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"Light Makes Right"
March 1, 1988
Volume 1, Number 3
Compiled by
All contents are copyright (c) 1988, 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 ray tracing FAQ.
- Eric
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'I'm currently hanging out at Apple thinking about "3D graphics for the rest of us" and how to keep the jaggies away from personal computers. (But there is this Cray sitting about 50 feet away. Hmmm...)'
# # John Peterson - bicubic splines, texturing # Apple Computer (graduated University of Utah, 1988) alias john_peterson hpfcrs!hpfcla!jp%apple.apple.com@RELAY.CS.NET
I asked him for ray tracers at the University of Utah. So, Tom Malley and Rod Bogart (whose initials are 'RGB') are now subscribers.
From Tom: My thesis research was similar to what John Wallace described, being a two pass approach to radiosity to include specular reflection and transparency. Form factors were all calculated via ray tracing, however. I did some brief examination of different ray intersection methods along the way (Rubin-Whitted, Kay-Kajiya, and Glassner).
# # Tom Malley - blending ray tracing and radiosity # Evans & Sutherland (graduated University of Utah, 1988) # (malley@cs.utah.edu, cs.utah.edu!esunix!tmalley) alias tom_malley hpfcrs!hpfcla!hplabs!malley@cs.utah.edu
To quote John Peterson about Rod Bogart:
Rod developed a really neat method for using ray tracing to integrate
computer generated pictures with real world images (coming soon to a
SIGGRAPH near you...).
# # Rod Bogart - blending ray tracing and images # University of Utah alias rod_bogart hpfcrs!hpfcla!hplabs!bogart%gr@cs.utah.edu
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Just a quick response to your football stadium/teapot example. When you subdivide a node, look at its children. If only one child is non-empty, replace the original node with its non-null child. Do this recursively until the subdivision criterion is satisfied. I do this in my spacetime ray tracer, and the results can be big. The ray propagation can get just a bit more complex, but there are clever rays to keep it simple (see John Amanatide's article in Eurographics '87, plus I have a scheme that I hope to write up soon...).
Better yet, go with a hybrid space subdivision/bounding volume scheme, such as the one described in my spacetime paper (poorly described in the Intro to RT notes, but better described in the version slated for the March issue of CG&A; I'd be happy to mail you a preprint). I think this hybrid scheme gives the best of both worlds, and you can use whatever space subdivision and bounding volume techniques that you like in the two distinct phases of the algorithm. I use adaptive space subdivision and Kay's bounding slabs, and that combination seems to work pretty well.
And now I have to get back to moving into my office!
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From: Eric Haines (with a few extra comments than my original letter to Jim)
Your article on efficiency is fascinating. I hope to read it more carefully tonight and (eventually--we just came under a crunch of work) comment on it. Sounds like you've done a lot of serious thought and speculation on the possibilities. I agree with the philosophy of objects each having their own private hierarchies, and having the ability to hook these hierarchies up however you want. We've done that on a small scale with our tesselated spline surfaces: automatic hierarchy a la Goldsmith & Salmon (IEEE CG&A, May 1987) for everything, but then octrees for the spline surfaces themselves. A nice feature of Goldsmith is that you can weight the cost of each primitive into the algorithm: multiply its area by some intersection cost (which you'll probably have to figure out through experimentation) to give it a weighting. In this way a torus surface which has the same size bounding volume as a quadrilateral can be given a higher weighting factor. A higher cost has the effect of making the hierarchical tree less horizontal near the complicated object, i.e. there are more bounding volumes overall, with a few complicated objects in each. This is what you want, since you'd rather spend a little extra time on intersecting bounding volumes than wasting a lot of time intersecting the empty space around costly objects.
____
Response from: Jim Arvo
I'm glad you found my article interesting. All your interesting mail finally motivated me to contribute to the discussion. I thought I would toss out a pet idea of mine and see if it sparked any debate. It turns out that Jeff Goldsmith also looked at simulated annealing for bounding box hierarchies. One day one of us will get some results. Hopefully not negative results!
With all the talk about octrees and such, it's clear that there are a number of potential papers "waiting in the wings". I've been thinking that by getting the right collaborations going, we (the ray tracing group) could easily "hand" IEEE several related papers, effectively defining a theme issue. What do you think?
____
My reply:
The efficiency article collection sounds possible. Another idea which someone (Mike Kaplan, maybe? I forget) mentioned at last SIGGRAPH was "A Characterization of Ten Ray Tracing Efficiency Algorithms". If well done, this would be a classic. There are probably entirely new schemes still to be found, and certainly trying to optimize and figure out good hybrid methods is an area ripe for development. But right now many of the structures and algorithms are in place, and still have not been fully compared. Timings are unconvincing, and statistics are worthwhile but don't tell the whole story. An in-depth comparison of the major algorithms and techniques to improve these would be wonderful. Someday, someday ... well, my hope is that a few of us could do some writing along these lines, even if it's just brainstorming on how to compare particular algorithms in a rigorous fashion (e.g. How can we simulate a scene mathematically? OK, idealize each object as a box or sphere for simplicity. Now, how do we distribute the points to get realistic clustering? Once we have a "scene generator" which could create various typical distributions of objects in a scene, then we have to analyze how this generator would interact with each algorithm, and be able to predict how each efficiency scheme deals with the scenes generated. Or there might be simpler ways to isolate and analyze each factor which affects the efficiency of a scheme. Anyway, whatever, but this stuff looks fun!). Understanding the strengths of the various techniques seems vital to being able to do any kind of "annealing" process for optimization.
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The obvious corollary to that idea has a little more reach to it. Since illumination rays form the bulk of the rays we trace, getting the nearest intersection is of limited value. In addition, if CSG is used, more times occur when the nearest intersection is of less value. This seems to indicate that space tracing techniques are doing some amount of needless work. Since it doesn't really cost that much, perhaps it is not a flaw, but maybe space tracers should consider approaches that don't worry about where along the path we are and optimize that problem instead.
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I agree completely with your comment about libraries. Mine is a crucial resource for me. Here are some of my favorite books that are in my office:
Geometry:
Computational Geometry for Design and Manufacture
Faux & Pratt
--an early CAD text. It has lots of good stuff
on splines and 3D math.
Differential Geometry of Curves and Surfaces
DoCarmo
--A super text on classical differential geometry.
(Not quite the same as analytic geometry.)
CRC Standard Math Tables
--This has an awesome section on analytic geometry.
Calculus, too. Can't live without it. It is not
the same as the first part of the Chemistry and
Physics one.
Analytic Geometry
Steen and Ballou
--Once was the standard college text on the subject.
That was a long time ago, but it is very easy to
read and it covers the fundamentals.
Computing:
Data Structures and Algorithms
--Aho, Hopcroft and Ullman
Read anything by these guys.
Data Structure Techniques
--Standish
More How-to than AHU's tome.
Numerical Analysis
--Burden, Faires, and Reynolds
I have the other two, as well. This is the
least complete of the three, but the algorithms
inside are childishly easy to implement. They
always seem to work, too. Best of all, for many
cases, they have test data and solutions.
Software Tools
--Kernighan and Plauger
How to write command line interpreters, editors,
macro expanders, the works. Great reading.
Fundamentals of Computer Algorithms
--Horowitz and Sahni
Less technical than AHU, but pretty technical.
Thicker. It may very well answer the problem
you can't figure out straight off.
The Art of Computer Programming
--Knuth
The "Encyclopedia"
Physics: (Seem awfully useful sometimes)
Gravitation
--Misner, Thorne, and Wheeler
The thickest book on my shelf. It's a paperback, too.
(It's bent three bookends permanently. Cheap JPL ones.)
Truly a tome on modern physics.
Modern Physics
--Tippler
Much easier to read than MTW. Has lots of good appendices.
University Astronomy
--Pasachoff and Kuttner
I read this book for fun. I wonder why I didn't read it
while I was taking Kuttner's course?
The Feynman Lectures on Physics
Awesome first course. Most of my needs are problems in
the text.
Graphics, etc:
Raster Graphics Handbook
--Conrac
All about fundamentals of the craft.
Light and Color in Nature and Art
--Williamson and Cummings
Much easier to read than Hall's thesis, but less
technical as well.
Etc, Etc:
The Random House Dictionary of the English Language,
College Edition
The best collegiate sized dictionary around.
By far.
The Chicago Manual of Style
Has most of the answers. Did you know that
to recreate is to have fun, but to
re-create is computer graphics?
The Elements of Style
The one that came before computers.
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This bug was one I had when implementing octree subdivision for ray tracing. The basic algorithm used was Glassner's: once you intersect the octree structure, move the intersection point in one half of the smallest cube's dimension in the direction normal to the wall hit. In other words, find out what cube is the next cube by finding a point that should be well inside of it, then translating this point into integer octree coordinates and traversing the octree downwards until a leaf node is found.
However, there are some subtle errors that can occur with moving to the next octree cube. My favorite is almost hitting the edge of a cube, moving into the next cube, then getting caught moving to the cube diagonal to this cube, i.e. moving from cube 1 to 2 to 3 ...
X-->
+---+---+
^ | 2 | $ | Numbers are the order of cubes moved through.
| +---#---+
Y | 1 | 3 |
+---+---+
^________ray started here, and hit almost at the "#".
(ray is in +X, +Y direction)
This went into an infinite loop, going between 2 and 3 forever. The reason was that when I hit the boundary 1&2 I would add a Y increment (half minimum box size) to the intersection point, then convert this to find that I was now in box 2. I would then shoot the ray again and it would hit the wall at 2&$. To this intersection point I would add an X increment. However, what would happen is that the Y intersection point would actually be ever so slightly low - earlier when I hit the 1&2 wall adding the increment pushed us into box 2. But now when the Y intersection point was converted it would put us in the 1+3 boxes, and X would then put us in box 3. Basically, the precision of the machine made the mapping between world space and octree space be ever so slightly off.
The infinite loop occurred when we shot the ray again at box 3. It would hit the 3/$ wall, get Y incremented, and because X was ever so slightly less than what was truly needed to put the intersection point in the 3+$ boxes, we would go back to box 2, ad infinitum. Another way to look at this is that when we would intersect the ray against any of the walls near the "#" point, the intersection point (due to roundoff) was always mapping to box 1 if not incremented. Incrementing in Y would move it to box 2, and in X would move it to box 3, but then the next intersection test would yield another point that would be in box 1. Since we couldn't increment in both directions at once, we could never get past 2 and 3 simultaneously.
This bug occurs very rarely because of this: the intersection points all have to be such that they are very near a corner, and the mapping of the points must all land within box 1. This problem occurred for me once in a few million rays, which of course made it all that much more fun to search for it.
My solution was to check the distance of the intersections generated each time: if the closest intersection was a smaller distance from the origin than the closest distance for the previous cube move, then this intersection point would not be used, but rather the next higher would be. In this way forward progress along the ray would always be made.
By the way, I found that it was worthwhile to always use the original ray origin for testing ray/cube intersections - doing this avoids any cumulative precision errors which could occur by successively starting from each new intersection point. To simulate the origin starting within the cube I would simply test only the 3 cube faces which faced away from the ray direction (this was also faster to test).
Anyway, hope this made sense - has anyone else run into this bug? Any other solutions?
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[I agree: my problem now is that Y=0 is the bottom edge of the screen when dealing with the graphics package (HP's Starbase), and Y=0 is the top when directly accessing the frame buffer (HP's SRX). -- EAH]
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All for now,
Eric
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