Ray Tracing News

"Light Makes Right"

March 20, 1990

Volume 3, Number 2

Compiled by Eric Haines [email protected] . Opinions expressed are mine.

All contents are copyright (c) 1990, 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.


Contents:

========Net News Cullings========

Introduction

Well, it's been awhile. I've been detoured by making demos for NCGA, but now that's over and I can catch up with editing the RT News. Actually, doing demos was interesting this time around: I wrote a personal visualizer ("personal" is definitely the right word; so far, only I can use it) for setting up the view, light sources, materials, and positions of objects (i.e. no modeling capability per se), along with some animation tools. Beats the daylights out of my old visualizer (aka known as Unix's "vi" editor). Anyway, interactive graphics is pretty enjoyable - I'd forgotten. Nice to have an image come up in less than an hour, let alone less than a second.

I've heard from a few people that Silicon Graphics' new machine is pretty hot: surface and reflection (environmental) texturing in hardware, and it's pretty fast at it. Intergraph evidentally has some kind of ability to change material attributes of objects in a ray traced image and have the changes to the image compute and display quite rapidly. They claim to NOT be storing the intersection trees for all of the pixels, so I'm looking forward to seeing this myself and figure out how they do it (my current theories of "it's just a videotape shown on the screen" and "they've made a pact with the devil" not being the most scientific).

By the way, the "Introduction to Ray Tracing" book is not out-of-print. Evidentally there was a temporary shortage, but they've reprinted it and it should be back in stock now.

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New People, Address Changes, etc

# Eric Chet - acceleration
# 4047 Forest Hill Drive
# Lorain, Ohio, 44053
alias   eric_chet   [email protected]

My main interest in ray tracing now is acceleration. I'm developing a ray tracer in 680x0 assembler to make it as efficient as possible with the algorithms I'm implementing. Spatial subdivision and ray coherence are the techniques I'm working with.

________

John McMillan, Department of Physics
               University of Leeds
               Leeds LS2 9JT
               West Yorks
               Great Britain
[email protected]

My interest is slightly different from your normal application of raytracing. I'm not interested in images at all. I design scintillation detectors in which light is produced in a medium in response to a charged particle passing through. Some of this light eventually makes its way to a photomultiplier (circular window) where it is converted into an electrical signal. I'm interested in following rays through various geometries of materials with different refractive indices and reflection coefficients. So I guess you can probably see why I'm interested in Ray Tracing News.

________

Marinko Laban - shading, anti-aliasing, CSG & Modelling
K.T.I. BV
Bredewater 26
2700 AB Zoetermeer (The Netherlands)
???-079-531521 (Don't know the USA access code)
e-mail address: hp4nl!hp4nl.nluug.nl!ktibv!ml

During my University study, I obtained various copies of your Ray Tracing Newsletter. These copies were given to me by the supervisor of my Master project, M. Frits Post (Tech.University of Delft, Holland).

Under his supervision I've written my Master Thesis about distributed ray tracing and I also wrote an implementation of one. I've got my Master degree for a few months now, and I'm currently working as a CAD software engineer at Kinetics Technology International.

My professional tasks are developing & evaluating CAD & Engineering software for Industrial Plant Design. I also keep myself busy with our UNIX computers, and all sorts of small bits and pieces. When I have the opportunity & time I have some SPARC's do some ray tracing from me ... I also keep my personal Amiga busy doing all kinds of graphics stuff.

________

David Tonnesen
Dept. of Computer Science
University of Toronto
Toronto, Ontario  M5S 1A4
(416) 978-6986 and 978-6619

research: modeling and rendering

e-mail:  [email protected]   (UUCP/CSNET/ARPANET)
         [email protected]      (BITNET)

I am a Ph.D. student at the University of Toronto and interested in a variety of graphic topics including ray tracing. Other areas I am interested in include models of deformable models, global illumination models, models of natural phenomena, physically based modeling, etc... Basically modeling and rendering.

________

Jim Arvo, of Apollo, has the new email address:

        [email protected]

________

Carl Bass, of Ithaca Software, is moving to California. He should have a new mailing address soon. His latest address has been updated to:

        [email protected]

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FTP Site List, by Eric Haines

This is my own collection of sites which have ftp-able software or documents that have some relevance to ray tracer. If you don't know how to use ftp, see Didier Badouel's article in this issue for an example. Recall that it's considered polite to download large amounts of stuff only after business hours. If a site has a software name with asterisks around it (e.g. *RT News*), this means that the site is the "home" of this stuff (or is updated often enough by the site that the site's offering is usually the most current version). The archive manager (more or less) is listed at the end of each entry. Please do send on any corrections or clarifications you have. Sites are always changing, so please do keep me posted. I'm not going to bother with "gif" image file sites (though they are useful for texturing), as the list would double in size. The sites below are listed more or less in the order of most to least extensive ray-trace related material stored.

Mark VandeWettering's MTV ray tracer was posted to comp.sources.unix and is postings v18i070-072. Sid Grange's ray tracer is v05i046. Craig Kolb's RayShade has just been posted to comp.sources.unix, v21i008. Note: patch4 is now available for RayShade.

cs.uoregon.edu [128.223.4.13]: /pub - *MTV ray tracer*, *RT News*, *RT bibliography*, other raytracers (including RayShade, QRT, VM_pRAY), SPD/NFF, OFF objects, musgrave papers, some Netlib polyhedra, Roy Hall book source code, Hershey fonts, old FBM. Mark VandeWettering ([email protected])

hanauma.stanford.edu [36.51.0.16]: /pub/graphics/Comp.graphics - best of comp.graphics (very extensive), ray-tracers - DBW, MTV, QRT, and more.

weedeater.math.yale.edu [130.132.23.17]: *Rayshade 3.0 ray tracer*, *color quantization code*, Utah raster toolkit, newer FBM. Craig Kolb ([email protected])

freedom.graphics.cornell.edu [128.84.247.85]: *RT News back issues, source code from Roy Hall's book "Illumination and Color in Computer Generated Imagery", SPD package, Heckbert/Haines ray tracing article bibliography, Muuss timing papers.

uunet.uu.net [192.48.96.2]: /graphics - RT News back issues, other graphics related material.

life.pawl.rpi.edu [128.113.10.2]: /pub/ray - *Kyriazis stochastic Ray Tracer*. George Kyriazis ([email protected])

geomag.gly.fsu.edu [128.186.10.2]: /pub/pics/DBW.src and DBW.microray.src - *DBW Render source*, ray traced images. Prem Subramanyan ([email protected])

xanth.cs.odu.edu [128.82.8.1]: /amiga/dbw.zoo - DBW Render for the Amiga (zoo format). Tad Guy ([email protected])

munnari.oz.au [128.250.1.21]: */pub/graphics/vort.tar.Z - CSG and algebraic surface ray tracer*, /pub - DBW, pbmplus. David Hook ([email protected])

cs.utah.edu [128.110.4.21]: /pub - *Utah raster toolkit*. Spencer Thomas ([email protected])

gatekeeper.dec.com [16.1.0.2]: /pub/DEC/off.tar.Z - *OFF objects*, /pub/misc/graf-bib - *graphics bibliographies (incomplete)*. Randi Rost ([email protected])

expo.lcs.mit.edu [18.30.0.212]: contrib - *pbm.tar.Z portable bitmap package*, *poskbitmaptars bitmap collection*, *Raveling Img*, xloadimage. Jef Poskanzer ([email protected])

venera.isi.edu [128.9.0.32]: */pub/Img.tar.z and img.tar.z - some image manipulation*, /pub/images - RGB separation photos. Paul Raveling ([email protected])

ftp.ee.lbl.gov [128.3.254.68]: *pbmplus.tar.Z*.

ucsd.edu [128.54.16.1]: /graphics - utah rle toolkit, pbmplus, fbm, databases, MTV, DBW and other ray tracers, world map, other stuff. Not updated much recently.

okeeffe.berkeley.edu [128.32.130.3]: /pub - TIFF software and pics. Sam Leffler ([email protected])

curie.cs.unc.edu [128.109.136.157]: /pub - DBW, pbmplus, /pub/graphics - vort. Jeff Butterworth ([email protected])

irisa.fr [131.254.2.3]: */iPSC2/VM_pRAY ray tracer*, /NFF - some non-SPD NFF format scenes. Didier Badouel ([email protected])

hc.dspo.gov [192.12.184.4]: {have never connected} Images?

netlib automatic mail replier: UUCP - research!netlib, Internet - [email protected]. *SPD package*, *polyhedra databases*. Send one line message "send index" for more info.

UUCP archive: avatar - RT News back issues. For details, write Kory Hamzeh ([email protected])

Non-sites (places which used to have graphics stuff, but do no longer):

albanycs.albany.edu [128.204.1.4]: no longer carries graphics stuff nl.cs.cmu.edu [128.2.222.56]: /usr/mlm/ftp/fbm.tar.Z - not found. Michael Maudlin ([email protected]) panarea.usc.edu [128.125.3.54](not found?): archive for maps?

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RayShade Posting and Patches and Whatnot, by Craig Kolb

[Craig's excellent public domain ray tracer RayShade 3.0 has been posted to comp.sources.unix. He has also just recently posted patch4, a set of fixes for this program.--EAH]

On the ray tracing front, I'm mulling over a total rewrite of rayshade, in an attempt to make it more flexible/extensible. Mark and I are talking about tying together the scanline rendered he's working on with a new version of rayshade. It would be nice if they shared a common modeling/texturing language, etc. I think it could be quite nice if done correctly.

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Common Rendering Language, by Eric Haines

One question which I've received and seen posted on comp.graphics with some frequency is "what input format/language should I use for scene description?". As the inventor of NFF (Neutral File Format), I recommend AGAINST this language as your first choice. Hey, I made for testing efficiency schemes - at one point I considered not even allowing the user to specify colors, but esthetics got the best of me. You currently cannot specify light intensity. As it stands, I don't plan on extending NFF - the language is supposed to be as minimal as possible and is for testing efficiency schemes.

I'd recommend anyone interested in this question to look at Craig Kolb's RayShade language. It's much fuller, includes many more primitives, texture functions, instancing, etc. You could always pick a subset that you have implemented if the language is too extensive for your tastes. One very nice thing provided with RayShade is an Awk script which translates NFF files to his format.

If you plan on making some money off of whatever you're doing, it's wise to look at RenderMan. There are definitely some grey areas in the spec as to how certain functions actually perform (i.e. what algorithm is used), as well as some procedures which force the use of certain algorithms (e.g. shadow maps). But most of the language is reasonable and well thought out, the "RenderMan Companion" is readable (at least you won't have to write documentation if you choose this language), and certainly other companies are signing on to using this language. Caveat: good luck beating Pixar at its own game in the marketplace, especially with their years of lead time.

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Avoiding Re-Intersection Testing, by Eric Haines

The problem: when shooting a ray through a grid (3DDDA) or octree (or any other scheme which can put an object into more than one reference location), you encounter the problem of how to avoid performing the intersection test more than once for the same ray and same object. For example, imagine you have a cylinder which overlaps two grid boxes. Your ray enters the first grid box and is tested against the cylinder, missing it. So, now your ray moves into the next grid box and the cylinder is listed in this second box. Obviously, the ray missed this cylinder on the previous test. You would like to avoid testing the cylinder against the ray again to save time. How to do it?

There are some fairly bad solutions to this problem. One is to keep a list of flag bits, one per object. When an object is tested for intersection, the flag bit is checked: if off, then it is set and the full test is performed. If on, then we know we've tested the ray against the object already and can move on. The problem with this solution is that you must reset the flag bits after each ray, which can be a costly procedure. For example, imagine you have 32000 objects in a scene. Even with 32 bit words used for the flags, you have to reset 1000 words to zero before EACH ray. There are variants on this scheme (e.g. you could store the locations to reset in a list, then simply reset just those in this list before the next ray), but happily there is a better solution with much less overhead. [Note: if you're really strapped for memory, you might still want to go with the above algorithm]

The algorithm: keep a list of integers, one per object - call this the "hit list" (alternately, simply add this field to each object). Initialize this list to zeroes. Also keep a counter which counts the total number of rays generated, i.e. when a new ray is generated, the counter is incremented. When a ray is to be tested against an object, check the object's hit list value. If this value does not match the ray's counter number, then set the hit list value to the ray's counter number and test the object. If the hit list value matches the ray's number, then this object has already been tested by the ray. If you use 32 bit words in the list, you probably won't have to worry about the ray counter overflowing (2**32 rays is a lot). However, you could even use byte length integers for the hit list. When the ray counter reaches 256, then you reset the whole hit list to zero and reset the count to 1. In some ways this technique is an extension of the flag bit technique, with the cost of a little more storage offset by the time savings of rarely (if ever) having to reset the flags.

Over the past few months I've noticed that there are still a few researchers who do not know about this technique. Personally, I had to invent this algorithm for my own use, and others have no doubt done the same. Asking around for references, I can see why people would not know about it. The only reference that I know which mentions this algorithm is:

%A Bruno Arnaldi
%A Thierry Priol
%A Kadi Bouatouch
%T A New Space Subdivision Method for Ray Tracing CSG Modelled Scenes
%J The Visual Computer
%V 3
%N 3
%D August 1987
%P 98-108
%K CSG

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Torus Equation Correction, by Pat Hanrahan

Pat took up my request last RTN to derive the ray/torus intersection equation on Mathematica. He found that in fact Larry Gritz's & my derivation still had one small bug - I left out the subscript of z0 in the very last term of a0. So, here's the final, correct equation (I hope). --EAH

        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-z0^2)
                                                        ^---I left this out

Pat sent me all of the equations in eqn format - here they are:

----
.EQ
define x0 'x sub 0'
define x1 'x sub 1'
define y0 'y sub 0'
define y1 'y sub 1'
define z0 'z sub 0'
define z1 'z sub 1'
define r11 '( x1 sup 2 + y1 sup 2 + z1 sup 2 )'
define r01 '( x0 x1 + y0 y1 + z0 z1 )'
define r00 '( x0 sup 2 + y0 sup 2 + z0 sup 2 )'
define r00ab '( r00 - ( a sup 2 + b sup 2 ) )'
.EN
.EQ
a sub 4 ~=~ r11 sup 2
.EN C
.EQ
a sub 3 ~=~ 4 r01 r11
.EN C
.EQ
a sub 2 ~=~ 2 r11 r00ab + 4 r01 sup 2 + 4 a sup 2 z sub 1 sup 2
.EN C
.EQ
a sub 1 ~=~ 4 r01 r00ab + 8 a sup 2 z sub 0 z sub 1
.EN C
.EQ
a sub 0 ~=~ r00ab sup 2 - 4 a sup 2 ( b sup 2 - z sub 0 sup 2 )
.EN
----

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"Introduction to Ray Tracing" Shading Model Errata, by Kathy Kershaw

p.148, section on distribution term D, 8th line, should say that alpha is the angle between N and H.

p.156, section 5.4, 2nd paragraph: I think Andrew meant "specular transmission curve".

p.158, in F_dt(lambda) and eq 24 it says "diffuse reflection" instead of "diffuse transmission" and "diffuse reflectance" instead of "diffuse transmittance".

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Comments on Last Issue, by Mark VandeWettering

Glad to see that you spent the time to include the MTV raytracer in your timings. I was meaning to compare them myself at some time, but lacked the time to do so.

You might be interested to know that I have eeked out a little time to make some modifications to the MTV raytracer. In particular, I too have switched to an Goldsmith-Salmon hierarchy generating scheme. It's been a while since I benchmarked this one against the one that is available for ftp, but I did realize significant speedups. I added some primitive support for super ellipsoids and "blocks" as well.

The main reason that I haven't released these changes is simple: Craig Kolb's raytracer is too good :-) It really is a slick piece of programming. If it had 2-d texture mapping, it would be ideal for a large variety of image rendering tasks.

I also think that more adaptive methods (particularly K-K bounding volumes) are better under a wide variety of image rendering tasks. Maybe I should construct an nff file for the "teapot in a stadium" idea and restore some of the dignity that the MTV raytracer had by kicking some sand back in Craig's face :-)

Another place where the MTV raytracer probably falls short is that for primitive objects, I still take the trouble to intersect their bounding volumes. For simple, tightly bounded objects like spheres, this is pretty wasteful. Craig's code is fairly careful to weed those out.

If I had a good block of time, I would like to go back and 'do it all over' with texture mapping primitives and other niceties. But now that I am out in the pseudo-real world of Princeton, such blocks of time are hard to come by.

Ah, if one only had infinite time.

Anyway, just an update from this side of the world.

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An Improvement to Goldsmith/Salmon, by Jeff Goldsmith

[Background: as written Goldsmith & Salmon's automatic bounding volume hierarchy generation algorithm (ABVH) has two insertion methods for an object: an object can become a new sibling of an existing bounding box, or a new bounding box can be created which replaces one of the existing siblings, and the existing sibling and object are put in this new bounding box.]

A new case for the ABVH programs: First insertion check-- consider the new node to be a sibling of the current root node. That is, consider making a new root with two children, one being the current root, and the other the new node. This should have a cost of 2*Area(new root). Everything else is the same, but this adds a case that I forgot and allows for less bushy roots when you need them.

I haven't tested this, and I'm not completely convince that 2A is the right cost, but I think it is. Since you use this algorithm, I'd appreciate some trials to see if it ever happens and if it has a (predicted at least) beneficial result on the final tree.

By the way, Pete Segal inspired the idea.

[In fact, I tried this out some time ago. The thrust of Jeff's comments are that at the root node, the root can only get bushier (more sons added) or else objects are added to existing sons which have little relation to those existing sons. His third case is to consider the root node itself a sibling of some imaginary "father of the root" (which has only the root as its son and is the same dimensions). In this way, the object could also be added to this "father" and not cause the root to become bushy.

This explanation implies a simple change to existing code: simply create this "father of the root" node at the start, and any time the above condition of a sibling being added to this father occurs, again create the father for this new root (i.e. that used to be the father of the root).

As an example, imagine some complicated scene that contains five spheres as light sources. The light sources are some distance outside the rest of the scene, i.e. not in the bounding volume containing this data. You now try to add these light sources. Under the old algorithm these lights would normally get added as separate siblings of the root node. So, when ray tracing, you would always attempt to intersect all of these light sources when you first looked in the root box. The new algorithm should cause the root to be less bushy and the lights may become a subcluster. At least in theory - I still want to think about it some more...--EAH]

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Fiddling with the Normal Vector, by H. 'ZAP' Anderson ([email protected])

When I Wrote my first raytracer, it was in Basic, only spheres, one lightsource, checkered ground, and rather primitive. A while has passed since then, and I have put behind me quite a few years of Raytracing both in my mind and in my computer. Not being fortunate enough to own a Cray III, or even a VAX 11/780, but a mere CompaQ 386/20e, I have a certain passion for tricks that enhance the picture quality without adding to the calculation time. So, besides Texture Mapping, my favorite hat trick, is 'Fiddling with the Normal Vector'

My first trick, is the simplest, and in my opinion the best (isn't it always so?). But first, some history: WHAT is it the human eye want's to see? WHAT make's a picture look 'real'? What makes a picture 'feel' realistic? There are, of course, MANY answers, but one of them is: Specular Highlights.

I was at a demo at Hewlett Packard in Stockholm, and they showed me (with badly hidden pride :-) their TurboSRX solids rendering engine. When the demo guy started to spin nurbs and superquadrics in realtime before my very eyes, those eyes fell upon the specular highlights on the surfaces. They moved along as the surface twisted, and i thought: 'gosh, THAT looks real!' Something VERY important for the eye, and our mind, to really 'feel' the solidity of an object, is when the specular highlights crawl around it's surface as we twist them (sorry for you Radiosity fans :-). But WHY does a computer image need more specular highlights? Aren't those only seen on cylinders and spheres, and perhaps (in a lucky instance) on another surface? The answer is a very very big NO!

Consider a coin. Place it on the table in front of you. Basically, this coin is a rather short cylinder. And if we would render it as such, it would look no way like a coin. Why is that? Clue: The microscope! As we watch closely, we see, that the coins edge is a bit rounded by years of transfer on the black market. The coin on your table almost ALWAYS have SOME part of it's edge in a direction that mirrors light, and you have a specular highlight. Taken further, this applies to ALL edges. NO edge in natural life is an exact 90 degree edge. ALL edges are a bit rounded, and therefore has a big probability of generating a specular highlight. Just look around the room, and you'll know I'm right.

Here goes the simple trick. Imagine a cylinder in the XY plane with a radius of 10 and a height of 10. When we want to obtain the normal vector, we normally get one pointing straight up (for the top face) and one pointing in one direction in the XY plane, depending on intersection point. This gives us the simple cylinder, and nothing like the coin mentioned above. BUT if we now twiddle a bit with our famous Normal Vector, so IF we hit the cylinder close to the top face (say .1 of cylinder height) we gently tweak the normal vector upwards, scaled such, that when we reach the top face exactly, we have twisted it UP along the Z axis 45 degrees. Now do the same for the top face. When you approach the edge of the cylinder, maybe .9 of the radius, you gently twiddle the little N vector outwards, again, scaled to obtain 45 degrees exactly at the edge. The result: A cylinder with a rounded edge, without extra calculation time or extra surfaces!! I have implemented this myself, and the resulting increase in image quality is stunning. Everything that once looked like synthetic and unreal cylindric objects, now turns out to look VERY real, once they get that little extra shine on the edge. This, of course, applies to ALL edges, and are just as simple to implement on other primitives.

Another 'Normal Vector Tricky' is the 'Modified surface smoothing' I use. Consider a staircase looking surface, and 'standard' smoothing, with one normal per vertex: (now watch Fig 1!!)

Fig. 1 Fig. 2

     I      N12     N23                I
     I    /       /                    I--N1  N2
     I  /       /                      I      I
     I/       /                        I      I
     ---------                         --------------
             I                                      I
             I                                      I---N3
             I                                      I

Imagine the standard smoothing applied to this surface. The surface between the 'vertex normals' N12 and N23 would be shaded as if it ALL had a normal vector same as N12 (or N23)!! That isn't correct, is it? Behold Fig. 2! With one normal vector per surface, but smoothing from the center of surface 1 to the center of surface 2, then smooth onwards from surf. 2 to surf. 3, you will get a better result, PLUS you save yourself the trouble of keeping interpolated vertex normals!

Now, no 'real' surfaces are perfect. Take a close look at your neighbours' ferrari in sunlight. You will see that even if it isn't a perfect spline, nurb, or anything like that. This can be simulated with gentle surface rippling a la' DBW-render, or by actually MAKING the surface non-perfect. But there is another way. When interpolating normals, you may use other functions than standard linear interpolation. Maybe use the square root of the distance to the normals, or the distance squared? This will yield a surface 'not so smooth' as a perfectly smoothed may be, something to consider?

Another thing I am currently trying to implement in my tracer, is something I have called 'profile mapping' (you may have been using a different term?) where I supply a 2d description of normal-vector-tweaking as a function of local surface coordinates. Simply put: Texture mapping for the Normal. I may be able to generate the engravings on our coin in the previous example, or other subtle surface characteristics. Has anyone any experience in this field? Please let me know!

And finally, a question: I would very much like to implement Octrees in my tracer, but I haven't REALLY understood how this works. Could somebody, in a few words, explain the basics for little o'l me?

ThanX in advance!! /H 'ZAP'

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A Note on Texture Sampling, by Eric Haines

[this is edited from a note I wrote to `Zap' Anderson about sampling texture maps. I hope it helps someone out there to understand the problem a bit better.]

There are two problems that need solving when using texture maps: interpolation (aka magnification) and decimation. Interpolation is needed whenever less than one texel (a sample on a texture map) covers a pixel. Decimation is needed when more than one texel falls into a pixel. Actually, the number is really "2 texels or less/more", due to the Nyquist frequency (see Heckbert's thesis), but forget that for now.

Interpolation is relatively easy: if a texel covers more than one pixel, then we should consider the texture map (if it's an image) to be representing a continuous sampling of something (e.g. the mandrill). So, each texel is just a sample along a continuous function. In this case, when we hit such a texel, we take the exact location on the function and interpolate the color from the nearby texels (e.g. you could use bilinear interpolation, which usually works well enough). Note that you might not always want to interpolate, e.g. if your map is a checkerboard, then you may want the sharp edges between the squares, not blurred edges.

Decimation is where the fun begins: you want to take the values of all the texels in the pixels and blend them. You also want to do this quickly, i.e. if 10,000 texels fall in the pixel, you want to quickly get the sum of all of these samples. This usually means doing some preprocess like mipmapping - see Lance Williams' paper in SIGGRAPH 83, first article. There are lots of other schemes (this topic is one of the great paper generators), see Paul Heckbert's thesis (highly recommended) on this.

[Zap talked about what you should use as your criteria for anti-aliasing: edge detection or luminosity differential (i.e. color change)]

Edge vs. luminosity difference detection is an interesting question: you actually probably want both, sorta. Doing all the edges might be overkill, since you could have something like a car body made of 36,000 polygons, with each polygon being almost exactly the shade of the next one (esp. with interpolated normals at the corners). In this case, edges are a waste of time, and you probably also want a threshhold luminosity to use for checking if the edge is worth antialiasing.

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Unofficial MTV Patches, by Eric Haines

These are the patches I've personally made to the MTV ray tracer, from bugs that Mark VandeWettering has noticed and from my own experience. They are unofficial patches, and Mark hopes to have official ones out sometime. The patches fix a cylinder rendering bug and a coredumping bug in the box intersector. There are also fixes to make the statistics more descriptive.

old/data.c
new/data.c
32a33
> /* Mark's default prune value
33a35,36
> */
> Flt           minweight = 0.0 ;       /* no pruning */
old/antialiasing.c
new/antialiasing.c
23a24
> /* >>>>>
24a26,27
> */
> #define MAXRAND               (32767.0)
28a32
>       /* >>>>>
29a34,35
>       */
>       return (((Flt) rand ()) / ((Flt) MAXRAND));
old/main.c
new/main.c
43a44,46
>       /* >>>>> */
>       srand(10001) ;
>
109c112
<       printf("number of rays cast:       %-6d\n", nRays);
---
>       printf("number of eye rays:        %-6d\n", nRays);
121a125,152
> }
>
> /* >>>>> */
> char *
> rindex(sp, c)
>      register char *sp, c;
> {
>   register char *r;
>
>   r = NULL;
>   do
>     {
>       if (*sp == c)
>       r = sp;
>     } while (*sp++);
>   return(r);
> }
>
> char *
> index(sp, c)
>      register char *sp, c;
> {
>   do
>     {
>       if (*sp == c)
>       return (sp);
>     } while (*sp++);
>   return (NULL);
old/cone.c
new/cone.c
242a243
>
244a246,248
>
>       VecNormalize(cd -> cone_u) ;
>       VecNormalize(cd -> cone_v) ;
old/intersect.c
new/intersect.c
61a62,64
>           /* check if ray is not parallel to slab */
>           if ( den[i] != 0.0 ) {
>
80a84,89
>           } else {
>               /* ray is parallel to slab - see if it is inside slab */
>               if ( ( obj -> o_dmin[i] - num[i] ) *
>                       ( obj -> o_dmax[i] - num[i] ) > 0.0 )
>                   return ;
>           }
104a114
>       Flt             dendot ;
113c123,128
<               den[i] = 1.0 / VecDot(ray -> D, Slab[i]) ;
---
>               dendot = VecDot(ray -> D, Slab[i]) ;
>               if ( dendot != 0.0 ) {
>                   den[i] = 1.0 / dendot ;
>               } else {
>                   den[i] = 0.0 ;
>               }
old/screen.c
new/screen.c
50d49
<       VecNormalize(upvec) ;
66a66,72
>        * Make sure the up vector is perpendicular to the view vector
>        */
>
>       VecCross(viewvec, leftvec, upvec);
>       VecNormalize(upvec);
>
>       /*
71c77
<       frustrumwidth = (view -> view_dist) * ((Flt) tan(view -> view_angle)) ;
---
>       frustrumwidth = ((Flt) tan(view -> view_angle)) ;
129c135
<                       Trace(0, 1.0, &ray, color);
---
>                       Trace(0, 1.0, &ray, color, &nRays);
173c179
<                       Trace(0, 1.0, &ray, color);
---
>                       Trace(0, 1.0, &ray, color, &nRays);
238c244
<                               Trace(0, 1.0, &ray, color);
---
>                               Trace(0, 1.0, &ray, color, &nRays);
old/shade.c
new/shade.c
112d111
<               nReflected ++ ;
115c114,115
<               Trace(level + 1, surf -> surf_ks * weight, &tray, tcol);
---
>               Trace(level + 1, surf -> surf_ks * weight, &tray, tcol,
>                       &nReflected);
120d119
<               nRefracted ++ ;
125c124,125
<               Trace(level + 1, surf -> surf_kt * weight, &tray, tcol) ;
---
>               Trace(level + 1, surf -> surf_kt * weight, &tray, tcol,
>                       &nRefracted) ;
old/trace.c
new/trace.c
19c19
< Trace(level, weight, ray, color)
---
> Trace(level, weight, ray, color, nr)
23a24
>  int *nr ;
34c35
<       nRays ++ ;
---
>       (*nr) ++ ;

back to contents

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

OFF Databases, by Randi Rost

Wondering where to get the famous teapot data?

As a service to the graphics community, Digital Equipment Corporation has donated disk space and established an archive server to maintain a library of (somewhat) interesting objects. The objects collected are in OFF format. Documentation on OFF, a library of useful OFF routines, and one or two useful OFF utilities are also available through this archive server.

The archive server lets you obtain ASCII files across the network simply by sending electronic mail. To obtain help about using this service, send a message with a "Subject:" line containing only the word "help" and a null message body to:

        [email protected]

To get an index of all that is available through this server, use a subject line of "send index" instead of "help". To get a list of objects that are available use a subject line of "send index objects" and a null message body.

In order to save disk space and transmission time, the more lengthy files available through this archive are compressed using the UNIX "compress" utility and then uuencoded so that they may be sent as ASCII files. For those of you who don't have access to these utilities, buddy up to someone who does.

As with other archive servers, it is only possible to get small portions of the database at a time. Small requests have priority over large ones. If you have ftp access, you can copy all of the objects and OFF programs from the file ~pub/DEC/off.tar.Z on the machine gatekeeper.dec.com.

Please respect the copyright notices attached to the objects in the .off header files. The original author usually worked pretty hard to create the model, and deserves some credit when it is displayed. If anyone out there knows something about any of the objects I've left uncredited, please let me know so that I can include the appropriate credits.

We'd *LOVE* to add to this collection of useful programs and objects. If you'd like to submit an object, an OFF program, or an OFF converter of some type for inclusion in the archive, send mail to:

        [email protected]

We cannot guarantee anything about when submissions will be made available as part of the object archive, since maintaining the archive is an after-hours activity. We can only promise that an interesting or useful object that is already in OFF format will make it into the archive more quickly than one that has to be converted from another format and then tested. To report problems with the archive server, send mail to:

        [email protected]

This same archive server will also be used to distribute Benchmark Interface Format (BIF) files for the Graphics Performance Characterization (GPC) Picture-Level Benchmark (PLB). These files contain commands that define how a picture or sequence of pictures is to be drawn. The time it takes to process the BIF file on a particular platform can be measured. It is therefore possible to create a BIF file that mimics the behavior of your favorite application area, process it on several platforms to which the PLB code has been ported, and get an apples-to-apples comparison of exactly the type of graphics performance that interests you most.

It is planned to release the PLB code and a sample set of BIF files at NCGA '90. When this happens, these things will be available as part of the object archive server, as well as by ftp access from gatekeeper. People that are interested in finding out more about PLB and BIF should contact Dianne Dean at NCGA, 2722 Merrilee Drive, Suite 200, Fairfax, VA 22031, (703) 698-9600 and request the most current BIF spec. We are also interested in redistributing interesting BIF files that people develop, or programs that convert other database types to BIF. Such submissions should also be mailed to [email protected].

Finally, we have added to the graphics bibliography that is also available through decwrl. Bibliographies from the years 1976-1981, 1983, and 1985-1986 are now available for use with the graf-bib server. This server can be accessed in the same manner as the object archive server by sending mail to:

        [email protected]

The years 1982 and 1984 have been received and await further editing before they can be included. We hope to make them available by the end of the month as well. The bibliographies will also be available for ftp access from gatekeeper once they are all ready to go. For more information on using the graf-bib server, see the April 1989 issue of Computer Graphics, pp. 185-186.

Randi J. Rost, [email protected]
Workstations Advanced Technology Development
Digital Equipment Corporation

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VM_pRAY is now available, by Didier Badouel

From: [email protected] (Didier Badouel)

VM_pRAY (Virtual Memory parallel RAYtracer) is a parallel raytracer (using NFF file format) running on an iPSC/2 and emulating a read-only shared memory.

VM_pRAY is now available from our site (irisa.fr (131.254.2.3)) by anonymous ftp access. ________________________________________ ftp 131.254.2.3 Name (131.254.2.3:yourname): anonymous Password: <your ident>

ftp>cd iPSC2/VM_pRAY
ftp>ls
VM_pRAYjan90.tar.Z
spirale.nff.Z
teapot.nff.Z
ftp>mget *
ftp>quit

uncompress *
tar -xvf VM_pRAYjan90.tar
_______________________________________

If you don't have ftp access, send me an e-mail; I will send you this software by return.

As I refer in the README file, I maintain a mailing list to inform interested persons of future VM_pRAY releases or patches. For this reason, I would like to get feedback from those who get this software.

Thanks.
________________________________________________________________
  Didier  BADOUEL                       [email protected]
  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
________________________________________________________________

back to contents


Superquadrics, by Prem Subrahmanyam, Patrick Flynn, Ron Daniel, and Mark VandeWettering

From: [email protected] (Daniel Ronald E )
Newsgroups: comp.graphics
Subject: Re: Superquadrics
Organization: Oklahoma State Univ., Stillwater

From article ([email protected]), by [email protected] (Patrick J. Flynn):
> In article ([email protected]) [email protected] (Prem Subrahmanyam) writes:
>> One of the new shapes that [DBW_render] supports is called a
>> superquadric. Now, I've attempted to look up info in IEEE CG&A about
>> them and found out that the first issue ever to come out had an article
>> about these, however, our library does not have this issue. So, can
>> anyone point out another source for info about these (the full equation
>> used for them, and how to do a ray-superquadric intersection (complete
>> with normal calculation for a given point))? Thanks in advance......
>
> Parametric form for a point on a superquad.:
>
> Let c(e,x) = (cos x)^e
> s(e,x) = (sin x)^e
>
> (x(u,v),y(u,v),z(u,v)) = ( c(e1,u)*c(e2,v) , c(e1,u)*s(e2,v), s(e1,u) )
>
> u and v are parameters of latitude and longitude. The parameters e1 and
> e2 control the shape of the primitive obtained when you sweep u and v
> over the sphere. The normal can be obtained by differentiation.
> . . .
> Patrick Flynn, CS, Mich. State U., [email protected]

The nice thing about superquadrics is that a wide range of shapes can be represented by varying only two parameters - e1 and e2. Cubes, cylinders, spheres, octahedrons, and double-ended cones are all special cases of a superquadric. All of the intermediate shapes are also available.

The equation for the normal vector of a superquadric (SQ) as a function of longitude and latitude is:

    (Nx(u,v),Ny(u,v),Nz(u,v)) =
       ( c(2-e1,u)*c(2-e2,v)/a1 , c(2-e1,u)*s(2-e2,v)/a2, s(2-e1,u)/a3 )

where e1, e2, u, and v are as before and a1, a2, a3 are the scale factors for the x,y, and z dimensions of the SQ. Unfortunately, both these equations require knowledge of u and v, which is not available for ray-tracing algorithms.

A more useful formulation is the implicit equation for superquadrics:

    F(x,y,z) = ((x/a1)^(2/e1) + (y/a2)^(2/e2))^(e2/e1) + (z/a3)^(2/e1)

(Note that if e1=e2=0, this degenerates to the implicit equation for a sphere.) This equation is for a superquadric centered at the origin, use standard transformations to translate and rotate it into world coordinates. If the point (x,y,z) is on the surface of the SQ, F=1. If (x,y,z) is inside the SQ surface, F < 1. If (x,y,z) is outside the SQ surface, F > 1. Ray- object intersections can be solved by finding zeros of the function (F-1). Standard techniques such as Newton or secant methods can be used to find the zeros, but they need some help. Depending on the values of e1 and e2, there can be from 0 to 4 roots. Finding the closest root can be difficult. The '89 SIGGRAPH proceedings has an article on restricting the search space of the root-finder to an area that bounds the first intersection. This technique will work for any implicit surface, not just superquadrics. The article is:

    Devendra Kalra and Alan Barr, "Guaranteed Ray Intersections with Implicit
    Surfaces", Computer Graphics, Vol.  23, No.  3, July 1989, pp.  297-306.

The expression for the normal vector as a function only of x,y,z (not u,v) is more complex. It can be obtained from the cross-product of the tangent vectors along the lines of latitude and longitude. The derivation is presented in an appendix of

    Franc Solina, "Shape Recovery and Segmentation with Deformable Part
    Models", GRASP Lab Tech. Rept. 128, Dept. Comp. and Info. Sci., U.
    Penn, Philadelphia, PA., Dec. 1987.

This is Franc's PhD dissertation, so it should also be available from University Microfilms. The results of the normal vector derivation are:

   nx = 1/x [1-(z/a3)^(2/e1)][(x*a2/y*a1)^(2/e2) / (1+(x*a2/y*a1)^(2/e2))]
   ny = 1/y [1-(z/a3)^(2/e1)][ 1 / (1+(x*a2/y*a1)^(2/e2))]
   nz = 1/z (z/a3)^(2/e1)

If your library does not have the first issue of IEEE CG&A you should have them issue an Inter-Library loan request for a copy of Barr's article. It has a lot of good stuff in it about other superquadric shapes, such as super- toroids. There is also another article that same year by Franklin and Barr, sorry that I don't have that reference handy - it is at the office. However, it deals more with generating fast polyhedral tilings of SQs, rather than with Ray-traced rendering of them.

Hope this helps.

Ron Daniel Jr. Electrical and Computer Engineering (405) 744-9925 202 Engineering South [email protected] (preferred) Oklahoma State University [email protected] Stillwater, OK 74078

________

From: [email protected] (Mark VandeWettering)
Organization: Princeton University

Ron Daniels gave a very good article on super quadrics, very informative. I thought I would just toss in the (probably obvious) information.

Super ellipsoids are a useful special subcase of the general super quadric equations. Their interesting geometric property is that they are all convex. The following ray intersection strategy works rather well, and was implemented by me, so I know it works :-) The only real limitation is that you eye should be "outside" the superquadric.

For a sphere, its implicit equation is

        F(x, y, z) = x^2 + y^2 + z^2

If F(x, y, z) < 1.0, then you are inside the sphere, otherwise, you are outside. You could perform intersection with a sphere by:

        1.      finding the close approach of the ray with the origin call
                this xc, yc, zc
        2.      if F(xc, yc, zc) < 1.0, we have an intersection, but we don't
                know where.
        3.      For a sphere, there is actually a formula for finding these
                intersections.  Alternatively, we have a point which is
                outside (the ray origin) and a point which is inside (xc, yc,
                zc).  Because the sphere is convex, we know that there is
                precisely one point in between for which F(x,y,z) = 1.0, which
                we find by binary searching the ray.

You can perform the analogous algorithm on superquadrics, and it works the same way. The implicit function for superquadrics was given by Daniels as:

F(x,y,z) = ((x/a1)^(2/e1) + (y/a2)^(2/e2))^(e2/e1) + (z/a3)^(2/e1)
                      ^^ error, should be e2....

For simplicity, we can pretend that a1 = a2 = a3 = 1.0. (These scale in each of the 3 directions, and we can handle that easier with transformation matrices, which we would need to have to rotate these anyway, so no loss)

F(x, y, z) = (x^(2/e2) + y^(2/e2))^(e2/e1) + z^(2/e1)

If F(x,y,z) < 1.0, then we are inside the super quadric, else we are outside. So, the algorithm runs as follows:

        1:      determine the ray closest approach to the origin.  call this
                point xc, yc, zc
        2:      if F(xc, yc, zc) is < 1.0, then you have a guaranteed hit,
                because xc, yc, zc is inside the quadric, and your eye is
                "outside".
        3:      because you know have a inside point and an outside point, and
                you know there is a single root in between, you can find it
                quite easily by binary searching.  Half the interval, check to
                see whether the midpoint is inside or outside, and collapse
                the other interval until some closeness criteria is met.

In practice, your eye may be far away from the super ellipsoid to start, you can substitute any outside point for you eye, I use the point where the ray intersected the bounding box, which I have anyway.

As long as you stick to the convex forms, (spheres, rounded boxes & cylinders, octahedra) this method works quite well.

back to contents


Graphics Textbook Recommendations, by Paul Heckbert, Mark VandeWettering, and Kent Paul Dolan

From: [email protected] (Paul Heckbert)

It's been a while now since Newman&Sproull and Foley&van Dam came out, and most of the graphics textbooks since then are either good but non-comprehensive (e.g. Rogers), or were written by typographic idiots for a readership of PC-hacking kindergarteners.

So I was pleasantly surprised to run across a couple of new graphics textbooks that are at the same time (1) current, (2) comprehensive, and (3) competent, (4) not overloaded with graphics standards pap. They are:

%A Alan Watt
%T Fundamentals of Three-Dimensional Computer Graphics
%I Addison-Wesley
%C Wokingham, England
%D 1989
Discusses radiosity, functionally-based modeling, stochastic sampling, and Fourier theory, among other topics.

%A Peter Burger
%A Duncan Gillies
%T Interactive Computer Graphics: Functional, Procedural,
and Device-Level Methods
%I Addison-Wesley
%C Wokingham, England
%D 1989
Discusses color image quantization, quaternions, and soft (blobby) objects, among many other topics.

I haven't read these books, but I was favorably impressed while browsing them in the bookstore. Has anybody else run across these books? Are there other undiscovered gems out there?

Paul Heckbert, CS grad student
508-7 Evans Hall, UC Berkeley           INTERNET: [email protected]
Berkeley, CA 94720                      UUCP: ucbvax!miro.berkeley.edu!ph

________

Aye, I was actually going to suggest that they be added above all others to the Frequently Asked Questions Posting, but you beat me to it. I really like the Watt book, and Burger and Gillies is also a good introductory text, much better than the old Foley & Van Dam, or Rogers (my old standby) in my opinion. I liked Watt's book so much when my sister's dog ate it over Christmas break, I immediately replaced it :-)

Both books have good sections about raytracing, and would make a good addition to your reference shelf.

Mark T. VandeWettering

________

After a brief gloss over the book (I looked at the contents, figures, listings, appendices, read the intro), this is the perfect transition for me from moving clipped 3D wireframe graphics, which I've done, to rendering.

Watt takes the reader step by step through:

the basics (a simple 3D model, transformations, deformations, viewing systems, the viewing pipeline);

reflection models (Phong, Cook & Torrance);

shading (Gouraud & Phong);

rendering (rasterization, hidden surface, composite models);

parametric representations (curves, surfaces, scan conversion);

ray-tracing (recursion, intersections, reflections & refraction, illumination, shadows, distributed processing, anti-aliasing, adaptive depth control, fancy bounding volumes, first hit speed up (?!?), spatial coherence, octrees, BSP trees);

diffuse illumination and radiosity;

shadows, texture, and environment mapping;

functionally based modelling (particle systems, fractal systems, 3D texture functions);

anti-aliasing (artifacts and Fourier theory, supersampling or postfiltering, prefiltering or area sampling, stochastic sampling);

animation (key frame, parametric, programmed with scripting, model driven/simulated, and temporal anti-aliasing);

color science (application, monitors, NTSC, models, colorimetry, the CIE standard, realistic rendering and reflection models);

and appendices covering viewing transformations, wireframes, implementation of a renderer, the Utah Teapot data set, a bit of theory, and highlight detection.

[There, I didn't _quite_ type in the whole table of contents! ;-) ]

Algorithms are in Pascal. Coding tricks for speed are mentioned occasionally, but the main emphasis is on clarity and correspondence to the theory, a deliberate choice by the author.

Graphics standards (PHIGS, PHIGS+, GKS-3D) are mentioned here and there in passing, but the model used throughout the book uses just two implementation dependent calls: paint pixel xy in color rgb, and inquire color rgb of pixel xy; much too simple a graphics system to require a "standard".

I am too much of a newbie here to "recommend" a book I've barely opened, but I'm sure going to enjoy this one, it covers exactly what I wanted to know and seems to have the right level of detail, too.

[email protected] [email protected] (Kent Paul Dolan)

back to contents


Where To Find U.S. Map Data, by Dru Nelson

From: [email protected] (Dru Nelson)
Newsgroups: comp.graphics

I have searched far and wide and have come up with a couple sources for U.S. Map data.

HANAUMA.STANFORD.EDU (36.51.0.16) has the world map as does the UCSD.EDU Anonymous FTP site. This database is the CIA World Bank II and it contains the data and some source files explaining the format. The World Bank II is Public Domain. Oh yes, I believe it also has the coordinates to some major cities. The data has the land boundaries, rivers, political boundaries, and one other thing I can't remember ;-)

The U.S. Map and state lines can also be purchased from Austin Code Works for a small fee. This is also public domain data.

At UCSD.edu there is also a mercator projection.

One last interesting database is on uunet.uu.net. There is a large Census file. I didn't get it, but it might help somebody out. I read an article in Byte showing that the census has maps of all the roads on CD and this might be one of their files. It might be handy to play with if you don't have the most recent CD of the data yet.

back to contents


References for Rendering Height Fields, Mark VandeWettering

Newsgroups: comp.graphics

>Could anyone recommend some good papers or books discussing the
>rendering of height fields? A friend of mine is implementing a
>height field raytracer and any references would be extremely useful.

I liked the following paper when I first read it, it proved useful in a couple of ways.

%A Sabine Coquillart
%A Michael Gangnet
%T Shaded Display of Digital Maps
%J IEEE Computer Graphics and Applications
%P 35-42
%D July, 1984
%K maps, terrain, ray tracing, priority list
%X Several methods for displaying height fields are presented.
Bilinear interpolation of patches is used to define the surface.  Efficient
algorithms, and quite elegant.  Reminiscent of Kajiya's cut planes for
surfaces of revolution.

Also, Musgrave had this Yale tech report. I ordered it from Yale Dept of Computer Science, but don't have who to contact over there anymore. Perhaps someone else has the information. Musgrave's approach was basically to make an adaptation of 3DDA uniform subdivision algorithms for height fields. I believe this code is also implemented in Craig Kolb's rayshade program.

%A F. Kenton Musgrave
%T Grid Tracing: Fast Ray Tracing For Height Fields
%J Research Report YALEU/DCS/RR-639
%D July, 1988

back to contents


RayShade 3.0 Released on comp.sources.unix, by Craig Kolb

Submitted-by: Craig Kolb ([email protected])
Posting-number: Volume 21, Issue 8
Archive-name: rayshade/part01

This is version 3.0 of rayshade, a raytracing program. Rayshade reads a multi-line ASCII file describing a scene to be rendered and produces a Utah Raster RLE format file of the raytraced image.

Rayshade features:

        Eight types of primitives (box, cone, cylinder, height field,
        polygon, sphere, superquadric, flat- and Phong-shaded triangle)

        Composite objects

        Point, directional, and extended (area) light sources

        Solid procedural texturing and bump mapping of primitives, objects,
                and individual instances of objects

        Antialiasing through adaptive supersampling or "jittered" sampling

        Arbitrary linear transformations on primitives,
                instances of objects, and texture/bump maps

        Use of uniform spatial subdivision or hierarchy of bounding
                volumes to speed rendering

        Options to facilitate rendering of stereo pairs

        Support for the C-Linda parallel programming language

Rayshade has been tested on many different UNIX-based computers. If your machine has a C compiler and enough memory (at least 2Mb), rayshade should be fairly easy to port. Be warned that rayshade uses yacc and lex to process input files. If you do not have lex and yacc, try to get flex and bison from the Free Software Foundation folks (ftp to prep.ai.mit.edu).

back to contents


Bibliography of Texture Mapping & Image Warping, by Paul Heckbert

From: [email protected] (Paul Heckbert)
Organization: University of California at Berkeley

Here is a fairly complete bibliography on texture mapping and image warping. About a year ago I posted a request for such references to comp.graphics in order to help me with my Master's thesis, and I got a number of helpful responses.

Incidentally, I finished my Master's thesis in May, and if you're interested in the properties of simple geometric mappings such as affine, bilinear, and projective (perspective), or the signal processing theory of resampling involved in texture filtering and image warping, you might want to check it out:

    Paul S. Heckbert
    Fundamentals of Texture Mapping and Image Warping
    Master's thesis, UCB/CSD 89/516
    CS Dept, UC Berkeley
    May 1989
    (order from CS Dept, UC Berkeley, Berkeley CA, 94720)
    [I highly recommend it--EAH]

The bibliography that follows includes articles on
    (computer graphics terms:)
        texture synthesis, geometric mapping, texture filtering
    (image processing terms:)
        image warping, geometric correction, distortion, image transformation,
        resampling, image interpolation and decimation, image pyramid

I've excluded references on rendering and signal processing in general, and most textbooks, since they're generally derivative. The list is in UNIX refer(1) format. %K is keywords, %Z is my comments. Please email me any additions/corrections.

Since this list is so long, I'll make recommendations. The best papers to read first are: Blinn-Newell76, Feibush-Levoy-Cook80, Catmull-Smith80; and good surveys are Heckbert86 (IMHO), Wolberg88.

Paul Heckbert, Computer Science Dept.
Evans Hall, UC Berkeley                 INTERNET: [email protected]
Berkeley, CA 94720                      UUCP: ucbvax!miro.berkeley.edu!ph

____

%E A. Rosenfeld
%T Multiresolution Image Processing and Analysis
%O Leesberg, VA, July 1982
%I Springer
%C Berlin
%D 1984
%K image pyramid

%A Narendra Ahuja
%A Bruce J. Schachter
%T Pattern Models
%I John Wiley
%C New York
%D 1983
%K tessellation, Voronoi diagram, triangulation,
point process, stochastic process, texture synthesis, height field

%A Masayoshi Aoki
%A Martin D. Levine
%T Computer Generation of Realistic Pictures
%J Computers and Graphics
%V 3
%P 149-161
%D 1978
%K texture mapping
%Z planar parametric mapping, no filtering

%A Alan H. Barr
%T Decal Projections
%B SIGGRAPH '84 Mathematics of Computer Graphics seminar notes
%D July 1984
%K texture mapping, ray tracing

%A Eric A. Bier
%A Kenneth R. Sloan, Jr.
%T Two-Part Texture Mappings
%J IEEE Computer Graphics and Applications
%V 6
%N 9
%D Sept. 1986
%P 40-53
%K texture mapping
%Z projection parameterizations

%A James F. Blinn
%A Martin E. Newell
%T Texture and Reflection in Computer Generated Images
%J CACM
%V 19
%N 10
%D Oct. 1976
%P 542-547
%Z early paper on texture mapping, discusses spherical sky textures
%K texture mapping, reflection, ray tracing

%A James F. Blinn
%T Computer Display of Curved Surfaces
%R PhD thesis
%I CS Dept., U. of Utah
%D 1978
%O (TR 1060-126, Jet Propulsion Lab, Pasadena)
%K texture mapping, bump mapping, shading, patch

%A James F. Blinn
%T Simulation of Wrinkled Surfaces
%J Computer Graphics
(SIGGRAPH '78 Proceedings)
%V 12
%N 3
%D Aug. 1978
%P 286-292
%K bump mapping

%A Carlo Braccini
%A Giuseppe Marino
%T Fast Geometrical Manipulations of Digital Images
%J Computer Graphics and Image Processing
%V 13
%P 127-141
%D 1980
%K image warp

%A Peter J. Burt
%T Fast Filter Transforms for Image Processing
%J Computer Graphics and Image Processing
%V 16
%P 20-51
%D 1981
%Z gaussian filter, image pyramid

%A Brian Cabral
%A Nelson Max
%A Rebecca Springmeyer
%T Bidirectional Reflection Functions from Surface Bump Maps
%J Computer Graphics
(SIGGRAPH '87 Proceedings)
%V 21
%N 4
%D July 1987
%P 273-281

%A Richard J. Carey
%A Donald P. Greenberg
%T Textures for Realistic Image Synthesis
%J Computers and Graphics
%V 9
%N 2
%D 1985
%P 125-138
%K texture mapping, texture synthesis

%A K. R. Castleman
%T Digital Image Processing
%I Prentice-Hall %C Englewood Cliffs, NJ
%D 1979
%K geometric correction

%A Edwin E. Catmull
%T A Subdivision Algorithm for Computer Display of Curved Surfaces
%R PhD thesis
%I Dept. of CS, U. of Utah
%D Dec. 1974
%Z bicubic patches, 1st texture mapping

%A Edwin E. Catmull
%A Alvy Ray Smith
%T 3-D Transformations of Images in Scanline Order
%J Computer Graphics
(SIGGRAPH '80 Proceedings)
%V 14
%N 3
%D July 1980
%P 279-285
%K texture mapping
%Z two-pass image warp

%A Alan L. Clark
%T Roughing It: Realistic Surface Types and Textures in Solid Modeling
%J Computers in Mechanical Engineering
%V 3
%N 5
%D Mar. 1985
%P 12-16
%K shading
%Z implementation of Cook-Torrance81

%A James J. Clark
%A Matthew R. Palmer
%A Peter D. Lawrence
%T A Transformation Method for the Reconstruction of Functions
from Nonuniformly Spaced Samples
%J IEEE Trans. on Acoustics, Speech, and Signal Processing
%V ASSP-33
%N 4
%D Oct. 1985
%P 1151-1165
%K signal processing, antialiasing
%Z reconstruct from nonuniform samples by warping the samples to be uniform

%A Robert L. Cook
%T Shade Trees
%J Computer Graphics
(SIGGRAPH '84 Proceedings)
%V 18
%N 3
%D July 1984
%P 223-231
%K shading, texture mapping

%A Robert L. Cook
%A Loren Carpenter
%A Edwin Catmull
%T The Reyes Image Rendering Architecture
%J Computer Graphics
(SIGGRAPH '87 Proceedings)
%V 21
%N 4
%D July 1987
%K rendering

%A S. Coquillart
%T Displaying Random Fields
%J Computer Graphics Forum
%V 4
%N 1
%D Jan. 1985
%P 11-19
%K texture

%A Ronald E. Crochiere
%A Lawrence R. Rabiner
%T Multirate Digital Signal Processing
%I Prentice Hall
%C Englewood Cliffs, NJ
%D 1983
%K resampling
%Z rational scale affine 1-D resampling

%A Franklin C. Crow
%T Summed-Area Tables for Texture Mapping
%J Computer Graphics
(SIGGRAPH '84 Proceedings)
%V 18
%N 3
%D July 1984
%P 207-212
%K antialiasing

%A William Dungan, Jr.
%A Anthony Stenger
%A George Sutty
%T Texture Tile Considerations for Raster Graphics
%J Computer Graphics
(SIGGRAPH '78 Proceedings)
%V 12
%N 3
%D Aug. 1978
%P 130-134
%K image pyramid

%A Karl M. Fant
%T A Nonaliasing, Real-Time Spatial Transform Technique
%J IEEE Computer Graphics and Applications
%D Jan. 1986
%P 71-80
%Z two-pass image warp, trivial

%A Eliot A. Feibush
%A Marc Levoy
%A Robert L. Cook
%T Synthetic Texturing Using Digital Filters
%J Computer Graphics
(SIGGRAPH '80 Proceedings)
%V 14
%N 3
%D July 1980
%P 294-301
%K texture mapping
%Z antialiasing polygon edges and textures

%A Eliot A. Feibush
%A Donald P. Greenberg
%T Texture Rendering Systems for Architectural Design
%J Computer-Aided Design
%V 12
%N 2
%D Mar. 1980
%P 67-71
%K texture mapping

%A Leonard A. Ferrari
%A Jack Sklansky
%T A Fast Recursive Algorithm for Binary-Valued Two-Dimensional Filters
%J Computer Vision, Graphics, and Image Processing
%V 26
%N 3
%D June 1984
%P 292-302
%Z summed area table generalized to rectilinear polygons

%A Leonard A. Ferrari
%A Jack Sklansky
%T A Note on Duhamel Integrals and Running Average Filters
%J Computer Vision, Graphics, and Image Processing
%V 29
%D Mar. 1985
%P 358-360
%Z proof of algorithm in their 1984 paper

%A Leonard A. Ferrari
%A P. V. Sankar
%A Jack Sklansky
%A Sidney Leeman
%T Efficient Two-Dimensional Filters Using B-Spline Functions
%J Computer Vision, Graphics, and Image Processing
%V 35
%D 1986
%P 152-169
%Z b-spline filtering by repeated integration

%A Eugene Fiume
%A Alain Fournier
%A V. Canale
%T Conformal Texture Mapping
%B Eurographics '87
%D 1987
%P 53-64
%K geometric mapping, parameterization

%A Alain Fournier
%A Eugene Fiume
%T Constant-Time Filtering with Space-Variant Kernels
%J Computer Graphics
(SIGGRAPH '88 Proceedings)
%V 22
%N 4
%D Aug. 1988
%P 229-238
%Z variant of pyramid techniques: precompute convolutions with patch fragments
note: memory required is O(1) with minor mods, not O(m^2) as they say

%A Donald Fraser
%A Robert A. Schowengerdt
%A Ian Briggs
%T Rectification of Multichannel Images in Mass Storage Using Image
Transposition
%J Computer Vision, Graphics, and Image Processing
%V 29
%N 1
%D Jan. 1985
%P 23-36
%Z texture mapping, two-pass image warp, just like Catmull & Smith 80!
see corrigendum vol. 31, p. 395

%A D. E. Friedmann
%T Operational Resampling for Correcting Images to a Geocoded Format
%B Proc. 15th Intl. Symp. Remote Sensing of Environment
%C Ann Arbor
%D 1981
%P 195-212
%Z two-pass image warp

%A A. Gagalowicz
%T Texture Modelling Applications
%J The Visual Computer
%V 3
%N 4
%D 1987
%P 186-200

%A Andre Gagalowicz
%A Song de Ma
%T Model Driven Synthesis of Natural Textures for 3-D Scenes
%B Eurographics '85
%D 1985
%P 91-108
%K texture synthesis

%A Michel Gangnet
%A Didier Perny
%A Philippe Coueignoux
%T Perspective Mapping of Planar Textures
%B Eurographics '82
%D 1982
%P 57-71
%K texture mapping, antialiasing
%O reprinted in Computers and Graphics, Vol 8. No 2, 1984, pp. 115-123

%A Michel Gangnet
%A Djamchid Ghazanfarpour
%T Techniques for Perspective Mapping of Planar Textures
%I Colloque Image de Biarritz, CESTA
%D May 1984
%P 29-35
%K texture mapping, antialiasing
%Z in french

%A Geoffrey Y. Gardner
%T Simulation of Natural Scenes Using Textured Quadric Surfaces
%J Computer Graphics
(SIGGRAPH '84 Proceedings)
%V 18
%N 3
%D July 1984
%P 11-20
%K tree, cloud
%Z 3-D fourier series texture function

%A Geoffrey Y. Gardner
%T Visual Simulation of Clouds
%J Computer Graphics
(SIGGRAPH '85 Proceedings)
%V 19
%N 3
%D July 1985
%P 297-303
%K quadric, texture

%A Andrew S. Glassner
%T Adaptive Precision in Texture Mapping
%J Computer Graphics
(SIGGRAPH '86 Proceedings)
%V 20
%N 4
%D Aug. 1986
%P 297-306
%Z adaptive texture filter according to local variance, uses summed area table

%A W. B. Green
%T Digital Image Processing - A Systems Approach
%I Van Nostrand Reinhold
%C New York
%D 1983
%K geometric correction

%A Ned Greene
%A Paul S. Heckbert
%T Creating Raster Omnimax Images from Multiple Perspective Views
Using The Elliptical Weighted Average Filter
%J IEEE Computer Graphics and Applications
%V 6
%N 6
%D June 1986
%P 21-27
%K texture mapping, image warp, antialiasing

%A Ned Greene
%T Environment Mapping and Other Applications of World Projections
%J IEEE Computer Graphics and Applications
%V 6
%N 11
%D Nov. 1986
%K reflection mapping
%Z revised from Graphics Interface '86 version

%A Shinichiro Haruyama
%A Brian A. Barsky
%T Using Stochastic Modeling for Texture Generation
%J IEEE Computer Graphics and Applications
%D Mar. 1984
%P 7-19
%O errata Feb. 1985, p. 87
%K texture mapping, bump mapping, texture synthesis, fractal

%A Paul S. Heckbert
%T Texture Mapping Polygons in Perspective
%I NYIT Computer Graphics Lab
%R TM 13
%D Apr. 1983
%K antialiasing

%A Paul S. Heckbert
%T Filtering by Repeated Integration
%J Computer Graphics
(SIGGRAPH '86 Proceedings)
%V 20
%N 4
%D Aug. 1986
%P 317-321
%K filter, integration, convolution
%Z generalizes Perlin's selective image filter and Crow's summed area table

%A Paul S. Heckbert
%T Survey of Texture Mapping
%J IEEE Computer Graphics and Applications
%V 6
%N 11
%D Nov. 1986
%P 56-67
%Z revised from Graphics Interface '86 version

%A Paul S. Heckbert
%T Fundamentals of Texture Mapping and Image Warping
%R Master's thesis, UCB/CSD 89/516
%I CS Dept, UC Berkeley
%D May 1989

%A Berthold K. P. Horn
%T Hill Shading and the Reflectance Map
%J Proc. IEEE
%V 69
%N 1
%D Jan. 1981
%P 14-47
%K shading, terrain, illumination map
%Z exhaustive survey of ad hoc and theoretical terrain shading methods

%A J. C. Hourcade
%A A. Nicolas
%T Inverse Perspective Mapping in Scanline Order
onto Non-Planar Quadrilaterals
%B Eurographics '83
%D 1983
%P 309-319
%K texture mapping, antialiasing

%A James T. Kajiya
%T Anisotropic Reflection Models
%J Computer Graphics
(SIGGRAPH '85 Proceedings)
%V 19
%N 3
%D July 1985
%P 15-21
%K texture mapping, levels of detail
%Z frame mapping

%A James T. Kajiya
%A Timothy L. Kay
%T Rendering Fur with Three Dimensional Textures
%J Computer Graphics
(SIGGRAPH '89 Proceedings)
%V 23
%N 3
%D July 1989
%P 271-280
%Z solid texture

%A A. Kaufman
%A S. Azaria
%T Texture Synthesis Techniques for Computer Graphics
%J Computers and Graphics
%V 9
%N 2
%D 1985
%P 139-145

%A Douglas S. Kay
%A Donald P. Greenberg
%T Transparency for Computer Synthesized Images
%J Computer Graphics
(SIGGRAPH '79 Proceedings)
%V 13
%N 2
%D Aug. 1979
%P 158-164
%Z 2.5-D ray tracing: refraction by warping background image,
contains better refraction formula than Whitted
%K ray tracing

%A Wolfgang Krueger
%T Intensity Fluctuations and Natural Texturing
%J Computer Graphics
(SIGGRAPH '88 Proceedings)
%V 22
%N 4
%D Aug. 1988
%P 213-220

%A J. P. Lewis
%T Algorithms for Solid Noise Synthesis
%J Computer Graphics
(SIGGRAPH '89 Proceedings)
%V 23
%N 3
%D July 1989
%P 263-270
%Z solid texture

%A Song de Ma
%A Andre Gagalowicz
%T Determination of Local Coordinate Systems for Texture Synthesis
on 3-D Surfaces
%B Eurographics '85
%D 1985
%P 109-118
%K texture synthesis

%A Nadia Magnenat-Thalmann
%A N. Chourot
%A Daniel Thalmann
%T Colour Gradation, Shading and Texture Using a Limited Terminal
%J Computer Graphics Forum
%C Netherlands
%V 3
%N 1
%D Mar. 1984
%P 83-90
%K dither

%A R. R. Martin
%T Recent Advances in Graphical Techniques
%B 1985 European Conference on Solid Modeling
%O London, 9-10 Sept 1985
%I Oyez Sci. and Tech. Services
%C London
%D 1985
%K texture mapping, ray tracing

%A Nelson L. Max
%T Shadows for Bump-Mapped Surfaces
%B Advanced Computer Graphics
(Proc. of CG Tokyo '86)
%E Tosiyasu Kunii
%I Springer Verlag
%C Tokyo
%D 1986
%P 145-156

%A Gene S. Miller
%A C. Robert Hoffman
%T Illumination and Reflection Maps:
Simulated Objects in Simulated and Real Environments
%B SIGGRAPH '84 Advanced Computer Graphics Animation seminar notes
%D July 1984
%Z reflection maps: how to make and use them
%K ray tracing, illumination map

%A Alan Norton
%A Alyn P. Rockwood
%A Philip T. Skolmoski
%T Clamping: A Method of Antialiasing Textured Surfaces by
Bandwidth Limiting in Object Space
%J Computer Graphics
(SIGGRAPH '82 Proceedings)
%V 16
%N 3
%D July 1982
%P 1-8
%K texture mapping

%A D. A. O'Handley
%A W. B. Green
%T Recent Developments in Digital Image Processing at the
Image Processing Laboratory of the Jet Propulsion Laboratory
%J Proc. IEEE
%V 60
%N 7
%P 821-828
%D 1972
%K geometric correction

%A Alan W. Paeth
%T A Fast Algorithm for General Raster Rotation
%B Graphics Interface '86
%D May 1986
%K image warp, texture mapping, two-pass, three-pass
%P 77-81

%A Darwyn R. Peachey
%T Solid Texturing of Complex Surfaces
%J Computer Graphics
(SIGGRAPH '85 Proceedings)
%V 19
%N 3
%D July 1985
%P 279-286
%K 3-D texture

%A Ken Perlin
%T A Unified Texture/Reflectance Model
%B SIGGRAPH '84 Advanced Image Synthesis seminar notes
%D July 1984
%K texture mapping, bump mapping
%Z making microfacet distribution functions consistent
with normal perturbations; hash function

%A Ken Perlin
%T Course Notes
%B SIGGRAPH '85 State of the Art in Image Synthesis seminar notes
%D July 1985
%K antialiasing, filter, blur
%Z generalizing Crow's summed-area tables to higher order filter kernels

%A Ken Perlin
%T An Image Synthesizer
%J Computer Graphics
(SIGGRAPH '85 Proceedings)
%V 19
%N 3
%D July 1985
%P 287-296
%Z texture functions, pixel stream editor

%A Ken Perlin
%A Eric M. Hoffert
%T Hypertexture
%J Computer Graphics
(SIGGRAPH '89 Proceedings)
%V 23
%N 3
%D July 1989
%P 253-262
%Z using solid texture as an implicit function to define density & surfaces

%A H. J. Reitsema
%A A. J. Word
%A E. Ramberg
%T High-fidelity image resampling for remote sensing
%J Proc. of SPIE
%V 432
%D 1984
%P 211-215

%A Marcel Samek
%A Cheryl Slean
%A Hank Weghorst
%T Texture Mapping and Distortion in Digital Graphics
%J Visual Computer
%V 2
%N 5
%D 1986
%P 313-320

%A Michael Shantz
%T Two Pass Warp Algorithm for Hardware Implementation
%J Proc. SPIE, Processing and Display of Three Dimensional Data
%V 367
%D 1982
%P 160-164
%K two-pass image warp

%A S. Shlien
%T Geometric Correction, Registration and Resampling of Landsat Imagery
%J Canad. J. Remote Sensing
%V 5
%D 1979
%P 74-89

%A Alvy Ray Smith
%T Planar 2-Pass Texture Mapping and Warping
%J Computer Graphics
(SIGGRAPH '87 Proceedings)
%V 21
%N 4
%D July 1987
%P 263-272

%A Alvy Ray Smith
%T TEXAS (Preliminary Report)
%I NYIT Computer Graphics Lab
%R TM 10
%D July 1979
%K texture mapping

%A Alvy Ray Smith
%T Incremental Rendering of Textures in Perspective
%B SIGGRAPH '80 Animation Graphics seminar notes
%D July 1980
%K texture mapping

%A A. Tanaka
%A M. Kameyama
%A S. Kazama
%A O. Watanabe
%T A Rotation Method for Raster Image Using Skew Transformation
%B Proc IEEE Conf on Computer Vision and Pattern Recognition
%D June 1986
%P 272-277
%K texture mapping, image warp

%A S. L. Tanimoto
%A Theo Pavlidis
%T A Hierarchical Data Structure for Picture Processing
%J Computer Graphics and Image Processing
%V 4
%N 2
%D June 1975
%P 104-119
%K image pyramid

%A D. Thalmann
%T A Lifegame Approach to Surface Modelling and Texturing
%J The Visual Computer
%V 2
%N 6
%D 1986
%P 384-390

%A Nuio Tsuchida
%A Yoji Yamada
%A Minoru Ueda
%T Hardware for Image Rotation by Twice Skew Transformations
%J IEEE Trans on Acoustics, Speech, and Signal Processing
%V ASSP-35
%N 4
%D Apr. 1987
%P 527-532
%K image warp

%A Ken Turkowski
%T The Differential Geometry of Texture Mapping
%R Technical Report No. 10
%I Apple Computer
%C Cupertino, CA
%D May 1988
%K mapping, filter

%A Douglass Allen Turner
%T A Taxonomy of Texturing Techniques
%R Master's thesis
%I Dept. of Computer Science, U of North Carolina, Chapel Hill
%D 1988

%A Carl F. R. Weiman
%T Continuous Anti-Aliased Rotation and Zoom of Raster Images
%J Computer Graphics
(SIGGRAPH '80 Proceedings)
%V 14
%N 3
%D July 1980
%P 286-293
%K image warp, line drawing, digital line, texture mapping

%A Lance Williams
%T Pyramidal Parametrics
%J Computer Graphics
(SIGGRAPH '83 Proceedings)
%V 17
%N 3
%D July 1983
%P 1-11
%K texture mapping, antialiasing

%A George Wolberg
%T Geometric Transformation Techniques for Digital Images: A Survey
%R TR CUCS-390-88
%I Dept. of CS, Columbia U.
%D Dec. 1988

%A George Wolberg
%T Skeleton-Based Image Warping
%J Visual Computer
%V 5
%D 1989
%P 95-108

%A George Wolberg
%A Terrance E. Boult
%T Separable Image Warping with Spatial Lookup Tables
%J Computer Graphics
(SIGGRAPH '89 Proceedings)
%V 23
%N 3
%D July 1989
%P 369-377

%A Geoff Wyvill
%A Brian Wyvill
%A Craig McPheeters
%T Solid Texturing of Soft Objects
%B CG International '87
%C Tokyo
%D May 1987

%A John F. S. Yau
%A Neil D. Duffy
%T A Texture Mapping Approach to 3-D Facial Image Synthesis
%J Computer Graphics Forum
%V 7
%N 2
%D June 1988
%P 129-134
%Z face

back to contents


More Texturing Functions, by Jon Buller

From: [email protected] (Jon Buller)
Organization: Dallas Semiconductor

Last April, when there were many raging requests for the RenderMan Noise function. I posted the one that I got from Gary Herron (one of my Profs at the time). After I had fixed the hashing it used, so that there would not be rows upon rows of blobs of the same shape, I posted it to comp.graphics. I didn't have it documented in the best form, since I posted it quickly to hopefully stem the tide of requests. There was a bug in it (that I knew about, but forgot to tell everyone about, and it needed several followups to explain how it worked and how to initialize it, etc.)

Well, I would like to get some various texture routines from the net at large, just to see what others are doing, and for a bit of fun... Of course, I don't just want take things without some sort of return, so to get your collections of 'new & unusual(tm)' textures started, I have included one of my favorites, The Planet Texture. It does not need watering, food, or specular reflection, just take a dot-product of the surface normal and the light source direction to add shadows, and have fun... It is written in Pascal. (No, I do not yet have a C compiler for my Mac, but that WILL change in a couple of months.) So you must translate it to your language of choice, but I believe it is a bit better documented than the first.

Anyway, I would like to see your favorite textures (call or write today!) and if there is a tremendous response, I may (or may not) compile them into a list, summarize, and post. Two textures I would REALLY like to see are 1) a good Marble texture (like the one in [Perlin85], (guess what this paper is.), and 2) something like the Wood_Burl texture I saw applied to your favorite teapot and mine in a book by (or maybe edited by) Andrew Glassner. I don't remember the title (Computer Graphics for Artists, maybe?)

If you don't have a Noise function of your own, mine was translated and should be around... or you can link it to whatever function you like if it returns a Real (er.. float) 8-).

Get Noise From UUNET (Is it still there? I can't find out anymore.) or a friend. Change it to initialize the random array pts[] to fill with (-1.0 to 1.0) instead of (0.0 to 1.0) like it says. My Thanks to Bill Dirks for doing that translation, BTW. (You may also notice that I am no longer a student at Colorado State University...)

I included my Turb function with this, because last time I checked UUNET (April '89) the noise file there said that Bill had not translated the Turb function yet, and in the interest of completeness (and reducing mail volume 8-), it is here, but you must translate it yourself...

[Perlin85] An Image Synthesizer, Ken Perlin,
     Proceedings of SIGGRAPH '85

If you haven't guessed (after reading the code, of course 8-):
Add([x1,y1,z1], [x2,y2,z2]) = [x1+x2, y1+y2, z1+z2]
Subtract([x1,y1,z1], [x2,y2,z2]) = [x1-x2, y1-y2, z1-z2]
Scale(s, [x,y,z]) = [s*x, s*y, s*z]
Color and Vector coerce the given type of a 3-vector into the other kind of 3-vector

(* ------- cut here ------- Planet&Turb.p ------- cur here ------- *)

function Turb (Size: Integer; ScaleFactor: Real; Loc: Vector): Real;
(* Size = Size of largest feature: Smallest feature size = 1,
   ScaleFactor is related to the fractal dimension of the turbulence,
   Loc = point of turbulence to compute *)
var CurScale, Result: Real;
        Cur: Integer;
begin
   Result := Noise(Loc);
   CurScale := 1.0;

   Cur := 1;
   while Cur < Size do Begin
      Cur := BSL(Cur, 1);
           (* Shift Left is MUCH quicker than a multiply *)
      CurScale := CurScale * ScaleFactor;
      Loc := Scale(2.0, Loc);
      Result := Result + Noise(Loc) * CurScale;
   end;
   Turb := Result;
end;

(* This was designed to work with a unit sphere.  I think it works well, you
   may (should) form your own opinions... *)
Function Planet (Loc: Vector): Color;
Const Land  := [0.28125, 0.1875, 0.09375];
               (* A reasonably nice brown color *)
      Sea   := [0.0    , 0.0   , 1.0];
               (* Oceans are usually blue *)
      Cloud := [1.0    , 1.0   , 1.0];
               (* And Clouds are white *)
      (* OK, this part isn't Pascal, (I wish it was though...)
         but it beats the way it's done in the real code... *)
Var C: Color;
    Amt: Real;
Begin
   If Turb(430, 0.7, Loc) > 0.25
        (* The sphere I use is 430 pixels across *)
   Then C := Land
   Else C := Sea;

   Amt := Turb(18, 0.6, Scale(24.0, Loc));
           (* Clouds I like are 18 pixels across *)
   If Amt > -0.25 Then
   C := Color(Add(Vector(C), Scale(Amt + 0.25,
          Subtract(Vector(Cloud), Vector(C)))));

   (* I Wish I could do it like this...
          C := C + (Amt + 0.25) * (Cloud - C)    *)
End;

-- Jon Buller [email protected] ..!texbell!vector!jonb

back to contents


Ray/Cylinder Intersection, by Mark VandeWettering

From: [email protected] (Mark VandeWettering)
Newsgroups: comp.graphics
Organization: Princeton University

>I am trying to do ray tracing of light through a
>cylinder coming at different angle to the axis
>of the cylinder. Could some one give me some
>pointers?

Ray cylinder intersection is (conceptually) just as easy as hitting a sphere. Most of the problems come from clipping the cylinder so it isn't infinite. I can think of several ways to do this, but first let me mention that you should consult Introduction to Ray Tracing edited by Andrew Glassner. Articles by Pat Hanrahan and Eric Haines go over most of this stuff.

It's easiest to imagine a unit cylinder formed by rotating the line x = 1 in the xy plane about the y axis. The formula for this cylinder is x^2 + z^2 = 1. If your ray is of the form P + t D, with P and D three tuples, you can insert the components into the original formula and come up with:

        (px + t dx)^2 + (pz + t dz)^2 - 1 = 0

or px^2 + 2 t dx px + (t dx)^2 + pz^2 + 2 t dz pz + (t dz)^2

or (px^2 + pz^2) + 2 t (dx px + dz pz) + t^2 (dx^2 + dz^2)

which you can then solve using the quadratic formula. If there are no roots, then there is no intersection. If there are roots, then these give two t values along the ray. Figure out those points using P + t D. Now, clipping. We wanted to have a finite cylinder, say within the cube two units on a side centered at the origin. Well, gosh, ignore any intersections that occur outside this box. Then take the closest one.

Now, to intersect with an arbitrary cylinder, work up a world transformation matrix that transforms points into the objects coordinate system. Transform the ray origin and direction, and voila. You do need to be careful to rescale it appropriately, but its really not all that hard.

You might instead want to implement general quadrics as a primitive, or choose any one of a number of different ways of doing the above. Homogeneous coordinates might make this simpler actually.... Hmmm.... And there is a geometric argument that can also be used to derive algorithms like this.

Think about it. It shouldn't be that difficult.

back to contents


C Code for Intersecting Quadrics, by Prem Subrahmanyam

From: [email protected] (Prem Subrahmanyam)
Newsgroups: comp.graphics
Organization: Florida State University Computing Center

Here is the code I wrote in C for doing 3-dimensional quadratics. The derivations are rather complex, so I tried to comment the code as best I could, but that's all I could do. I hope people find this interesting.

--

#define TINY (float)1e-3

int hitconic(offset,eye,v,p,t,a,b,c,d,e,f,g,start,stop)

/* offset is the triple representing where the conic is to be moved */
/* from 0,0,0. */
/* eye and v represent the ray, with eye being the start point and v */
/* being the direction vector */
/* p is the point into which the intersection point value will be */
/* copied */
/* t is the value into which the line parameter will be copied for the */
/* ray. */
/* a,b,c,d,e,f,g are values for the 3-dimensional quadratic equation */
/* a*x^2 + b*y^2 + c*z^2 + d*x + e*y + f*z = g */
/* start and stop represent the bounds (when the equation is centered
   at 0,0,0) in which to test the conic */
   /* example: if the bound around a conic were set at -1,-1,-1 to 1,1,1
      and the offset was 4,5,6 then the actual spatial extent of the
      object would be from 3,4,5 to 5,6,7 . */
/* So, the conic (3-d quadratic) should contain within its own data
   structure the offset, extent values (start,stop), and a,b,c,d,e,f,g
   constants */

vector offset,
       eye,
       v,
       p;

float     *t,
           a,
           b,
           c,
           d,
           e,
           f,
           g;

vector start,
       stop;

    {
    /*************************************************/
    /* this code is a little messy, but it does work */
    /*************************************************/

      /* create some local points to use in testing */
      vector m,p2;
      float radical,Ay,Be,Ce,t1,t2; /* constants for quadratic formula */
      /* generated for solving for the intersection of the equations for
         the line and the equation for the quadratic */
      /* subtract offset from the ray start position to align ray and
         quadratic*/
      m[0] = eye[0] - offset[0];
      m[1] = eye[1] - offset[1];
      m[2] = eye[2] - offset[2];

      /* Now, using the constant values, create values for the intersection
         test formula */
      Ay = (a*v[0]*v[0]) + (b*v[1]*v[1]) + (c*v[2]*v[2]);
      Be = (2*a*m[0]*v[0]) + (2*b*m[1]*v[1]) + (2*c*m[2]*v[2]) +
                (d*v[0]) + (e*v[1]) + (f*v[2]);
      Ce = (a*m[0]*m[0]) + (b*m[1]*m[1]) + (c*m[2]*m[2]) +
                (d*m[0]) + (e*m[1]) + (f*m[2]) - g;
      radical = ((Be*Be) - (4*Ay*Ce));
      if (radical < 0.0) {
         return FALSE;
      }
      t1 = ((-1*Be) + sqrt(radical))/(2*Ay);
      t2 = ((-1*Be) - sqrt(radical))/(2*Ay);

   /* immediately eliminate cases in which return is false */
      if (((t1 < 0)&&(t2 < 0))||
          ((t1 < 0)&&(fabs(t2) < TINY))||
          ((t2 < 0)&&(fabs(t1) < TINY))||
          ((fabs(t1) < TINY)&&(fabs(t2) < TINY)))
      {
         return FALSE;
      }else{
         /* t1 a bad parameter, but t2 may not be */
         if ((t1 < 0)||(fabs(t1) < TINY)) {
           if (!(fabs(t2) < TINY)) /* prevent spurious self-shadowing */
           {
             /* using the parameter, find the point of intersection */
             p[0] = m[0] + v[0]*t2;
             p[1] = m[1] + v[1]*t2;
             p[2] = m[2] + v[2]*t2;
             /* test to see if the point is within the bounds for the
             quadratic section */
             if ((start[0] <= p[0])&&
                 (stop[0] >= p[0])&&
                 (start[1] <= p[1])&&
                 (stop[1] >= p[1])&&
                 (start[2] <= p[2])&&
                 (stop[2] >= p[2]))
             {
               /* if it lies within the bounds, add offset back on and return
                  point */
                p[0] = p[0] + offset[0];
                p[1] = p[1] + offset[1];
                p[2] = p[2] + offset[2];
                *t = t2;
                return TRUE;
             } else { /* point does not lie within the bounds */
                return FALSE;
             }
           }else{ /* t2 a bad parameter as well */
             return FALSE;
           }
         }

         if ((t2 < 0)||(fabs(t2) < TINY)) {
         /* t2 a false parameter, so test to see if t1 is good */
           if(!(fabs(t1) < TINY))
           { /* find point by parameter */
             p[0] = m[0] + v[0]*t1;
             p[1] = m[1] + v[1]*t1;
             p[2] = m[2] + v[2]*t1;
             if ((start[0] <= p[0])&&
                 (stop[0] >= p[0])&&
                 (start[1] <= p[1])&&
                 (stop[1] >= p[1])&&
                 (start[2] <= p[2])&&
                 (stop[2] >=p[2]))
             { /* same as above, see if point lies within bounds */
                p[0] = p[0] + offset[0];
                p[1] = p[1] + offset[1];
                p[2] = p[2] + offset[2];
                *t = t1;
                return TRUE;
             } else {
                return FALSE;
             }
           }else{
                return FALSE;
           }
         }
         /* if the program has gotten here, t1 and t2 are greater than 0 */
         /* and greater than TINY */
         p[0] = m[0] + v[0]*t1;
         p[1] = m[1] + v[1]*t1;
         p[2] = m[2] + v[2]*t1;

         p2[0] = m[0] + v[0]*t2;
         p2[1] = m[1] + v[1]*t2;
         p2[2] = m[2] + v[2]*t2;

         /* see if the first point is within bounds */
         if ((start[0] <= p[0])&&
             (stop[0] >= p[0])&&
             (start[1] <= p[1])&&
             (stop[1] >= p[1])&&
             (start[2] <= p[2])&&
             (stop[2] >=p[2]))
         { /* now, see if second point is as well */
             if ((start[0] <= p2[0])&&
                 (stop[0] >= p2[0])&&
                 (start[1] <= p2[1])&&
                 (stop[1] >= p2[1])&&
                 (start[2] <= p2[2])&&
                 (stop[2] >=p2[2]))
             {  /* both points are within bbox */
                if (t1 <= t2) /*see which one is smaller */
                { /* t1 yields a closer point */
                    *t = t1;
                    p[0] = p[0] + offset[0];
                    p[1] = p[1] + offset[1];
                    p[2] = p[2] + offset[2];
                    return TRUE;
                } else {
                 /* t2 yields a closer point */
                    *t = t2;
                    p[0] = p2[0] + offset[0];
                    p[1] = p2[1] + offset[1];
                    p[2] = p2[2] + offset[2];
                    return TRUE;
                }
             } else { /* second point not within box */
                *t = t1;
                p[0] = p[0] + offset[0];
                p[1] = p[1] + offset[1];
                p[2] = p[2] + offset[2];
                return TRUE;
             }
         } else { /* t1 not within bbox */
            if ((start[0] <= p2[0])&&
                (stop[0] >= p2[0])&&
                (start[1] <= p2[1])&&
                (stop[1] >= p2[1])&&
                (start[2] <= p2[2])&&
                (stop[2] >=p2[2]))
            { /* see if t2 is within bbox */
                *t = t2;
                p[0] = p2[0] + offset[0];
                p[1] = p2[1] + offset[1];
                p[2] = p2[2] + offset[2];
                return TRUE;
            } else { /* neither is within bounding box */
                return FALSE;
            }
        }
      }
 }

/* HERE IS THE PORTION OF THE CODE THAT RETURNS THE NORMAL TO THE
   QUADRATIC */
void findnormal(np,p,n)
   node       *np;
   vector       p,
       n;
/* np is the pointer to the object node, p is the point of intersection,
   and n is the normal vector returned */
  {
    vector point;
    switch (np->kind) {
       /* conic section a la Prem */
       case CONIC    : point[0] = p[0] - cptr(np)->offset[0];
                       point[1] = p[1] - cptr(np)->offset[1];
                       point[2] = p[2] - cptr(np)->offset[2];
                       n[0] = 2.0*cptr(np)->a*point[0] + cptr(np)->d;
                       n[1] = 2.0*cptr(np)->b*point[1] + cptr(np)->e;
                       n[2] = 2.0*cptr(np)->c*point[2] + cptr(np)->f;
                       normalize(n);
                       break;
       }

back to contents


Parallel Ray Tracing on IRISs, collected by Doug Turner

From: Douglass Turner ([email protected])

Here is the collection of responses that I got from various people kind enough to respond to my query about doing parallel ray tracing on the IRIS.

________

This is from George Drettakis:

I'm just finishing my MSc here, and I designed and implemented a hierarchical scheme that uses several IRIS connected over an ethernet. The rendering algorithm is a global illumination approach developed locally that goes one step further than radiosity and ray-tracing combined. The approach is based on space-subdivision that splits the original 3-d scene into cubes adaptively depending on the difficulty in each volume. I assign a group of sub-volumes to each iris, and then do the processing for the volume on each IRIS in parallel. This actually includes a bit of ray-casting that we do for various purposes in our algorithm. I use the taskcreate/taskdestroy calls to implement this, and I use the usnewsema and usnewlock call for locking and synchronization. The man pages are pretty straightforward, but if you have trouble I can put together a sample program and send it to you. I found using the m_get_myid function from the "sequent compatibility library" was also useful, as it gives you a unique 1 to n-1 proc id, for n procs. For ray-tracing, all you need to do is to split the screen, and give each pixel to a processor, and you're done. The key is to avoid using any global variables, and speaking from painful experience, other peoples code is full of it, no pun intended, as they didn't have parallelism in mind.

George Drettakis (416) 978 5473 Dynamic Graphics Project Internet: [email protected] Computer Systems Research Institute Bitnet: [email protected] Toronto, Ontario M5S 1A4, CANADA

________

This is from Steve Lamont:

I use brute force, forking off multiple processes. This is probably not optimum, but is guaranteed to work on a number of platforms, including a Cray Y-MP running UNICOS (no shared memory between processes )-: ), a Stardent Titan, a Convex C-220, and a SGI 4D/280GTX. If you're interested, I'll be glad to send you the code -- it is based on the MTV ray tracer, with extensions.

Steve Lamont, sciViGuy  (919) 248-1120          EMail:  [email protected]
NCSC, Box 12732, Research Triangle Park, NC 27709

________

This contribution is from Gavin [Bell--EAH] at SGI (not Gavin Miller!).

In it he mentions a demo tape that IRIS users can purchase ($100.00) that contains source code for numerous demos including the "flyray" demo he discusses. I haven't gotten my copy yet but intend to soon. The demos and source code for other interesting looking stuff is listed in a pamphlet you can get from IRIS (its free) called "IRIS software exchange". I recommend it.

Have you seen the 'flyray' interactive ray-tracer demo running on a GTX? It used to be a two-processor ray-tracer (one processor computing ray/scene intersections, the other feeding the graphics pipe) until I fully parallelized it. It will now use one processor to do send scene data (showing the ray-trace going on) to the geometry subsystem, and the other N-1 to compute the ray/scene intersections (if running over the Ethernet using the Distributed Graphics Library all processors compute the ray/scene intersections, with an extra process called on every once in a while to send the results down wire). [Excellent demo, by the way - see it. --EAH]

I used the sproc() system call to fork off processes, and set up a queue which the main program (responsible for displaying the bitmap produced and showing the rays being traced) reads from and all the child processes write into. This queue is protected using the hardware lock feature of GTX systems (see the usinit, usnewlock, ussetlock, and usunsetlock manual pages).

Rays are traced in blocks of up to 256 at a time (16x16 chunks), which cuts down on the overhead associated with accessing the queue. The program runs amazingly fast on a 8-processor system, but could benefit from tracing even larger chunks.

Source code to the flyray program is available from Silicon Graphics; Monica Schulze is the person to contact (she handles distribution of demo source code). Try calling her at 415-962-3320.

For your application, you probably don't need to do any inter-process synchronization; each process will be busy computing its quarter of the image and storing it in memory. You might want to look at the m_fork() manual page; your application will look something like:

        initialize_stuff (create the voxel space, etc);
        m_fork(child_process);
        m_kill_procs();
        save_image (or whatever you want to do with it)
        exit()

        ... and each child_process does:
        int mynum = m_get_myid();
        int np = m_get_numprocs();
        ... based on mynum and numprocs, do part of the screen here...
        return

The m_fork commands are nice because you get automatic synchronization (the m_fork command returns after all child processes are finished), and it figures out how many processors the system has for you.

Re: Distributed Graphics library:

Yes, it is very easy to use; instead of linking with -lgl_s, you link with -ldgl (and possibly some other libraries, depending on your networking situation; usually, you need to add -lsun -lbsd also). After doing a little setup (you have to tell inetd to listen for DGL requests on a particular port number and start up the DGL daemon), you put your program on the machine that will execute it, and rlogin in to that machine from the SGI machine on which you want the graphics to appear. Then run the program. All the graphics get sent over the network and appear on the machine you are sitting at.

However, ethernet speeds are fairly slow, so if you so a lot of drawing you can easily overwhelm the ethernet bandwidth and slow down. The best way around this is to use the GL display-list commands; the object will be stored on the display machine, and only one call needs to be sent over the network to get it displayed. Of course, as networks get faster this will become unnecessary.

Feel free to redistribute any of this information.

--gavin
gavin%[email protected]

________

This is source code from Michael John Muuss. I haven't looked at it closely. His email path is [email protected]

/*
 *                      M A C H I N E . C
 *
 *  Machine-specific routines for doing raytracing.
 *  Includes parallel and vector support, replacement library routines, etc.
 *
 *  Author -
 *      Michael John Muuss

 ...

[for brevity (this issue is already a monster), I've deleted this code - look on the net, or contact Doug Turner or Michael Muuss if you are seriously interested.]

________

Heres a plug from Frank Phillips for SGI's course on writing parallel applications.

just for reference, SGI offers a very good class (in Mt.View) on writing parallel applications, using several different methods. Definitely recommended.

[email protected]
frank phillips
SGI inSane Diego

________

I hope people find this info useful. I know I will. Thanks to all who responded so quickly. A big unthank you to myself for waiting so long to post.

Cheers,
Doug Turner
[email protected]
408-974-0484

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Eric Haines / [email protected]