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- _ __ ______ _ __
- ' ) ) / ' ) )
- /--' __. __ , --/ __ __. _. o ____ _, / / _ , , , _
- / \_(_/|_/ (_/_ (_/ / (_(_/|_(__<_/ / <_(_)_ / (_</_(_(_/_/_)_
- / /|
- ' |/
-
- "Light Makes Right"
-
- January 2, 1990
- Volume 3, Number 1
-
- Compiled by Eric Haines, 3D/Eye Inc, 2359 Triphammer Rd, Ithaca, NY 14850
- NOTE ADDRESS CHANGE: wrath.cs.cornell.edu!eye!erich
- [distributed by Michael Cohen <m-cohen@cs.utah.edu>, but send
- contributions and subscriptions requests to Eric Haines]
- All contents are US copyright (c) 1989,1990 by the individual authors
- Archive locations: anonymous FTP at cs.uoregon.edu (128.223.4.1) and at
- freedom.graphics.cornell.edu (128.84.247.85), /pub/RTNews
- Other sites: uunet.uu.net:/graphics
-
- Contents:
- Introduction
- New People
- Archive Site for Ray Tracing News, by Kory Hamzeh
- Ks + T > 1, by Craig Kolb and Eric Haines
- Quartic Roots, and "Intro to RT" Errata, by Larry Gritz and Eric Haines
- More on Quartics, by Larry Spence
- Question: Kay and Kajiya Slabs for Arbitrary Quadrics?
- by Thomas C. Palmer
- Ambient Term, by Pierre Poulin
- Book Reviews on Hierarchical Data Structures of Hanan Samet,
- by A. T. Campbell, III
- Comparison of Kolb, Haines, and MTV Ray Tracers, Part I, by Eric Haines
- Raytracer Performance of MTV, by Steve Lamont
- BRL-CAD Ray Tracer Timings, by Gavin Bell
- BRL-CAD Benchmarking and Parallelism, by Mike Muuss
- ======== USENET cullings follow ========
- Rayshade Patches Available, by Craig Kolb
- Research and Timings from IRISA, by Didier Badouel
- Concerning Smart Pixels, by John S. Watson
- Input Files for DBW Render, by Tad Guy
- Intersection with Rotated Cubic Curve Reference, by Richard Bartels
- Needed: Quartz surface characteristics, by Mike Macgirvin
- Solution to Smallest Sphere Enclosing a Set of Points, by Tom Shermer
- True Integration of Linear/Area Lights, by Kevin Picott
-
- -------------------------------------------------------------------------------
-
- Introduction
-
- This issue's focus is on timings from various people using a wide
- selection of hardware and software. Much of the delay in getting out this
- issue was my desire to finish up my own timing tests of MTV's, Kolb's, and my
- own ray tracers on the same machine. I hope some of you will find this
- information of use.
-
- Another feature of this issue is a pair of book reviews. One of the
- purposes of the RT News is to provide people with sources of information
- relevant to ray tracing. So, I would like to see more reviews, or even just
- brief descriptions of articles and books that you come across. Keeping up to
- date in this field is going to take more time as the years go by, so please do
- pass on any good finds you may have. Also, if you're an author, please feel
- free to send a copy of the abstract here for publication. This service is
- already provided to a certain extent by SIGGRAPH for thesis work. However,
- even a duplication of their efforts is worthwhile, since an electronic version
- is much easier to search and manipulate.
-
- Finally,
-
- -------------------------------------------------------------------------------
-
- New People
-
- # Kory Hamzeh
- # 6640 Nevada Ave.
- # Canoga Park, Ca 91303
- # Email: UUCP: avatar!kory or ..!uunet!psivax!quad1!avatar!kory
- # INTERNET: avatar!kory@quad.com
- alias kory_hamzeh quad.com!avatar!kory
-
- I'm not professionally involved in ray tracing. Just personally fascinated by
- it. I have written a couple of ray tracers (who hasn't yet?) and I'm in the
- midst of designing a 24 bit frame buffer. Since I don't do this on a
- professional level, I lack some of the resources required to develop real
- products. I maintain a archive site with a lot of graphics related items
- (including Ray Tracing News). If you need to access the archive (anonymous
- uucp only) please send me mail.
-
- --------
-
- #
- # Steve Lamont, sciViGuy - parallelism
- # NCSC,
- # Box 12732,
- # Research Triangle Park, NC 27709
- alias steve_lamont cornell!spl%mcnc.org
-
- --------
-
- # Bob Kozdemba - novice tracer, futures, also radiosity
- # Hewlett-Packard Co.
- # 7641 Henry Clay Blvd.
- # Liverpool, NY 14450
- # (315-451-1820 x265)
- alias bob_kozdemba hpfcla!hpfcse!hpurvmc!koz
-
- I work for HP in Syracuse, NY as a systems engineer. I will be attending SU
- starting in Jan. `89 working toward my BS with a focus in computer graphics.
- My job responsibilities are to provide technical support to customers and
- sales in the areas of Starbase graphics and X Windows. Lately I have been
- experimenting with HP's SBRR product [radiosity and ray tracing part of the HP
- graphics package] and trying to keep abreast of futures in graphics. I have
- written an extremely primitive ray tracer and I am looking for ideas on how to
- implement reflections and transparency.
-
- --------
-
- # Robert Goldberg
- # Queens College of CUNY
- # Comp. Sci. Dep't
- # 65-34 Kissena Blvd.
- # Flushing, N.Y. 11367-0904
- # Work : 3d Modeling algorithms, with appl. to graphics and image processing
- # Phone: Work - (718) 520-5100
- alias robert_goldberg rrg@acf8.nyu.edu
-
- --------
-
- # John Olsen - refraction, radiosity, antialiasing, stereo images.
- # Hewlett-Packard, Mail Stop 73
- # 3404 E. Harmony Road
- # Ft Collins, CO 80525
- # (303) 229-6746
- # email: olsen@hq.HP.COM, hplabs!hpfcdq!olsen
- alias john_olsen hpfcdq.hp.com!olsen
-
- Currently, I've been spending some time tinkering with the DBWrender ray
- tracer making it produce 24 bit/pixel QRT-format images. I like the QRT
- output format, but I like some of the features of DBWrender, such as
- antialiasing and fading to a background color.
-
- I've thought about writing my own ray tracer with all the features I want, but
- so far I've resisted this evil temptation, and only looked for fancier ones
- already done by others who could not resist the temptation. :^)
-
- I've just installed an alias for a local ray tracing news distribution. You
- can send it to raylist@hpfcjo.HP.COM (or if you can't reach, try something
- like hplabs!hpfcdq!hpfcjo!raylist).
-
- --------
-
- # Andrew Hunt, andrew@erm.oz
- # Earth Resource Mapping, 130 Hay St, Subiaco, Western Australia 6008
- # Phone: +61 9 388 2900 Fax: +61 9 388 2901
- # ACSnet: andrew@erm.oz
- alias andrew_hunt uunet!munnari!erm.erm.oz.au!andrew
-
- In 1987 I implemented a "Three Dimensional Digital Differential Analyser"
- (3D-DDA) algorithm, along the lines of Fujimoto and Iwata`s, and used it to
- speed up a raytracing system under development at the Computer Science
- Department at Curtin University of Technology.
-
- Recently I have got a bit busy developing commercial image processing software
- to devote much time to Ray Tracing.
-
- Sometime during 1990 I plan to try to port our Ray Tracing system to a
- Transputer based platform.
-
- --------
-
- # Nick Beadman - Distributed Ray Tracing, Efficiency
- # School of Information Systems
- # University of East Anglia
- # Norwich
- # Norfolk
- # United Kingdom
- alias nick_beadman cmp7112@sys.uea.ac.uk
-
- At the moment I'm trying to implement a distributed ray tracer on 8 t800s on a
- meiko computing surface using C, with little success I should add. It all
- part of a big third year computing project worth a sixth of my degree.
-
- --------
-
- # Peter Miller - algorithms, realism
- # 18 Daintree Cr
- # Kaleen ACT 2617
- # AUSTRALIA
- # CONTACT LIST ONLY: subscription through melbourne
- #Phone: +61-62-514611 (W)
- # +61-62-415117 (H)
- # UUCP {uunet,mcvax,ukc}!munnari!neccan.oz!pmiller
- # ARPA pmiller%neccan.oz@uunet.uu.net
- # CSNET pmiller%neccan.oz@australia
- # ACSnet pmiller@neccanm.oz
- alias peter_miller cornell!uunet!munnari!neccan.necisa.oz.au!peter
-
- I have been interested in ray tracing since 1984, when I wrote a ray tracer
- before I knew it was called ray tracing! Since then I have been reading
- journals and tinkering with my ray tracer.
-
- The last 3 years were spent marooned off the net, with very poor graphics
- output devices; so while some work was done on the ray tracer, I now have a
- lot of catching up to do.
-
- --------
-
- # Mike J. McNeill
- # VLSI and Graphics Research Group,
- # EAPS II,
- # University of Sussex,
- # Falmer, BRIGHTON, East Sussex, BN1 9Qt
- # TEL: +44 273 606755 x 2617
- # EMAIL: (JANET) mikejm@syma.sussex.ac.uk | (UUCP) ...mcsun!ukc!syma!mikejm
- alias mike_mcneill mike@syma.sussex.ac.uk
-
- I am currently researching into parallelising the RT algorithm on a
- multiprocessor architecture. I'm using object space subdivision using a fast
- octree traversal algorithm. At the moment I'm simulating the architecture
- using C via TCP/IP protocols on a distributed Apollo network. Interested in
- all aspects of speed-up, parallel architectures, coherency and radiosity -
- dare I mention animation and Linda? Also does anyone know of a modelling
- package for use on the Apollos?
-
- -------------------------------------------------------------------------------
-
- Archive Site for Ray Tracing News, by Kory Hamzeh
-
- Avatar is an archive site which archives Ray Tracing News, comp.source.unix,
- comp.sources.misc, and other goodies. Archived files can be access by any
- one using anonymous uucp file transfers. A list of all files in the archive
- can be found in avatar!/usr/archive/index. Note that this file is quite
- large (about 40K). If you are only interested in the graphics related
- archives, snarf the file avatar!/usr/archive/comp/graphics/gfx_index.
- All Ray Tracing News Archives (except for the first few) are stored in
- /usr/archive/comp/graphics directory. They are named in the following
- fashion:
-
- RTNewsvXXiYY.Z
-
- Where XX is the volume number, YY is the issue number. Note that all files
- (except index and gfx_index) are compressed.
-
- Before trying to access avatar, your L.sys file (or Systems file, depending
- on which flavor of UUCP you have) must be edited to contain the following
- info:
-
- #
- # L.sys entry for avatar.
- #
- # NOTE: 'BREAK' tells uucico to send a break on the line. This keyword
- # may vary from one flavor of UUCP to another. Contact your system
- # administrator if your not sure.
- #
- # 1200 baud
- avatar Any ACU 1200 18188847503 "" BREAK "" BREAK ogin: anonuucp
- #
- # 2400 baud
- avatar Any ACU 2400 18188847503 "" BREAK ogin: anonuucp
- #
- # 19200 baud (PEP mode) for Telebit Trailblazers only
- avatar Any ACU 19200 18188847503 ogin:-\n-ogin: anonuucp
-
- After the previous lines are entered in you L.sys file, you may use the
- following command to get the index file:
-
- uucp avatar!/usr/archive/index /usr/spool/uucppublic/index
-
- This command will grab the file from avatar and put it in your
- /usr/spool/uucppublic directory using the name index. For example,
- to get Ray Tracing News Volume 2, Issue 5, execute the following
- command:
-
- uucp avatar!/usr/archive/comp/graphics/RTNewsv02i05.Z /tmp/RTnewsv02i05.Z
-
- NOTE that some shells (like csh) use the "!" as an escape character, so
- use a "\" before the "!".
-
- If you experience problems getting to any of the files, I can be reached
- via e-mail at:
-
- UUCP: avatar!kory or ..!uunet!psivax!quad1!avatar!kory
- INTERNET: avatar!kory@quad.com soon to be kory@avatar.avatar.com
-
-
- Enjoy,
- Kory Hamzeh
-
- -------------------------------------------------------------------------------
-
- Ks + T > 1, by Craig Kolb and Eric Haines
-
- From: Craig Kolb <craig@weedeater.math.yale.edu>
-
- While adding adaptive tree pruning to rayshade (and discovering a bug), I came
- across a question I've had regarding the SPD for a while.
-
- Some objects have Ks + T > 1. How can this be? For example, the spheres in
- "mountain" have Ks = .9 and T = .9. Unless I'm completely out to lunch (which
- is possible), ths means that subsequent specularly reflected rays are weighted
- by .9, and that transmitted rays are also weighted by .9. This leads to
- "glowing" objects pretty quickly.
-
- What's wrong in the above description? Be warned that in "nff2shade.awk", I
- set the "specular reflectance" to be min(Ks, 1. - T).
-
- --------
-
- My reply:
-
- Actually, true enough, Ks + T > 1 does occur in the SPD stuff.
- I use T in a funny way, since I was trying to make databases that would
- display both using hidden surface and ray tracing algorithms. Hmmm, how
- to explain? Well, imagine you have a glass ball: under the hidden surface
- system (without transparency), you'd like the ball to appear opaque, and
- so a high Kd is in order. Now if the thing's transparent, you don't want
- Kd to be high. So what I do is lower Kd and Ks by ( 1 - T ). An admittedly
- weird shading model, which I've now changed a bit (i.e. reflectance and
- transmittance are now entirely separate). So, your solution of turning down
- the reflectance is fine. I should add that I didn't really explain all this
- as it's irrelevant for timings (all we care about is what rays get generated,
- not the final color), but I agree, it would be nicer to get a good resulting
- picture as a check. I'll change that in the next update of SPD, actually...
- thanks for pointing it out!
-
- --------
-
- Craig's reply:
-
- Ah, I get it.
-
- I brought it up because it does make a difference timing-wise if you're using
- adaptive tree pruning. Although you say in the SPD stuff that pruning
- shouldn't be used, Mark's raytracer currently has no option to turn it off. I
- was comparing pruned vs. pruned, and noticed that I had many fewer reflected
- rays, since my reflectance for the transparent gears was .05 rather than .95.
-
- -------------------------------------------------------------------------------
-
- Quartic Roots, and "Intro to RT" Errata,
- by Larry Gritz (vax5.cit.cornell.edu!cfwy)
-
- I was trying to find the solution to a quartic equation to solve a
- ray-torus intersection test. I've gotten lots of replies, but generally fall
- into one of two categories: either solve the quartic equation (I forget the
- reference now, but I'll send you either a reference or the formula if you want
- [It's in the _CRC Standard Math Tables_ book - EAH]), or by some iterative
- method. Everybody says (and I have confirmed this experimentally) that
- solving the equation is very numerically unstable. I have chosen to use the
- Laguerre method from Press, et. al. _Numerical Recipes in C_, which is slow,
- but seems to work, and finds all roots without needing to specify brackets for
- the roots. (An advantage since although I can bracket all possible real roots
- with the bounding box test that I already do, I'm not really sure how many
- roots lie within the brackets.)
-
- What actually turns out to be a bigger problem is that I got the quartic
- coefficients from the SIGGRAPH '88 Ray Tracing Course Notes (on page 3-14 of
- Pat Hanrahan's section).
-
- [Larry and I thrashed this out over a number of passes (boy, I wish I had access
- to Mathematica or somesuch), and came out with the following corrected
- equation set for those on page 93 of _An Introduction to Ray Tracing_:
-
- a4 & a3 - Pat's are OK.
- a2 = 2(x1^2+y1^2+z1^2)((x0^2+y0^2+z0^2)-(a^2+b^2))
- + 4 * (x0x1+y0y1+z0z1)^2 + 4a^2z1^2
- a1 = 4 * (x0x1+y0y1+z0z1)((x0^2+y0^2+z0^2)-(a^2+b^2))
- + 8a^2 * z0 * z1
- a0 = ((x0^2+y0^2+z0^2)-(a^2+b^2))^2 - 4a^2(b^2-z^2)
-
- - EAH]
-
- -------------------------------------------------------------------------------
-
- More on Quartics, by Larry Spence
- From: larry@csccat.UUCP
- Newsgroups: comp.graphics
- Subject: Re: Solution to quartic eqn?
-
- >I didn't ask the question, but thanks for your input. However, Ferrari's
- >theorem yields a fast and very accurate answer.
- ^^^^
- Are you sure about this? If it's the same closed-form solution that you find
- in the CRC books, etc., doesn't it use trig functions and cube roots? Seems
- to me there was a paper by Kajiya in the early '80s on numerical ray tracing,
- and there have been several in the last few years. My advice would be to go
- look at SIGGRAPH proceedings from 1981 on. Certainly, a closed form solution
- like the one suggested wouldn't take advantage of any coherence in the problem,
- unless you wrote all the trig stuff yourself.
-
- [Comments, anyone? I never saw any replies. - EAH]
-
- -------------------------------------------------------------------------------
-
- Question: Kay and Kajiya Slabs for Arbitrary Quadrics?
- by Thomas C. Palmer <palmer@mcnc.org>
-
- Here's a question regarding slabs for arbitrary quadrics. Kay & Kajiya '86
- discusses computing slabs for polygons and implicit surfaces. The method for
- implicit surfaces using Lagrange multipliers and gives an example using
- spheres. This is easy and works quite nicely for canonical (i.e. centered
- and axis aligned) quadrics. K&K handle object rotations and translations
- during the slab computation. What about quadrics that have been transformed
- by some arbitrary matrix prior to input and look like this:
-
- ax^2 + 2bxy + 2cxz + 2dxw + ey^2 + 2fyz + 2gyw + hz^2 + 2izw + jw^2 = 0 ?
-
- The xy, xz, and yz terms prevent a simple solution via Lagrange multipliers.
- Has anyone done this? How do you handle quadric bounding planes? Note that
- K&K cheated for the tree branchs in the tree models. Each cylinder has
- endpoint capping spheres so the cylinder's extent is just the combined extent
- of the two spheres.
-
- Thanks for your help -
-
- -Tom
-
- Thomas C. Palmer North Carolina Supercomputing Center
- Cray Research, Inc. Phone: (919) 248-1117
- PO Box 12732 Arpanet: palmer@ncsc.org
- 3021 Cornwallis Road
- Research Triangle Park, NC
- 27709
-
- -------------------------------------------------------------------------------
-
- Ambient Term, by Pierre Poulin (poulin@dgp.toronto.edu)
-
- I just read your Tracing tricks in the latest Ray Tracing News. Thanks for
- passing that on to us, this was very interesting.
-
- One trick you mentioned was to put a light source at the eye position in
- order to eliminate the ambient term. This is a simple trick I did not know.
- However, you noted that highlights appears as artifacts.
-
- Since you know that this light does not need any shadow rays, you could use
- only the diffuse intensity created by this light to approximate the ambient
- term, hence creating no undesirable highlights.
-
- I know, this is very easy and everyone probably knows that. But just in
- case you would not have thought about it, I wanted to indicate it to you. I
- just hope I am not the 10,000th to tell you :^)
-
- --------
-
- My reply:
-
- I'm glad to hear that you enjoyed the "Tracing Tricks" article -
- sometimes I worry that I'm just publishing ideas that everyone already knows.
- I've tried having the ambient light have no highlight, and it's sort of
- interesting, but the lack of highlight can look a little strange for those
- objects where there really would be a highlight (it sort of makes them look
- less shiny, though it also depends upon the other lights in the scene).
- Nonetheless, turning it off is definitely worth exploring. You're the first
- person to comment on this, actually. Thanks for taking the time to write, and
- do keep in touch.
-
- -------------------------------------------------------------------------------
-
- Book Reviews on Hierarchical Data Structures of Hanan Samet,
- by A. T. Campbell, III (atc@cs.utexas.edu)
-
-
- "The Design and Analysis of Spatial Data Structures", and
- "Applications of Spatial Data Structures", by Hanan Samet,
- Addison-Wesley, 1990.
-
- Reviewed by A. T. Campbell, III
-
- This two-volume series of books is one man's effort to provide a guide to the
- study of hierarchical data structures. The topic has extensive influence on
- many fields, particularly computer graphics, image processing, and
- computational geometry. Hanan Samet is a well-established expert in the
- field, with literally dozens of publications. As a computer graphics
- researcher, I eagerly anticipated the books' publication. A close examination
- of both volumes leads to one conclusion: the books are extremely worthwhile.
-
- The integration of diverse material is remarkable. Comprehensive research
- results throughout the spectrum of science are drawn together seamlessly.
- Samet has really done a thorough job of pulling together literature from a
- vast collection of conferences and journals, both major and minor.
-
- The level of explanation is good. Samet has obviously read all of his
- references thoroughly. The descriptions of algorithms reflect an
- understanding of what is really going on. Even algorithms mentioned briefly
- are given a good essential description.
-
- Numerous topics are covered. Algorithms for such problems as
- proximity-searching, efficient storage of image and volume data, constructive
- solid geometry, data structure conversion, hidden surface removal, and
- ray-tracing fill the books. Pseudo-ALGOL code examples present detailed
- explanations of how to build and traverse many of the data structures.
- Ray-tracing enthusiasts in particular will enjoy a detailed description of how
- to trace a path through an octree.
-
- There are, however, a few problems with the presentation. Despite the
- ambitious titles of the volumes, there is nowhere near as much theory or
- practical advice as one might expect. The emphasis is instead on explaining
- literally everything at an understandable level. While this makes the books a
- wonderful introduction to all sorts of stuff, the reader still needs guidance
- in choosing what techniques to actually use.
-
- The title of the first volume, "The Design and Analysis of Spatial Data
- Structures", obviously invokes comparison with the classic text "The Design
- and Analysis of Computer Algorithms", by Aho, Hopcroft, and Ullman. However,
- Samet's approach differs greatly from that of Aho et al. While the data
- structures are described and discussed in detail, the analysis is not very
- formal. Theorems and proofs, as well as detailed algorithm analysis, are not
- much in evidence. A more appropriate title might simply be "An Introduction
- to Spatial Data Structures".
-
- The second book, "Applications of Spatial Data Structures", covers basically
- every research result in hierarchical algorithms, major or minor. It is
- exceptionally good at explaining techniques succinctly. The depth is not
- sufficient enough to implement the techniques without referring to the
- original papers, however. Additionally, the reader is given no good feel for
- which results should actually be used. If a technique is commonly used in
- industry or never used because of impracticality, Samet never says so. The
- reader who expects a "cookbook" solution to his problem will be disappointed.
-
- The books are primarily of use for two purposes. First, they provide a good
- introduction to those aspects of computational geometry and image processing
- which are most likely to be of interest to a person working in graphics.
- Second, they provide a very complete guidebook to the literature. I would
- suggest that researchers and practitioners have these volumes on their
- reference shelves. Due to the sheer volume of material presented, I would not
- recommend them for use as course textbooks.
-
- -------------------------------------------------------------------------------
-
- Comparison of Kolb, Haines, and MTV Ray Tracers, Part I, by Eric Haines
-
- I decided to compare the MTV ray tracer, the Kolb "rayshade" software,
- and my own modified "SBRR" ray tracing package to see the efficiency of each.
- My goal was to see what sort of performance was obtained by each ray tracer
- and note the strengths and weaknesses of each. This first section of the
- report marks the state of current results, consisting of timings from the
- "gprof" command for each package, using the Standard Procedural Database (SPD)
- package. All three packages were run on an HP 350 workstation with a floating
- point accelerator board. The compiler options were "-g -G +ffpa" (debug,
- profile, with special floating-point only compile), using HP-UX 6.5.
-
- The three ray tracers were selected from all the existing packages by
- having the following properties: (1) Each could handle all the primitives in
- the SPD package, and (2) each had some automatic efficiency scheme. Other
- packages do not support all the primitives (e.g. DBW does not have cylinders,
- cones, or n-sided polygons), or do not have automatic efficiency generation
- (e.g. QRT lets you explicitly create bounding boxes, but has no way for this
- to happen automatically).
-
- The MTV ray tracer was created by Mark VandeWettering, and uses the
- Kay/Kajiya hierarchy approach (i.e. sorting objects along X/Y/Z and splitting
- each group, recursively). To make it conform to the requirements of the SPD
- tests, "minweight" was set to 0.0 in order to disable tree pruning a la Hall's
- method.
-
- Craig Kolb's "rayshade" ray tracer uses a 22x22x22 grid on all scenes.
- Because of the use of grids (i.e. 3DDDA), it was found to be sensitive to the
- background polygons used in the SPD package. In four of the SPD scenes
- (balls, gears, rings, and tree) there is a "ground" polygon. The "rayshade"
- software allows some user intervention in how the database is structured. It
- was found that faster timings (sometimes strikingly quicker) could be obtained
- by leaving this background polygon out of the grid structure. Changing the
- database in this manner is forbidden by the SPD tests, but both sets of
- results are presented because of the difference in timings.
-
- The SBRR package is not public domain, but rather is part of the
- graphics software in all HP workstations using the Turbo-SRX graphics
- accelerator. It uses the Goldsmith and Salmon automatic bounding volume
- hierarchy method. It should also be noted that this package is full featured,
- which has a corresponding slowdown effect when intersection computations are
- performed. For example, polygons can be single or double sided, with
- different materials, colors per vertex, normals per vertex, and other
- combinations available. Since the package has a "hardware assist" by using
- the graphics engine as an item buffer (see Weghorst and Hooper), timings are
- given both with and without this assist. The times without are the fairer of
- the two for comparison.
-
- Without further ado, here are the timings:
-
- MTV Basic
- ----- -----
- balls 12604
- gears 38123
- mount 9307
- rings 24286
- tetra 1081
- tree 8056
-
-
- Kolb Basic Modified
- ----- ----- --------
- balls 14871 3224
- gears 12601 11449
- mount 2989 2989 (i.e. same - no modification needed)
- rings 8348 8103
- tetra 836 836 (i.e. same - no modification needed)
- tree 18957 2505
-
-
- SBRR Basic Item Bfr
- ----- ----- --------
- balls 5027 4126
- gears 13561 12776
- mount 5440 3749
- rings 11044 10446
- tetra 1187 457
- tree 3229 2719
-
-
- So, considering the MTV ray tracer as 1.00, here are the relative performance
- times of each tracer - (MTV time / RT time) - i.e. higher is faster, and can
- be thought of as how many times faster it is:
-
- SPD MTV-Base Kolb-Bas Kolb-Mod SBRR-Bas SBRR-Bfr
- ----- -------- -------- -------- -------- --------
- balls 1.00 0.85 3.91 1.40 3.05
- gears 1.00 3.02 3.32 2.81 3.33
- mount 1.00 3.11 <--same 1.71 2.48
- rings 1.00 2.91 3.00 2.20 2.32
- tetra 1.00 1.29 <--same 0.91 2.37
- tree 1.00 0.42 3.22 2.50 2.96
-
- Some interesting phenomena are revealed by the statistics. The "tetra"
- database is pretty much the same absolute speed for everyone. However, given
- the performance for other scenes, it is noteworthy that MTV performs
- relatively faster on this than others. I've noticed this, too, when trying
- Kay/Kajiya myself - this scheme just soars on tetra, though I am not sure why.
- Perhaps it is the smallness and regularity of the objects, which would go well
- with Kay/Kajiya's assumption that using the centroid of these is reasonable.
- For other databases one can imagine better hierarchies that those constructed
- by Kay/Kajiya. For example, with mount, the four spheres above the fractal
- mountain should be in their own cluster just off the top of the hierarchy
- tree.
-
- The "tetra" scene is a strange test in that most (around 81%) of the scene
- is background, so what we tend to test here is affected more by how fast one can
- traverse a scene, set up rays, shade, and store values in a file. It will take
- further analysis to see where the time is spent.
-
- The Kolb ray tracer is interesting in how much its efficiency scheme is
- affected by the geometry of the scene. The "teapot in a football stadium"
- effect I've written about previously hits grid efficiency schemes with a
- vengeance. For example, moving the ground polygon from the grid subdivision
- to outside of it makes rayshade perform 4.6 times faster for balls, and 7.7
- times faster for tree! The point is that grids perform best when the scene is
- relatively "compact". The large ground polygons in these scenes cause the
- entire grid to get larger in two directions, and so make many more objects
- fall inside but a few grid squares, thereby ruining much of the efficiency of
- the grid.
-
- Comparing Kolb to MTV, we see that overall Kolb is faster. Kolb does worse on
- balls and tree using the unmodified database, but otherwise outperforms MTV,
- being about twice as fast. When the ground polygon is taken out of the grid
- subdivision, Kolb is more than 3 times faster for all cases except tetra.
-
- Comparing SBRR and MTV shows SBRR to be faster for most cases, with MTV being
- slightly faster for tetra. Overall SBRR is almost twice as fast with its
- basic performance, and about 2.75 times faster when the item buffer is used.
-
- Comparing SBRR and Kolb is a bit tricky, since there are two tests of each.
- Taking the basic tests in each, Kolb and SBRR are comparable: Kolb outperforms
- SBRR in four cases, and SBRR outperforms Kolb in two (and for one of those,
- tree, it is almost 6 times faster). SBRR has some things to learn from Kolb
- (which is why I'm doing all this, anyway), as Kolb's modified database results
- point towards the fact that faster performance is possible.
-
- So, on the basis of pure raw timings, Kolb and SBRR without modifications or
- accelerators are of comparable speed. With user intervention into the
- database structure, Kolb can become noticeably faster. It should also be
- noted that Kolb uses a default of 22x22x22 grid cells, which is under user
- control and so could be tuned to further improve performance.
-
- Actually, this is an interesting open question: what heuristics can be used
- to determine a reasonable grid size for a scene? Also, is there a reasonable
- way to determine if such performance destroyers such as ground polygons are
- present automatically, and so remove them from the grid subdivision itself?
- David Jevans' and Brian Wyvill's work on nested grid subdivisions ("Adaptive
- Voxel Subdivision for Ray Tracing", Proceedings of Graphics Interface '89, p.
- 164-172) might lead to a less variable performance and to greater overall
- speed. Craig and I have discussed this, but unfortunately he has no time to
- try this out - perhaps someone out there can experiment and compare
- results.
-
- As mentioned, this is research in progress. My next step will be to analyze
- the statistics generated by each program and see where time is spent.
-
- -------------------------------------------------------------------------------
-
- Raytracer Performance of MTV, by Steve Lamont
-
- > Could you pass on your timings on ray tracer performance on various
- > machines and any thoughts or experiences you want to share about the subject?
-
- The parallelization was done in a brute force manner, forking processes and
- dividing the work by the number of processes. The parent process remains
- behind and reads the scanlines in a round robin fashion from pipes. There is
- no communication from the parent to the child processes once the forking has
- been done; the ray tracing routines simply march down the scan lines. This
- approach works well on a homogeneous architecture where all processes run at
- approximately the same speed and no process "dries up" or runs out of work to
- do.
-
- This works well for single frames. However, my approach for a large animation
- is to simply parcel out work on a frame per processor basis.
-
- I've built the MTV raytracer on the Cray, the IRIS, and the Ardent Titan...
- and here are some preliminary results on a 128 x 128 test image (the balls
- image with reflections but no refractions, 3 light sources, 11 primitives (16
- with bounding volumes)
-
- processes
- (CPU seconds)
- Machine 1 4 Notes
-
- Y-MP/8-432 4.0 1.0 -hopt,intrinsics,vector
- IRIS (4D/240)* 8.2 2.1 -O2 (MIPS R3000/3010)
- Titan (P2) 30.0 7.7 -O3 (MIPS R2000 + prop. vector/fp unit)
- Titan (P3) 7.2 --- Run by vendor. (MIPS R3000/3010 +
- proprietary vector unit)
-
- Wall clock times improved by a factor of 2.5 to 3, which squares pretty well
- with Amdahl's law as extended for small parallel architectures.
-
- These are *preliminary* results with respect to the Titan -- we've only had it
- for a couple of weeks. On none of the machines did MTV vectorize in any way
- to speak of. In fact, turning off vectorization improves performance for
- several "short vector" loops; e.g., loops of vector length 3.
-
- Timings were done on a fairly heavily loaded Cray and an empty IRIS and Titan.
-
- The Cray is a Y-MP with four processors (upgradable to 8, hence the 8-4) and
- 32 mWords of central memory. There is also a 128 mWord SSD (Solid-state
- storage device). We also have 40 gBytes of rotating storage (a combination of
- DS-40s and DD-49s).
-
- [*] Actually, this machine is a CDC Cyber 910-624 but the only difference
- between it and a "genuine" Silicon Graphics IRIS 4D/240 is the color of its
- box and the binding on the manuals.
-
- [Disclaimer: These comments are solely the responsibility of the author and
- no endorsement by the North Carolina Supercomputing Center should be inferred]
-
- Steve Lamont, sciViGuy EMail: spl@ncsc.org
- NCSC, Box 12732, Research Triangle Park, NC 27709
-
- -------------------------------------------------------------------------------
-
- BRL-CAD Ray Tracer Timings, by Gavin Bell (gavin@krypton.sgi.com)
-
- These results are third-hand; I can vouch for the accuracy of our machine's
- results, but the BRL people may have more recent results to share. The only
- experience I have with ray-tracing timing on our machines is with a simple,
- interactive ( :-> ) ray-tracer demo called 'flyray'. I modified it to be
- fully parallelized; it uses one CPU to display a real-time display of the
- scene being ray-traced (complete with rays shooting into and bouncing around
- the scene), and the other N-1 CPUs to compute ray-object intersections (these
- results are shown in a separate window). As for timing... runs REAL fast on
- an 8 CPU system.
-
- What follows is a form letter I've been sending to people who asked for
- ray-tracing timings.
-
- ------------------------
-
- This is a response to all of those people who asked me for the BRL-CAD
- ray-tracing benchmark results. I'm surprised at how many of you there are!
-
- First, a little bit about myself. I work in Technical Marketing, the 'Demos
- and Benchmarks' group here at Silicon Graphics. I'm not usually involved in
- benchmarks; I work mainly on our demos.
-
- The rest of this text comes directly from a 'SGI Benchmark Summary' prepared
- by one of our Marketing people. The numbers are communicated to him by the
- software engineer who did the benchmark. These benchmark summaries are
- communicated to salespeople in a weekly newsletter as soon as the results come
- in. Other summaries done include:
-
- 'INDUSTRY STANDARD':
- Dhrystones, Digital Review Labs, Linpack, Livermore Fortran Kernals, MUSBUS,
- Whetstones.
-
- OTHERS:
- LES50 (computational fluid dynamics), Moldflow (finite element analysis),
- Molecular Dynamics, Nord, UFLA, GROMOS (all computational chemistry).
-
- If you want more information on any of these benchmarks, please see a SGI
- sales rep-- I can't keep typing in all of these numbers!! Also, please
- remember that these benchmarks were done for a specific customer, who was
- interested in a specific machine, so most of them were not benchmarked on our
- whole product line (the 'Industry Standard' benchmarks, however, are usually
- run on all of our products).
-
- APPLICATION BENCHMARK NAME CUSTOMER
- ----------- -------------- --------
- Rendering BRL-CAD 3.7 US Army Ballistic Research Lab
-
- LANGUAGE SUMMARY DATE
- -------- ------------
- C 9/5/89
-
- DESCRIPTION
- -----------
- The BRL-CAD benchmark is a part of the US Army Ballistic Research Laboratory's
- BRL-CAD package. The core of the BRL-CAD benchmark is a ray-tracing program
- which consists of about 150,000 lines of C code. Computations are performed
- in double precision floating point.
-
- Five separate data bases are input to the ray tracing program, resulting in
- six performance ratings (one for each, plus a total which is the mean of the
- other five) . When rendered, each data base will produce a 512x512x24 bit
- color shaded image. The images are of increasing complexity, and are
- identified as 'Moss', 'World', 'Star', 'Bldg' and 'M35'.
-
- RESULTS
- -------
- The result of this benchmark is reported as rays traced per second, and
- referred to as Ray Tracing Figure of Merit (RTFM). Higher numbers indicate
- better performance.
-
- The code was parallelized by inserting user directives to create multiple
- processes to trace rays.
-
- RESULTS FOR SGI MACHINES:
- Note: The actual report has nice graphs here.
- Machine RTFM
- -------------------
- 1x16 (4D/80) 714
- 2x16 (4D/120) 1358
- 4x25 (4D/240) 5034
- 8x25 (4D/280) 7434
- Note: NxMM numbers refer to the number of processors in the
- machine (N) running at MM MHZ.
-
- COMPETITIVE RESULTS:
- Machine # Processors RTFM Relative Performance
- --------------------------------------------------
- Vax 780 1 77 1.0
- Sun3 1 88 1.1
- Convex C120 1 163 3.6
- Sun4 1 435 5.6
- SGI 4D/120S 2 1358 17.5
- Alliant FX/80 8 2783 33.6
- SGI 4D/240S 4 4456 70.4
- Cray X-MP/48 4 7217 116.1
- SGI 4D/280 8 7434 119.7
-
- ANALYSIS
- --------
- The BRL-CAD benchmark exhibits excellent speedup as processors are added.
- This is due to the coarse granularity inherent in the ray tracing problem
- being solved. Each ray is processed independently, with no data dependencies
- among the rays. This means that multiple processors can each work on separate
- rays simultaneously, with minimal need for synchronization among processors.
-
- While the code is highly parallelizable, it is not efficiently vectorizable
- because of short vector lengths. The combination of these two
- characteristics explain the phenomenal performance of Silicon Graphics
- machines relative to vector machines like Cray and Alliant.
-
- The characteristics of this benchmark that lead to high performance by the
- Silicon Graphics machines are common to all ray tracing applications.
-
- --------
-
- Here is another note from Gavin:
-
- My only experience with the BRL ray-tracer came when I was at Princeton
- University - I installed it on Silicon Graphics machines there for the
- Graphics Lab. That was two years ago; as far as I could tell, it didn't use
- octrees or any other space-partitioning algorithm. I used a ray-tracer
- written at Princeton (the precursor of what is now Craig Kolb's rayshade
- program; Craig and I had the same thesis advisor) which did do octrees; it was
- infinitely faster than the BRL beast.
-
- -------------------------------------------------------------------------------
-
- BRL-CAD Benchmarking and Parallelism, by Mike Muuss (mike@BRL.MIL)
-
- I'm sort of on vacation right now, so I'm going to cop out and just send you
- the TROFF input for several things that I have handy about how we benchmark
- ray-tracing in the BRL-CAD Package.
-
- The first one is our benchmark summary paper.
-
- The second one is a portion of a paper that I wrote called ``Workstations,
- Networking, Distributed Graphics, and Parallel Processing''.
-
- You may publish and/or redistribute both documents as you wish. Note that the
- United States Government holds the "copyright", ie, it is not permissible to
- copyright this material.
-
- [These papers are rather lengthy, so I won't include them in this issue.
- If you would like copies, look at the archive sites for Muuss.benchmrk and
- Muuss.parallel, or write me. - EAH]
-
-
- ======== USENET cullings follow ===============================================
-
- Rayshade Patches Available, by Craig Kolb
- From: craig@weedeater.math.yale.edu
- Newsgroups: comp.graphics
- Organization: Math Department, Yale University
-
- Patches 1-3 for rayshade v3.0 are available via anonymous ftp from
- weedeater.math.yale.edu (new address: 130.132.23.17) in directory
- pub/rayshade.3.0/patches. The patches fix several minor bugs, clean up the
- documentation, and provide new features.
-
- Several people have expressed an interest in 'trading' rayshade input files.
- If you have an interesting input file that you'd like to share, feel free to
- deposit it in the "incoming" directory on weedeater or send it to me via
- email. I will make these files available in the pub/Rayinput directory on
- weedeater.
-
- Rayshade is supposedly "on the verge" of appearing in comp.sources.unix,
- patches and all.
-
- -------------------------------------------------------------------------------
-
- Research and Timings from IRISA, by Didier Badouel
- From: badouel@irisa.irisa.fr
- Newsgroups: comp.graphics
- Organization: IRISA, Rennes (Fr)
-
- We have a parallel raytracer (called PRay) at IRISA which as MTV uses NFF
- description databases. This raytracer has been implemented on an iPSC/2, on a
- SEQUENT BALANCE and also on serial computers (SUN3, GOULD NP1) to make better
- comparisons.
-
- I give you the various synthesis times for the well known 'Teapot' database.
- The image has been rendering with a 512X512 resolution with 3 light sources.
- Results are as follows :
-
- #PEs Time (in sec.)
- ________________________________________
- SUN3: 8877 (~ 2h27mn)
- ________________________________________
- GOULD NP1: 1642 (~ 27mn)
- ________________________________________
- SEQUENT BALANCE 1 37121 (~ 10h18mn)
- 2 18567
- 3 12381
- 4 9285
- 5 7431
- 6 6197
- 7 5311
- 8 4656
- 9 4138 (~ 1h9mn)
- ________________________________________
- iPSC/2 1 6294 (~ 1h45mn)
- 2 3332
- 4 1700
- 8 860
- 16 440
- 32 224
- 64 119 (~ 2mn)
- ________________________________________
-
- The code running on the iPSC/2 emulates a virtual shared memory over the local
- PEs. The database is not duplicated but all the local memories are used. The
- remaining memory after loading code and data is used as a cache to speed up
- low global accesses.
-
- -----
-
- In order to benchmark our parallel raytracer running on an iPSC/2,
- which use Eric Haines' NFF file format as input, we would like to know
- if other people have a parallel raytracer using these databases
- in order to make some comparisons.
-
- One of our goals is to render the largest possible
- database. For the moment, we have rendered the 'tetra10'
- database:
- - the database contains more than 1 million polygons (1048576
- polygons)
- - the size of the database with its 'object access structure' (a
- grid) is 140 MO.
- - the synthesis time is 526 seconds on the iPSC/2 with 64 nodes
- and 4 MO node memory.
- - however, on account of using NFF text file format, reading the
- input is very slow (more than 3 hours for 'tetra10') when using
- YACC and LEX. Furthermore, our iPSC/2 configuration does not have
- I/O node system.
-
- ________________________________________________________________
- Didier BADOUEL badouel@irisa.fr
- INRIA / IRISA Phone : +33 99 36 20 00
- Campus Universitaire de Beaulieu Fax : 99 38 38 32
- 35042 RENNES CEDEX - FRANCE Telex : UNIRISA 950 473F
- ________________________________________________________________
-
- -------------------------------------------------------------------------------
-
- Concerning Smart Pixels, by John S. Watson
- From: watson@ames.arc.nasa.gov (John S. Watson)
- Newsgroups: comp.graphics
- Organization: NASA - Ames Research Center
-
- In article <207400033@s.cs.uiuc.edu> mccaugh@s.cs.uiuc.edu writes:
- >
- > Does anyone know of a system with "smart" pixels?
-
- Once upon a time I wrote a ray tracer in which the pixels used heuristics to
- determine their sampling rate. Since the reason for doing it was to speed
- things up, the heuristic had to be simpler than casting a ray( s, if
- sub-sampling). I used difference in previous pixels values, with a little
- randomness tossed in. So pixels changing quickly were sampled every frames,
- while pixels that were hardly ever changing were sampled only once every 10
- frames. The results: much faster, but with a graininess on the edges of
- moving objects. I needed to make the pixels more aware of what was happening
- with its neighbors. Never got around to doing that.
-
- Another problem is big pictures have lots of pixels ... 512x512 = 0.25 million.
- To be smart you must have a memory.
-
- To save memory, I combined the above with an Area-of-Interest/Variable Acuity
- (AOIVA) Ray Tracer.
-
- Hope this helps,
- John S. Watson, Civil Servant from Hell ARPA: watson@ames.arc.nasa.gov
- NASA Ames Research Center UUCP: ...!ames!watson
- Any opinions expressed herein are, like, solely the responsibility of the, like,
- author and do not, like, represent the opinions of NASA or the U.S. Government.
-
- -------------------------------------------------------------------------------
-
- Input Files for DBW Render, by Tad Guy
- From: tadguy@cs.odu.edu (Tad Guy)
- Newsgroups: comp.graphics
- Organization: Old Dominion University, Norfolk, VA
-
- In article <6475@pt.cs.cmu.edu> te07@edrc.cmu.edu (Thomas Epperly) writes:
- I was wondering if anyone had any neat input files for DBW_Render available
- for anonymous ftp.
-
- xanth.cs.odu.edu as /amiga/dbw.zoo. If you have a network of, say, sun
- workstations, you might as well get /amiga/distpro.zoo, which will allow to
- distribute the computations over many machines.
-
- -------------------------------------------------------------------------------
-
- Intersection with Rotated Cubic Curve Reference, by Richard Bartels
- From: rhbartels@watcgl.waterloo.edu
- Newsgroups: comp.graphics
- Organization: U. of Waterloo, Ontario
-
- In article <1445@tukki.jyu.fi> toivanen@tukki.jyu.fi (Jari Toivanen) writes:
- :
- :I would like to know is there any simple and effective solution to
- :following problem:
- :
- : [intersecting a ray with a rotated cubic curve]
- :
- :Jari Toivanen Segments are for worms ;-)
- :University of Jyvaskyla, Finland Internet: toivanen@tukki.jyu.fi
-
- Look at the article:
-
- Ray Tracing Objects Defined By Sweeping Planar Cubic Splines
- Jarke J. van Wijk
- ACM Transactions on Graphics
- Vol. 3, No. 3, July, 1984, pp. 223-237
-
- I believe that the author subsequently wrote a whole book on the subject.
-
- [Incidentally, this article also has a method for quickly intersecting a tight
- fitting bounding volume around such curves. I've found this test useful for
- use as a torus bounding volume. Also, does anyone know of the existence and
- the name of the book Richard mentions? - EAH]
-
- -------------------------------------------------------------------------------
-
- Needed: Quartz surface characteristics, by Mike Macgirvin
- From: mike@relgyro.stanford.edu
- Newsgroups: comp.graphics
- Organization: Stanford Relativity Gyro Experiment (GP-B)
-
- I am in need of the surface characteristics for fused quartz. Ambient,
- diffuse and specular color characteristics, Phong coefficent, reflectance,
- and transparency. I have the index of refraction (Well, I have to average it,
- c'est la vie).
-
- I have attempted to derive these experimentally, but find the resulting traced
- image lacking in many ways, and a simulation visualization I am working on
- requires accuracy.
-
- I am using Kolb's 'rayshade' if it affects your responses.
-
- Please respond via e-mail if possible.
-
- -------------------------------------------------------------------------------
-
- Solution to Smallest Sphere Enclosing a Set of Points, by Tom Shermer
- From: shermer@cs.sfu.ca
- Newsgroups: comp.graphics
- Organization: School of Computing Science, SFU, Burnaby, B.C. Canada
-
- >I need the solution for the following problem:
- >find the smallest sphere that encloses a set of given points, in both
- >2-D and 3-D (or even n-D, if you like).
- >
-
- This problem can be solved in linear time (in any fixed dimension)
- by the technique of prune-and-search (sometimes called ``Megiddo's
- Technique''), either directly or by first converting the problem
- to a linear program. The most relevant reference (for 2d & 3d) is:
-
- Linear-time Algorithms for Linear Programming in R^3 and Related Problems,
- Nimrod Megiddo, SIAM J. Comput, v. 12, No. 4, Nov 1983, pp. 759-776.
-
-
- Other related references:
-
- Linear time algorithms for two- and three- variable linear programs,
- M.E. Dyer, SIAM J. Comput, v. 13, 1984, 31-45.
-
- On a multidimensional search technique and its application to the
- Euclidean one-center problem,
- M. E. Dyer, Dept. Math and Stats TR, Teesside Polytechnic,
- Middlesbrough, Cleveland TS1 3BA, UK, 1984.
-
- Linear programming in linear time when the dimension is fixed,
- N. Megiddo, JACM 31, 1984, 114-127
-
- The weighted Euclidean 1-center problem,
- N. Megiddo, Mathematics of Operations Research 8, 1983, 498-504
-
- On the Ball Spanned by Balls
- N. Megiddo, manuscript (this may have appeared in the literature
- by now)
-
- -------------------------------------------------------------------------------
-
- True Integration of Linear/Area Lights, by Kevin Picott
- From: kpicott@alias.UUCP
- Newsgroups: comp.graphics
- Organization: Alias Research Inc.
-
- Has anyone seen any work done on evaluating the diffuse and specular
- illumination produced by linear and/or area lights? I have checked all the
- standard sources and all information I find gets to the point where the
- integration is set up and then a little hand waving is performed accompanied
- by the magical words "numerically integrated". This works but is too slow
- for my purposes. Does anyone know of any work done in different directions
- (ie faster evaluation) ?
-
- --------
-
- Thanks to all who replied to my query about linear and area lights.
-
- In the area of linear lights, two papers on analytical solutions were found.
- The first, by John Amanatides and Pierre Poulin has been submitted to
- Eurographics '90 and I'll hopefully get a look at that soon.
-
- The second, "Shading Models for Point and Linear Sources", ACM TOGS, 4(2),
- April 1985, pp. 124-146. by T. Nishita, I. Okamura, E. Nakamae, proposes
- an analytic solution to the diffuse component, but only under certain
- circumstances.
-
- The latter unfortunately reduces to numerical integration in the majority of
- cases where spline surfaces are involved, although a method of optimization is
- given that reduces computation time for the numerical integration. This
- method would seem to be suited to lighting parallel and perpendicular to the
- illuminated surfaces.
-
- There was also a paper entitled "A Comprehensive Light-Source Description for
- Computer Graphics", IEEE CG&A, July 1984, by Channing P. Verbeck and Donald
- P. Greenberg that approximates both linear and area light sources as a series
- of point sources. This is a compromise to numerical integration, but is still
- computationally expensive.
-
- In summary, the analytical solution to linear sources exists and is
- calculable, at least for the diffuse component. The specular component
- exists, but direct calculation is almost expensive as numerical integration.
-
- As far as area light sources are concerned... no analytical solutions were
- found. In fact, from the work examined I was left with the impression that
- even if the solution existed it would not be very useful from a light
- illumination point of view (ie non-radiosity). (Comments?)
-
- --
- Kevin Picott aka Socrates aka kpicott%alias@csri.toronto.edu
- Alias Research Inc. R+D Toronto, Ontario... like, downtown
-
- -------------------------------------------------------------------------------
- END OF RTNEWS
-