve minimal total (preprocessing +tracing+shading) time to render an image of a scene need not be the preprocessing time to achieve constant time property for the scene. With the increase of the tracing+shading time, the trade-off shifts toward increasing tracing time complexity and reducing preprocessing time complexity.

____

Brian Corrie responds:

It is true, once the scene is fixed, then pre-processing is fixed, so multiple frames can be produced without that overhead in certain situations. That is, if the camera moves, lights go on and off, attributes change, then the preprocessing does not need to be re-computed. Only if the geometry changes is this step needed.

It is also true that if I render complex images with complex shading and scene interaction (reflection/refraction), the preprocessing time can rapidly become insignificant again. Insignificance is all in the eye of the renderer I suppose.

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I'm currently trying to get my Honours project sorted out for next year. The idea is to produce some kind of raytracing/radiosity rendering chip. Yup, thats right, put the whole rendering system on a single piece of silicon. I've been trying to track down any past work on this. So far the only mention I've found is that of Ullner's work in "An Introduction to Raytracing". Can anyone suggest any papers I should be looking for?

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George Kyriazis (kyriazis@rdrc.rpi.edu) writes:

Oh boy.. I'll be a bit negative on this. This is only my opinion, so I'd like to get some feedback from other people to see how much this makes sense..

Ray-tracing and radiosity is a VERY computational intensive job. Additionally, it's a bit unhomogeneous. What I mean by that is that there are lots of different algorithms that need to be done: Traversing the space subdivision hierarchy, various intersection algorithms, (possibly) various shading algorithms, etc. Not to mention the immense amount of data that has to be fed in those poor processing elements.

In the past the market tried to provide special-purpose hardware that is perfect for just one problem, but has REAL trouble for others.. For example, the Pixel Machine was great doing ray-tracing, but it had problems with interactive graphics. An SGI-style graphics pipeline is perfect for interactive 3-D applications, but it just was not designed for ray-tracing or radiosity-type applications. On the other hand, general-purpose floating point accelerators are getting faster and faster.. So, my guess is that a whole bunch of fast, general purpose machines will eventually win, 'cause the can provide more functionality and a smaller overall design cost.

Now, let's try to be constructive a bit here.. As I said before, doing raytracing the traditional way is unstructured. You are tracing a ray who knows how many levels of reflections deep, but you don't really know what type of primitive you are going to hit, so the rendering algorithm should be ready for anything. There has been some work a couple of years ago (I could be mistaken, but I think at UIUC) about using an SIMD machine for ray-tracing. Now, if you think of normal ray-tracing as a depth-first algorithm (we go as many levels deep as possible on the first pixel, then go ahead on the next pixel, etc.), you can think of the SIMD work as implementing ray-tracing in a breadth-first kind of way. Finish up the first level of intersections for all pixels in the image, then the ones who survive go on to the second level of reflection, etc. This brings some more structure into the algorithm.

____

Peter De Vijt (devijt@imec.be) writes:

A number of people did some studies on implementing a part of the algorithm (the intersection calculations) in silicon. No real silicon has been demonstrated upto now. Here are some refs.

%A Ron Pulleyblank %A John Kapenga %T The Feasibility of a VLSI Chip for Ray Tracing Bicubic Patches %J IEEE Computer Graphics and Applications %V 7 %N 3 %D March 1987 %P 33-44 %O also appears as "A VLSI Chip for Ray Tracing Bicubic Patches" in Advances in Computer Graphics Hardware I, W. Strasser (ed.), 1987, p. 125-140 and in Tutorial: Computer Graphics Hardware: Image Generation and Display, Computer Society Press, Washington, 1988, p. 328-339

%A Kadi Bouatouch %A Yannick Saouter %A Jean Charles Candela %T A VLSI Chip for Ray Tracing Bicubic Patches %J Eurographics '89 %I Elsevier Science Publishers %C Amsterdam, North-Holland %D Sept. 1989 %P 107-24

%A Alle-Jan van der Veen %T Intersection Test for NURBS %B Proc. of the IEEE Symp. on Computer Architecture & Real Time Graphics %D June 1989 %C Delft, The Netherlands %P 101-14

Implementing a complete raytracing/radiosity algorithm on one chip is IMHO not possible. The problem is that the algorithm itself is quite complex. You'll have to calculate intersection points for various primitives, reduce the search space for the primitives you are going to calculate the intersections with, do shading calculations, ...

Given the huge amount of work you'll have to perform, you will still need a multiprocessor solution to get the images at a reasonable rate (After all you've put a lot of effort in it, so you want some performance back) You need a very good scheduling mechanism to get more than an impressive number of Mythical FLOPS.

The basic algorithm for ray-tracing is pretty simple. The intelligent implementation isn't. If you put the basic algorithm in silicon, an intelligent software version will easily outperform your system. A good vlsi implementation will have to implement the more elaborate and complex algorithm. (Yeah such is life)

The kind of parallelism you need for vlsi is different than the one you need for software. On a general purpose multiprocessor system you can use all kinds of parallelism, in vlsi you can't. An ASIC can only be better than a uP if it can take advantage of some specific aspects of an algorithm. If the algorithm is too complex, you can not take advantage of that, and the ideal implementation looks pretty much like an ordinary general purpose uP. (We better leave that to the big R&D teams). So forget about doing it on one chip.

The only thing you can do is to break the algorithm apart and implement each part or only the most interesting parts (= inner loops ) that will give you a performance gain (such as the intersection calculations).

Here at IMEC we're doing just that as a sort of design exercise. We're planning to implement a part of the algorithm on a couple processors.

The algorithm is split in three big pieces: rendering, narrowing the search space for the intersection calculations and the intersection calculations themselves. The rendering will be done on general purpose processors for flexibility. Data base search and spline intersection calculations on two custom processors. The other intersection calculations will again be done on GP uP's for flexibility. Also a special processor is being built for scheduling the operations in a multiprocessor environment.

The whole system is designed in such a way that each of these processors can be replaced by a general purpose one and that some operations can be modified (eg. more primitives than we planned a specific processor for). This way we can build the system in different stages (first the intersection processor, the scheduler, the data base searcher, and last an optional MMU) First versions of the intersection processor and the scheduler should be ready around july.

I must agree with George Kyriazis that eventually a GP machine will win, but again this is only a design exercise and it's FUN.

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Jon Leech (leech@cs.unc.edu) writes:

I think the original poster would be better off doing some regular part of a rendering kernel, perhaps a ray-tracing hierarchy traversal chip.

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Sam Uselton (uselton@nas.nasa.gov) writes:

Two comments to add on the previous discussion.......

(1) the SIMD parallel ray tracing I know of, was done at Thinking Machines on a Connection Machine by Hubert Delaney, who recently was kind enough to send me 2 tech reports, which I haven't had time to read yet.

(2) Gershon Kedem (and probably some other folks) were working on VLSI support for ray tracing of CSG defined objects several years ago. The work was being done at Duke University, although other NC Research Triangle entities were probably involved. I discussed the project with him in his office something like 3 years ago. Sorry, I don't have a reference. [Cornell is also involved. See ray tracing bibliography under Kedem or Ellis. - EAH]

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Thierry Priol (priol@irisa.fr) writes:

I agree with you, ray-tracing is so irregular (data driven) that designing a VLSI processor for ray-tracing algorithms is a hard task. We have done some works on MIMD machine. General purpose parallel MIMD machines are able to produce very high efficiency for ray-tracing algorithms especially if you are using a shared virtual memory on these kinds of machines! (see "Ray Tracing on Distributed Memory Parallel Computers: Strategies for Distributing Computation and Data" in "Parallel Algorithms and architectures for {3D} Image Generation", ACM Siggraph'90 Course 28).

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From: rkaye@polyslo.csc.calpoly.edu (Dega Dude):

I would suggest to approach the problem from a different angle. While it would be an extreme job to implement an entire ray tracing/radiosity system in silicon, you could implement some generic routines that usually take a lot of CPU time quite easily.

You could code intersection and normal calculation routines for the basic primitives you would like to have in your system. Some other things to code would be generic routines required by your acceleration techniques, such as voxel-object intersection routines or bounding volume routines.

There are many 'generic' CPU intensive routines that can be implemented in silicon. The software can then adapt around the chip's capabilities, giving you the flexibility to change the system.

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The most important thing to remember about the moon is that while it is spectacularly un-specular, it is by no means a Lambertian reflector -- this is why Phong shading can't model it well, contrary to hollasch@kpc.com (Steve Hollasch @ Kubota Pacific Computer, Inc.).

An ideal full moon is equally bright everywhere -- its brightness does not drop off toward the edges! (The real moon differs from the ideal moon only in that its albedo is non-uniform. For example, the maria are darker than the mountains.)

A model that works well for the moon is to think of it as covered in a dust of microscopic Lambertian reflectors. When viewed from the light source direction, the dust particles will reflect light equally, regardless of the direction of the moon's surface normal.

When viewed from some other direction (i.e. when the moon is not full), the dust particles still reflect light equally, but some of them are shadowed by others. Shadowing increases when the angle between the light and the viewing direction increases so that the reflected light travels through more dust, and when the angle between the surface normal and the light direction increases, so that the incident light travels through more dust. Of course, the total light reflected from the dust particles varies with viewing angle as well because they are only lit on one side.

There are many ways to convert this qualitative description into an analytic model, depending on exactly how you model self-shadowing of dust. Jim Blinn has a paper on illumination functions for clouds of dust (in 1979 Siggraph proceedings, I think -- I don't have the precise reference at my fingertips) that describes this in fair detail and gives a lunar reflection model that works really well.

I suspect that even people without my astigmatism have trouble telling by looking at its shape whether the moon is exactly full or one day away from it. The difference in shading, however, is fairly dramatic. When its full, the moon looks like a silver dollar in the sky. Even one day away and still looks like a perfect circle, it shades off to one side or the other by a noticeable amount.

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[Derek sent me his responses, some of which are below. - EAH]

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From Samuel P. Uselton (uselton@wk207.nas.nasa.gov)

I'm pretty sure that general Monte Carlo evaluation of an integral of a function is a general, well known mathematical idea, and as such not patentable. If the PIXAR patent is valid, it must patent some particular method (=implementation) for doing this evaluation. I assume it is the jitter sampling idea presented in papers by Cook, et al.

I think our implementation of the integral evaluation is sufficiently different that it is OK. See Redner, Lee, Uselton, "Statistically Optimised Sampling for Distributed Ray Tracing", SIGGRAPH '85.

Sorry I can't supply code. The original source code we wrote (actually mostly written by Lee) belongs to Amoco, and is in Fortran for an IBM 3090 anyway. There is a plan to create a "liberated" version, but it is not available at least from us.

If you, or anyone, wants to convince me I'm wrong and that we really DO infringe the patent, or that an arguable case could be made, please let me know, because we ARE extending our results.

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From Lawrence Kesteloot (lkestel@gmuvax2.gmu.edu)

The method you describe can be easily modified to make the lamp a rectangle instead of a sphere. This makes the light into a fluorescent tube.

This method is quite good and realistic but, as you said, the noise is fairly bad for low n's (<64). Another way which I thought about (and I don't know if anyone's done it yet), but haven't actually implemented yet, is to use some kind of approximation formula. For example, if you've got a sphere sitting on a surface and you're trying to evaluate the darkness of that shadow at some point below the sphere, you can run a ray from the point on the surface to the light, find the two roots of the intersection, and use the DISTANCE between the two roots, in some kind of formula which would involve the radius of the sphere and lamp and distance to the lamp and surface, to determine the darkness at that point. It is not scientific, but points that intersect close to the edge of the sphere will get two roots that are close together and this would make that shadow lighter. I haven't even implemented this or thought of a formula, but if you get any kind of results with it please let me know. It would be very fast, as you can imagine. It will most likely fail in strange circumstances such as points that are shadowed by two objects at once. I guess that's the penalty for getting away from pure ray-tracing...

I can also think of another way to do it, but much harder to explain in
writing. It is similar to yours but would probably reduce the noise. Imagine
that you run a ray from the point in question to the light center. You then
find a circle, centered at the light, radius of the light, which is
perpendicular to the ray. You then pick

[This was tried by Brigitta Lange, and is in her paper "The Simulation of Radiant Light Transfer with Stochastic Ray-Tracing", Second Eurographics Workshop on Rendering, Barcelona, Spain, May 1991. Proceedings should be published by Springer-Verlag realsoonnow. Anyway, her results were mixed, giving "ring" artifacts as I recall. - EAH]

Let me know what you think.

Oh! I almost forgot. This is very important: Don't sent

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John responds:

> You then pick

> and run rays through them. This will give you good soft shadows

> and low noise.

And very visible banding. Oh well. What I am looking for is finding the plane perpendicular to the ray at the light, and using a pre-computed table of random offsets with a poisson distribution.

I still don't have a quick and elegant system of finding the plane and two basis vectors.

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From: philip@bigben.dle.dg.com (Philip Gladstone)

The standard trick is to do adaptive sampling. In my ray-tracer, I shoot a number of rays through each pixel, and then randomly select a point on the surface of the light source to for shadow calculations. After a few rays have been cast, the standard deviation of the values returned is calculated to see if more rays need to be cast. [This is oversimplifying quite a lot, as the points are not really chosen at random as there is a nearness check. Further, subsampling only takes place in an area of high standard deviation.]

This also buys you antialiasing on edges etc. This gives a very nice output for very little increase in cost -- I start out with four rays per pixel (though this should probably be increased somewhat) with a limit of 200 rays. This givs an average number of rays per pixel of a reasonable picture of about 6, with a few pixels having 200!

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From: shirley@iuvax.cs.indiana.edu (peter shirley)

Just like pixel sampling, light source sampling works better is the "random" points are replaced by "quasi-random" points. Quasi-random points can be generated by making sure no two points are too close, or by hand generating them for storage in lookup tables.

See the ray tracing book under jittering or Poisson disk sampling for further details.

PS- I think you'll have better luck choosing points on the projected area of the light source. Choosing from within the sphere would be correct if the light originated throughout the sphere.

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The book can be ordered by mail directly from Jones and Bartlett Publishers, 20 Park Plaza, Boston, MA 02116, or by phone, 1-800-832-0034 or by e-mail, kpeters@math.harvard.edu. Prepaid orders (MC, VISA or check) will not be charged postage or handling.

The problem of quickly generating three-dimensional synthetic imagery has remained challenging for computer graphics researchers due to the large amount of data which is processed and the complexity of the calculations involved. This book involves a thorough investigation into the problem of using a massively parallel computer to perform three-dimensional computer graphics rendering. The algorithms which are analyzed in this monograph present several alternative approaches to image space decomposition as well as remote memory access. A number of pointers are given so that researchers intending to develop their own parallel rendering algorithm will be able to obtain high performance and good speedup from a variety of multiprocessor architectures.

Table of Contents:

1. Introduction 1.1. Problem Description 1.2. Overview of Accelerated Rendering Techniques 1.3. Research Context 1.4. Document Overview 2. Overview of Parallel Methods for Image Generation 2.1. Criteria for Evaluation of Parallel Graphics Display Algorithms 2.2. Taxonomy of Parallel Graphics Decompositions 2.3. Conclusions 3. Issues in Parallel Algorithm Development 3.1. Architectural Choices 3.2. Comparison of MIMD Methodologies 3.3. The BBN Programming Environment 3.4. Summary 4. Overview of Base Level Implementation 4.1. Design of the Basis Algorithm 4.2. Testing Procedures 4.3. Performance Analysis 4.4. Summary 5. Comparison of Task Partitioning Schemes 5.1. Data Non-Adaptive Partitioning Scheme 5.2. Data Adaptive Partitioning Scheme 5.3. Task Adaptive Partitioning Scheme 5.4. Conclusions 6. Characterization of Other Parameters on Performance 6.1. Shared Memory Storage and Referencing 6.2. Machine Parameters 6.3. Scene Characteristics 6.4. Conclusions 7. Conclusion 7.1. Summary 7.2. Future Work References Appendix A. Information on Test Scenes B. Data for Various Algorithms C. Supplementary Graphs Index

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Eric Haines / erich@acm.org