*"Light Makes Right"*

October 1, 1990

Volume 3, Number 4

Compiled by

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.

- Introduction
- New People, Address Changes, etc
- Photorealism, and the color Pink (TM), from Andrew Glassner
- DKBTrace v2.0 and Ray Tracing BBS Announcement, by David Buck, Aaron Collins
- Article Summaries from Eurographics Workshop, by Pete Shirley
- Convex Polyhedron Intersection via Kay & Kajiya, by Eric Haines
- New Radiosity Bibliography Available, by Eric Haines
- A Suggestion for Speeding Up Shadow Testing Using Voxels, by Andrew Pearce
- Real3d, passed on by Juhana Kouhia, "Zap" Andersson
- Utah Raster Toolkit Patch, by Spencer Thomas
- NFF Shell Database, by Thierry Leconte
- FTP list update and New Software, by Eric Haines, George Kyriazis

- Humorous Anecdotes, by J. Eric Townsend, Greg Richter, Michael McCool, Eric Haines
- Graphics Interface '91 CFP
- Parametric Surface Reference, by Spencer Thomas
- Solid Light Sources Reference, by Steve Hollasch, Philip Schneider
- Graphics Gems Source Code Available, by Andrew Glassner, David Hook
- Graphics Gems Volume 2 CFP, by Sari Kalin
- Foley, Van Dam, Feiner and Hughes "Computer Graphics" Bug Reports, by Steve Feiner
- Radiosity via Ray Tracing, by Pete Shirley
- Algorithm Order Discussion, by Masataka Ohta, Pete Shirley
- Point in Polygon, One More Time..., by Mark Vandewettering, Eric Haines, Edward John Kalenda, Richard Parent, Sam Uselton, "Zap" Andersson, and Bruce Holloway
- Quadrant Counting Polygon In/Out Testing, by Craig Kolb, Ken McElvain
- Computer Graphics Journals, by Juhana Kouhia

Pike (the moderator): "Who's biographical sketch reads as follows-"

BUZZ!

Team 1 (with no other information): "Turner Whitted!?"

Pike: "No, wrong. Now let me read the question" and proceeds to read some biographical data.

BUZZ!

Team 2: "Is it Turner Whitted!?"

Pike: "Still wrong."

Team 3, sadly, did not guess "Turner Whitted?", but, rather, declined to answer.

________

Does anyone have a nice, compact version of the Teapot? That is, just the spline description (which I do have) and a tessellator which will turn it into quads/triangles (which I have, but it's deeply buried in some scary code)? This would be a nice addition to SPD 3.0, but I don't have one easily accessible. Here's your chance to get your code distributed in the next release. I'm willing to massage your code into outputting NFF format.

I'll also announce that there is a new version of the ray tracing bibliography which I've finished as of today. Many of the new articles listed are due to the untiring work of Tom Wilson, who says the librarians now hate him. This new version should be available via FTP by October 5th on freedom.graphics.cornell.edu and cs.uoregon.edu (see the FTP site list later in this issue for more information).

Important dates: Graphics Interface papers due October 31st Graphics Gems, Volume 2 submissions due November 1st

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```
# Tom Wilson - parallel ray tracing, spatial subdivision
# Center for Parallel Computation
# Department of Computer Science (407-275-2341)
# University of Central Florida
# P.O. Box 25000
# Orlando, FL 32816-0362
alias tom_wilson [email protected]
```

I am a Ph.D. student at UCF. I am working in the area of parallel processing with ray tracing as an application. I am working on a nonuniform spatial subdivision scheme that will eventually be implemented on our BBN Butterfly GP1000.

________

```
# Steve Hollasch - efficiency, algorithms, ray-tracing
# Master's Student in C.S., Arizona State University
# 1437 West 6th Street
# Tempe, AZ 85281-3205
# (602) 829-8758
alias steve_hollasch [email protected]
```

I'm working on completing my thesis in December 1990 or January 1991. The research basically covers viewing 4D objects (as physical entities, not 3D scalar fields). I'm working on a 4D raytracer right now that handles hyperspheres and tetrahedrons, and I hope to extend it to hyperellipsoids, hypercones, hypercylinders and so on. I'd also like to learn how to tessellate 4D solids with tetrahedrons to be able to view arbitrary 4D solids. Practical uses? I'm still trying to think off something... =^)

________

# Christophe Vedel - improving radiosity # LIENS, Ecole Normale Superieure # 45, rue d'Ulm # 75230 PARIS Cedex 05 FRANCE # (33) 1 43 26 59 74 e-mail [email protected] [email protected]

I'm interested in improving the radiosity method for finer results or larger scenes. Spatial subdivision techniques developed for ray tracing should help to achieve this goal. I'm also working on interactivity with lighting simulation programs.

________

# Frederic Asensio - behavioral animation, radiosity # LIENS, Ecole Normale Superieure # 45, rue d'Ulm # 75230 PARIS Cedex 05 FRANCE # (33) 1 43 26 59 74 e-mail [email protected] [email protected]

I am interested in interactive radiosity methods, which could be used in the design process and in stochastic methods for light sampling with rays.

________

```
# Scott Senften - efficiency, scientific visualization
# McDonnell Douglas Corp.
# McDonnell Aircraft Co.
# Mail Code 1065485
# St. Louis, MO 63166
# (314)232-1604
alias scott_senften senften%[email protected]
alias senften_tu [email protected]
```

Presently I'm doing research in neural nets. There is a real need in the NN society for some good scientific visualization. I'm presently doing work in speech recognition, diagnostics, flight reconfiguration, and signal processing, as well as graphic visualization of neural networks. My graduate work was in Ray Tracing efficiency.

________

Sam Uselton

```
Internet:
[email protected]
```

Work Home Phone: (415) 604-3985 (415) 651-6504

USMail: Samuel P. Uselton, PhD Sam Uselton Computer Sciences Corp. M/S T 045-1 1216 Austin St. NASA Ames Research Center Fremont, CA 94539 Moffett Field, CA 94035

Ray Tracing interests: efficiency, accuracy, distributed ray tracing, parallel implementations

At NASA I'm working on volume visualization for computational fluid dynamics. I've used this as an excuse ( :-) ) to write a ray caster (no bounces) that integrates through the volume, accelerated by taking advantage of the special grids, as well as an item buffer-like initial hit finder.

I'm also working with Redner & Lee on extending our distributed ray tracing work to handle diffuse illumination, caustics, wavelength dependent refraction, and other realistic effects.

Once these problems are completely solved ( :-) :-) ), there are several parallel machines here that I would like to wring out.

Oh yes, we (Lee, Steve Stepoway, Scott Senften and myself) have yet another Acceleration technique we like better than any of the popular ones. (Actually it can combine with bounding boxes.) It is somewhere between regular space subdivision (a la medical volume folks and Japanese SEADS..) and the bounding slabs idea (Kaplan? [no, Kay]). It was written and submitted for pub once, but we keep thinking of new tweaks, so it is being re-written.

________

```
# Juhana Kouhia
# Ylioppilaankatu 10 C 15
# 33720 Tampere
# Finland
alias juhana_kouhia [email protected]
```

I have done my wireframe, scanline and ray tracing programs with Jim Blinn's modeling language.

[Another renderer with a last name starting with K! There's Kajiya, Kaplan, Kay, Kirk, Kolb, Kuchkuda, Kyriazis, just to mention a few. --EAH]

________

```
# Michael L. Kaufman - speed, ray tracing on a PC, ray tracing fractal images
# Northwestern University
# 2247 Ridge Ave #2k
# Evanston IL, 60201
# (708) 864- 7916
# [email protected]
```

I am just getting started in Ray-Tracing. I am interested in coming up with algorithms that are fast enough to do on a 386 PC. I am also interested in using Ray-Tracing techniques as a new way of looking at certain types of fractal images.

________

Stephen Boyd Gowing - light transmission, motion, art B.App.Sc (Computing) Undergraduate. University of Technology, Sydney4/10 Short St, Glebe 2037 AUSTRALIA (home)

alias stephen_gowing [email protected]

I'm currently half way through a project to study the effect of light passing through sphere(s). The eventual aim is to produce a short animation showing a single sphere inverting an image which breaks (unmerges?) into two spheres one behind the other and study the "flow" of the image through them. At the moment I am still rewriting the tracer I used for my 2nd-last graphics assignment last year. I'd like to do it in C++ but this would make things awkward as we don't have access to a compiler. I'd also like to implement some sort of shading language into the image description - probably using something like forth.

________

# Rick Brownrigg -- efficiency, texturing, visualization, DTM displays # Kansas Geological Survey # University of Kansas # 1930 Constant Avenue # Lawrence, KS USA 66046 # 913 864 4991

________

**Mail,**
from Andrew Woo, George Kyriazis, Zap Andersson

from Andrew Woo:

I have gone through many changes in the last year, from graduating with a M.Sc. at University of Toronto, to working at SAS Institute, to working at Alias Research - which is my current working address. My e-mail at Alias is [email protected].

I checked out your latest RT News. I think David Jevans was a little too hard on you about not knowing about the ray id for voxel traversal. In fact, in GI 90, one of the authors was unaware of it, too (in the "Approximate Ray Tracing" paper). So you are not alone. In fact, there is an explicit mentioning of ray id in an early paper that David did not mention:

John Amanatides, "A Fast Voxel Traversal Algorithm for Ray Tracing", EuroGraphics, 1987, pp. 1-10.

On the claim that David Jevans made about wasting time on more intersection culling schemes, I tend to agree. In fact, I have stopped looking for more clever ways to cull intersections. But I intend to check out another route to ray tracing savings. Once I get some promising results, I will share the idea with you (to avoid any embarrassments in case the idea backfires).

On renaming DIstributed Ray Tracing, I am more of a fan of coming up with amusing acronyms for the algorithms. For Cook's, I thought DiRT might be interesting. I also came up with an acronym for my paper in GI 90 - Voxel Occlusion Method as an Intersection-culling Technique, which spells VOMIT.

________

from George Kyriazis:

I was reading the last RTN issue I received. In there it states about a program that converts sculpt4d to NFF, and it also commented that Sculpt4D is an exceptional modeler. Well, I have my doubts. Last spring I was working on a program to raytrace Scultpt4D files and animations on a Pixel Machine. Well, the file format is far from being strait-forward. We had to call Byte by Byte for a few questions and stayed on the phone for more than an hour. One of the Sculpt4D unwanted 'features' was that it normalized the intensity of all displayed pixels wrt the brightest. The result on the Pixel Machine was disastrous! Images were either overexposed or totally black! :-) Well, this is one of the problems faced, but I don't want to list more...

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"Traditional workstations can't handle reality. They create a simulated world... With Dynamic Visualization, reality and simulation are brought together by TekImaging (TM), powerful image-processing software... [and now, the big one -ag] TekImaging lets you transform real-world images into photo-realistic scenes, complete with light, shadow, and texture."

So now I can take a picture of myself, and using their software make it look photo-realistic and indistinguishable from a real picture - what a breakthrough!

________

Beware of the colors you pick for your images. Here's a footnote in an Owens-Corning Fiberglas ad in this month's [August?] Popular Science (pg 21):

"* The color Pink is a trademark of Owens-Corning Fiberglas Corp."

I think I'll get a trademark on red before all the good colors are taken...

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- primitives for spheres, planes, triangles, and quadrics - constructive solid geometry - solid texturing using a Perlin-style noise function - image mapping (IFF and GIF formats) - hierarchical bounding boxes - transparency - fog - 24 bit output files - adaptive anti-aliasing using jittered supersampling - "quick" previewing options

The raytracer was developed on an Amiga computer, but it is easily portable to other platforms. The interface to the raytracer raytracer is a scripting language (sorry, no GUI). The language is quite readable compared to many other input file formats.

The source and Amiga executables are available by anonymous FTP from alfred.ccs.carleton.ca [134.117.1.1]. The source and executables are freely distributable.

As with any raytracer, there are still things that need to be done, added, or improved with DKBTrace. The image mapping was added at the last minute, so it only uses a simple projection scheme. This means that the mappings look bizarre when viewed from the sides or the back. For the most part, however, the solid textures are quite powerful and can create some very interesting effects.

To implement transparency, I decided to add the transparency value value to the color structure. A color contains red, green, blue, and alpha components. This makes it much easier to use in textures.

The textures also allow you to define your own color map and to have the colors automatically interpolated from one range to the next. Interpolating the colours makes the images look much better than just a simple step function.

Questions and comments concerning the raytracer can be directed to [email protected] on BITNET. The IBM port (and several enhancements) were done by Aaron Collins. Aaron can be reached on Compuserve.

________

DKBtrace dox info:

Aaron Collins can be reached on the following BBS'es

Lattice BBS (708) 916-1200 The Information Exchange BBS (708) 945-5575 Stillwaters BBS (708) 403-2826

AAC: As of July of 1990, there will be a Ray-Trace specific BBS in the (708) Area Code (Chicago suburbia) for all you Traceaholics out there. The phone number of this new BBS is (708) 358-5611. I will be Co-Sysop of that board. There is also a new Ray-Trace and Computer-Generated Art specific SIG on Compuserve, GO COMART. And now, back to the DOCS...

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INCREMENTAL RAY TRACING by Murakami and Hirota (Fujitsu)

A extension of Parameterized ray tracing that allowed moving some scene
objects in addition to changing material properties. Used tables of
changed voxels to determine if a ray's interaction with geometry has
changed. Included implementation on multiple CPUs. Also includes
reference to a paper in Japanese by Matsumoto on Octree ray tracing in
1983!

PARAMETRIC SURFACES AND RAY TRACING by Luc Biard (IMAG, France)

Like most parametric patch papers, this one went over my head, but
it seems to be an interesting paper, and includes some implementation results.

A PROGRESSIVE RAY TRACING BASED RADIOSITY WITH GENERAL REFLECTANCE FUNCTIONS
by Le Saec and Schlick (France)

A proposal for general BRDF radiosity (very similar to what I propose in the
paper above). Also includes method for interactive display - display only
non-mirrors until viewer stops, then ray trace (UNC style).

LIGHT SOURCES IN A RAY TRACING ENVIRONMENT by Roelens et al. (France)

A method for showing 'cone of light' effect when there is not very
dense participating media in a room (primary scattering only).

METHODS FOR EFFICIENT SAMPLING OF ARBITRARILY DISTRIBUTED VOLUME DENSITIES
by Hass and Sakas (FRG)

Methods of sampling a volume density along a ray.

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To review:

Their idea is to form a bounding volume around an object by making slabs. A
slab is the volume between two parallel planes. The intersection of all slabs
is the bounding volume (i.e. the volume which is inside all slabs). The
intersection method works by intersecting each slab and checking out
intersection conditions for it alone, then comparing these results to the
answer for previous slabs. That is, first we get the near and far
intersection points for the ray with the slab. If the far hit is behind the
ray's origin (i.e. negative distance) or the near hit is beyond the maximum
distance (i.e. you might limit how far the ray can travel by keeping track of
the closest object hit so far, or the distance to the light if this is a
shadow ray), then the ray cannot hit the bounding volume.

If the near and far hits are within bounds, then we essentially do a set operation of this line segment and any previous slab line segments formed. For example, if this is the second slab tested, we try to find the overlap of the first slab's hits and this slab's hits. If the two segments do not overlap, then there is no point along the ray that is inside both slabs. In other words, there is no point inside the bounding volume, since this volume is the logical intersection of all slabs. To get the logical intersection of the slab segments, we merely store the largest of the near hits and the smallest of the far hits. If this largest near hit is greater than this smallest far hit, there was no overlap between segments, so the bounding volume is missed. If near is less than far, this new high-near, low-far segment is used against successive slab segments. If the ray survives all segment tests, then the resulting near and far values are the distance along the ray of the near and far hits on the bounding volume itself.

What's interesting about this test is that it is essentially doing Constructive Solid Geometry operations between slabs, similar to [Roth 82]. This simple idea can be extended further, allowing you to quickly intersect convex polyhedra. Another good feature is that the polyhedra can be defined entirely by the plane equations for the faces, so no vertices have to be stored.

Imagine that you have defined a convex polyhedron by specifying each face using a plane equation, Ax + By + Cz + D = 0. Have each face's normal {A,B,C} point outwards.

To intersect this object with a ray, simply test the ray against each face: if you hit a plane that faces towards the ray (i.e. the dot product of the normal and the ray direction is negative), then use this as a hit for near; if you hit a plane facing away, then use this as a hit for far. Now, instead of having a line segment for each slab, you have an unbounded ray for each plane. For example, if you have a hit for a near distance (i.e. you hit a forward facing plane), then you would first check if this near is beyond your current maximum distance. If not, then you would store the maximum of this near value and the previous (if any) near value. If at this point the stored near value is greater than the stored far value, the ray has missed. This process continues with each plane until you miss or you run out of planes. The near and far points are then your intersection points with the polyhedron.

Essentially, this process is an extension of Kay & Kajiya: the ray is tested against each face and the intersection point is used to form a segment which is unbounded (infinite) on one end. This segment is tested for validity against the ray's segment and the polyhedron's current intersection segment. If the polyhedron's segment is valid at the end of the process, then the ray hit the polyhedron. Basically, each face of the polyhedron defines a half-space in which the inside of the polyhedron must lay. The intersection of these half-spaces is the polyhedron itself.

One minor problem is what happens when the ray is parallel to the plane. You could use Kay & Kajiya's suggestion of using some epsilon for the divisor, but I prefer handling this special case separately. If parallel, then we want to check if the ray origin is inside the half-space: if it is not, then the ray cannot ever hit the polyhedron (since the ray does not cross into the volume of valid intersections formed by this half-space). In other words, if we substitute the origin into the plane equation, the result of the expression must be negative for the point to be inside the half-space; if not, the ray must miss the polyhedron.

The pseudo-code [note: fixed 7/18/97 to follow my Graphics Gems II code]:

Maxdist = maximum distance allowed along ray Tnear = -MAXFLOAT, Tfar = MAXFLOAT For each plane in the polyhedron: Compute intersection point T and sidedness dp = ray.direction DOT plane.normal do = (ray.origin DOT plane.normal) + plane.d If ( dp == 0 ) /* ray is parallel to plane - check if ray origin is inside plane's half-space */ If ( do > 0 ) /* ray is outside half-space */ return MISSED Else /* ray not parallel */ T = -do / dp If ( dp < 0 ) /* front face - T is a near point */ If ( T > Tfar ) return MISSED If ( T > Tnear ) Tnear = T Normal = plane.normal Else /* back face - T is a far point */ If ( T < Tnear ) return MISSED If ( T < Tfar ) Tfar = T endfor return HIT

At the end, Tnear is the intersection distance and Normal is the surface normal. Tfar is the exit distance, if needed. If Tnear is < 0.0 and Tfar == Maxdist then the ray is inside but hit no face in the test direction (i.e. the polyhedron is not closed).

That's it: instead of laborious inside/outside testing of the polygon on each face (and storing all those vertices), we have a quick plane test for each face. If the number of planes is large, it might have been better to store the polygons and use an efficiency scheme. However, the method above is certainly simpler to code up and is pretty efficient, compact, and robust: for example, there are no special edge intersection conditions, as there are no edges!

An aside:

One thing that I hadn't mentioned is how we can better initialize the near and
far hit distances before the slab tests. It turns out that when testing
bounding volumes we can set Tnear (the near distance) to 0 and Tfar to the
maximum ray distance (if any - else set it to "infinity"). This corresponds
to the segment formed by the ray: we consider points between 0 and the
maximum ray distance to be valid points on the ray, and so want to find slab
segments that overlap this segment. Note that these initial conditions gets
rid of some complication for the algorithm: we now don't have to test our
slab segment against the ray's segment and the previous bounding volume
segment, but rather are always testing against a single segment which
represents the intersection of both of these. This idea is not in Kay &
Kajiya's presentation, by the way.

Note that there is one change that occurs if you initialize the near and far distances in this way: the near and far distances computed when a volume is hit will not yield the true surface intersections, but rather will give the first and last points inside the volume. This is useful for bounding volumes, since we usually just want to know if we hit them and have some idea of the distance.

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freedom.graphics.cornell.edu [128.84.247.85]: /pub/Radiosity

It's a compressed package using "refer" format. Articles related to radiosity or "non-classical" rendering (soft shadows, caustics, etc) are included here. This version is significantly improved from the version I posted some months ago. Many thanks to all who helped update it.

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Requirements: ------------This method is applicable to any type of spatial subdivision. It is probably best suited to those of us who tessellate our objects to ray trace them.

Method: ------I've expanded on Eric Haines' method of storing the last object hit by a shadow ray with each light source, I now save a pointer to the voxel which contains the last object hit (or at least the voxel the intersection occurred in if the object spans multiple voxels). My rationale is that if the shadow ray does NOT intersect the "last object" which shadowed that light source, then the likelihood of it hitting something in the neighborhood of that same object is pretty good. If we save the voxel which the shadowing occurred in for the previous ray, we can examine the other objects in that voxel for possible light source occlusion WITHOUT the ray startup and voxel traversal costs. Now this assumption is likely untrue if you're just tracing spheres and checker boards (some slight intended :^) but it works quite well for tessellated objects (NURBS patches in my case).

I NULL my pointers to both the last object and last voxel if no shadow intersection was found on the last shadow ray to this light.

I store a ray_id with every object to insure that any given ray is tested for intersection with an object ONLY ONCE even if it spans multiple voxels. Each ray has a unique id. (I thought, as did David Jevans, that this was a well known technique). So, even if the shadow ray misses all of the objects in "last voxel" and must be traced like a regular shadow ray, we are likely not losing much since if the shadow ray enters the "last voxel" during it's traversal of the voxels, the ray will see that it has already been intersected with all of the objects in that voxel, and that voxel will be skipped relatively quickly (slightly slower than an empty voxel; the time it takes to compare the ray ID against the ray ID stored with each object).

Pseudo-code: ----------- /****************************************************************************/ /* Obviously we cannot use the "last object hit" for transparent */ /* objects since multiple objects may be involved in the shadowing process. */ /* The code outlined below assumes that we only store the "last object" and */ /* "last voxel" for shadow rays generated from a primary ray intersection. */ /* What we really should have is a tree indicating what was hit at each */ /* level of recursion. Ie. What object shadowed the intersection point */ /* generated by the last refraction ray, generated from a reflection ray */ /* generated by a primary ray? */ /****************************************************************************/ float check_shadowing(ray, light) RAY_REC ray; /* ray from shading point to light source */ LIGHT_REC light; /* the light source we are interested in */ { if (light.last_object != NULL) { /* intersect_object() marks object as having been */ /* intersected by this ray. */ hit = intersect_object( ray, light.last_object, &object); if (hit) { return(1.0); /* full shadowing */ } if (light.last_voxel != NULL) { /* implied !hit */ /* intersect_object_in_voxel_for_shadows() returns hit = TRUE */ /* on first affirmed intersection with a non-transparent * object. */ /* It ignores transparent objects altogether. */ hit = intersect_objects_in_voxel_for_shadows( ray, light.last_voxel &object); if (hit) { light.last_object = object; return(1.0); } } } /* traverse_voxels_for_shadows() DOES intersect transparent objects and */ /* sorts the intersections for proper attenuation of the light intensity. */ /* If it hits multiple objects, the object returned is the transparent one. */ hit = traverse_voxels_for_shadows(ray, &object, &voxel, &shadow_percent); if (!hit) { light.last_object = light.last_voxel = NULL; return(0.0); } if (object.transparency_value > 0.0) { /* the object is transparent */ light.last_object = light.last_voxel = NULL; } else { light.last_object = object; light.last_voxel = voxel; } return ( shadow_percent ); }

Results: -------(For the discussion below, "positive occlusion" means we have guaranteed that the point we are shading is shadowed from the light source.)

The "last object hit" method provided a positive occlusion 52% of the time, and if the "last object hit" method did not provide positive occlusion, the "last voxel" method provided a positive occlusion 76% of the time.

I performed a "pixie" of the code with and without this opt. on an SGI Personal Iris with no other code changes or scene changes, there is ONE light source in the scene which is casting shadows. The ray tracer with the "last voxel" optimization used 2% fewer cycles. (Actual system times vary wildly based on load, but the last voxel version did run about 10% faster using the UNIX "times()" system call, but I don't trust "times()"). Two percent doesn't seem like an awful lot, but this is just a quick and dirty hack, and I would expect to save 2% on EACH light source which casts shadows.

The test scene I'm using is a snare drum with a shadow casting spotlight on it. See IEEE Computer Graphics & Applications, Sept. 1988, the cover story includes a tiny reproduction of the image should you wish to see what I'm playing with, although the image in CG&A was done with a 2D projective renderer (ray casting), not ray tracing. The reflections in the floor and on the chrome in that image were realised using two separate cubic environment maps, the shadows were done with a depth map, the wallpaper is a simple parametric map and the floor boards have 6 separate solid wood textures randomly assigned to them.

The test scene contains approximately 60,000 triangles and I'm rendering at 512x512 resolution with no anti-aliasing, and a limit of one recursion level for both shadow and reflection rays for a total of 638,182 rays. There is only one light in the scene which casts shadows.

I'll be doing tests on more scenes with various levels of voxel subdivision, and object distribution. I'll let you know the results, even if they're negative! (The above results did surprise me a little).

Additional Note: I urge anyone doing ray/triangle intersections to use Didier Badouel's "An Efficient Ray-Polygon Intersection" (Graphics Gems pp. 390-393). I have implemented both Badouel's method and Snyder/Barr's barycentric method, and Badouel's method is about 19% faster (I optimized the snot out of my implementation of the barycentric method, but I used most of those same opts in Badouel's method as well). This result is from comparing the same scene ray traced with the two versions.

_________________________________________________________________________

[A second article followed some days later - EAH]

More results from the voxel/shadow optimization: -----------------------------------------------

One thing I neglected to mention in the previous message was that you should be sure to NULL out your last object and last voxel hit pointers at the end of each scanline.

NEW TEST SCENES: ---------------The test scenes producing the results below are 40x40x40 arrays of polygons (each polygon is broken down into 8 triangles). The polygons are distributed at unit distances from each other, and then their orientations are jittered (rotations) and their positions are jittered (translate of -1. to +1.). Each polygon is roughly a unit in width and height. The polygons are inside of a larger box (the room) with 15 shadow casting lights in a 5x3 array just below the "ceiling". There were no reflection or refraction rays generated. All images were computed at 645x486 pixels with 4 supersamples per pixel. Every intersection generated 15 shadow rays. The "sparse" scene had every polygon scaled by 0.2 in all dimensions. The resulting sparse image looks like an exploding particle system (due mainly to the 145 degree field of view). In the dense image, almost no background can be seen.

CHART DESCRIPTION: -----------------"Last Voxel" speed up refers to the percentage fewer cycles the "last voxel" method took to compute the same image. Since this percentage is calculated based on the number of cycles the entire ray trace took, it is an exact measure of the speed up. Negative numbers mean that the "last voxel" method was slower. It is important to note that file read, tessellation and spatial subdivision time is included in the count of the cycles, so the actual speed up to the ray tracing alone may be greater than is stated, depending on how you want to measure things.

Average Hits Per Ray is included as a general measure of the density of the scene, it is the number of confirmed ray/triangle intersections divided by the total number of rays (shadow rays included). In the sparse scene it is less than one since most of the shadow rays made it to the light sources without hitting anything. The dense scene is greater than one because some confirmed intersections are abandoned due to nearer intersections being found in the same voxel.

Average Hits Per Primary Ray is the number of confirmed ray/triangle intersections divided by the number of primary (eye) rays.

--------------+-----------------+-----------------+ Scene | 64,000 jittered | 64,000 jittered | Description | polygons (0.2) | polygons (1.0) | | (sparse) | (dense) | --------------+-----------------+-----------------+ Number of | 551,408 | 551,408 | Triangles | | | --------------+-----------------+-----------------+ Number of | | | Shadow Casting| 15 | 15 | Lights | | | --------------+-----------------+-----------------+ Number of Rays| 11,324,318 | 8,427,904 | --------------+-----------------+-----------------+ "Last Object" | | | Success Rate | 50.7% | 90.9% | --------------+-----------------+-----------------+ "Last Voxel" | | | Success Rate | 23.4% | 39.3% | --------------+-----------------+-----------------+ "Last Voxel" | | | Speed Up | 1.04% | 3.6% | --------------+-----------------+-----------------+ Average Hits | | | Per Ray | 0.265 | 1.001 | --------------+-----------------+-----------------+ Average Hits | | | Per Primary | 2.363 | 6.638 | Ray | | | --------------+-----------------+-----------------+

It is encouraging that there is a speedup even in very sparse scenes (however slight a speed-up it is). These "random" scenes are not very indicative of the type of scenes we are generally interested in ray tracing. (Really, these scenes look like particle systems, I can think of much better ways to render them with to produce similar images :^). So, here's the same chart for the snare drum with increasing numbers of lights. The extra lights are scattered around the "room" and all point towards "Spanky" the snare drum.

--------------+---------+---------+---------+ Scene | Snare 1 | Snare 3 | Snare 6 | Description | Shadow | Shadow | Shadow | | Light | Lights | Lights | --------------+---------+---------+---------+ Number of | 59,692 | 59,692 | 59,692 | Triangles | | | | --------------+---------+---------+---------+ Number of | | | | Shadow Casting| 1 | 3 | 6 | Lights | | | | --------------+---------+---------+---------+ Number of Rays| 638,182 |1,097,569|1,737,021| --------------+---------+---------+---------+ "Last Object" | | | | Success Rate | 52.6% | 89.0% | 88.7% | --------------+---------+---------+---------+ "Last Voxel" | | | | Success Rate | 76.3% | 77.0% | 76.9% | --------------+---------+---------+---------+ "Last Voxel" | | | | Speed Up | 1.97% | 3.37% | 4.39% | --------------+---------+---------+---------+ Average Hits | | | | Per Ray | 0.75 | 0.67 | 0.59 | --------------+---------+---------+---------+ Average Hits | | | | Per Primary | 1.84 | 2.84 | 3.94 | Ray | | | | --------------+---------+---------+---------+

Well, the speed-up isn't quite 2% per light as I said in my previous article, but it is there. The "last voxel" trick has not slowed down the ray tracing process in any of these tests which is quite encouraging.

________________________________________________

Another helpful hint if you are ray tracing tessellated or planar surfaces: In general when spawning a shadow ray, one must be careful to avoid intersecting the object just struck. Usually this is done by adding some small epsilon to the origin of the shadow ray along it's direction of travel. However, if you store a ray id with every object (triangle) to record if that object has been tested against the current ray, then you can use that id to avoid testing your shadow ray against the intersected object which generated the shadow ray. Before spawning the shadow ray, place the id number of the shadow ray into the ray id field of the object which has just been intersected. This method won't work for objects which can self shadow (eg. parametric or implicit surfaces), but it works fine for planar surfaces (eg. triangles from surface tessellations).

- Andrew Pearce, Alias Research, Toronto, like Downtown - pearce[email protected] | [email protected]

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Real 3D FEATURES ----------------

Real 3D is design and animation program for producing high quality, realistic pictures of three dimensional objects. It provides an impressive set of advanced features including:

Ray Tracing A ray tracing of Real 3D is strongly based on the physical reality of the real world. Real 3D produces pictures by simulating the laws of physics, and consequently they represent reality with astonishing accuracy.

Speed Innovative methods and new ray tracing algorithms make Real 3D really fast. When using fastest ray tracing mode, rendering time is typically from 1 to 15 minutes.

Hierarchical With Real 3D you can create hierarchical objects. Object This means that objects you create can be made of Oriented subobjects, and these subobjects may have their Construction own substructure and so on. This kind of a tree of Objects structure is well known in the context of disk operating systems, in which you can create directories inside directories. In Real 3D counterparts of these directories are used to collect objects into logical groups. This kind of approach makes for example object modifications extremely easy, because it is possible to perform operations to logical entities. If you want to copy a DOS directory, you don't have to take care of the files and directories inside it. In the same manner, you can stretch a complex object in Real 3D as easily as one part of it.

True Solid Real 3D includes a true solid modeler. Solid model is the Model most sophisticated way to represent three dimensional objects. This modeling technique requires much computing power and therefore it has earlier been used only in environments, which are many times faster than Amiga. Now it is possible to Amiga owners to reach all the advantages of solid model, thanks to ultimate optimizations carried out when developing Real 3D.

Smoothly Curved In addition to plane surfaces, Real 3D includes several Surfaces curved surfaces, such as ball, cylinder, cone and hyperboloid. This means that no matter how much you enlarge a ball created by Real 3D, you don't find any edges or corners on its surface. Furthermore, this makes the program much faster. And what is most important, the produced pictures look really good.

Boolean Solid model allows Boolean operations between objects. Operations It is possible, for example, to split an object into two pieces and move the pieces apart so that the inner structure of the object is revealed. Operations can also be done so that the properties of the material of the target object are changed. By using a brilliant cylinder one can drill a brilliant hole into a matt object. Operations are a powerful way to create and modify objects. Especially in modeling technical objects these Boolean operations are indispensable.

Properties of A user of Real 3D is not restricted to use some basic Surfaces surface brilliancies such as matt or shiny. Instead, the light reflection properties can be freely adjusted from absolute matt to totally mirrorlike, precisely to the desired level.

Properties of Due to solid model, it is possible to create objects Materials from different materials, which have suitable physical properties. Just as surface brilliancy, also transparency of a material can be adjusted without any restrictions. Even light refraction properties are freely adjustable so that it is possible to create optical devices from glass lenses. These devices act precisely as their real counterparts: a magnifying glass in Real 3D world really magnifies!

Texture Mapping The texture mapping properties of Real 3D are not restricted to a typical chequered pattern: Any IFF picture can be used to paint objects. You can create pictures with your favorite painting program as well as with a video digitizer or a scanner. For example, by digitizing a wood filament pattern, it is easy to create wooden objects looking very realistic. Pictures can be located precisely to desired places, with desired sizes and directions. Real 3D offers as many as seven texture mapping methods, including parallel, cylinder, ball and spiral projections.

Light Sources Unlimited number of light sources of desired color and brightness. The only restriction is amount of memory.

Animation As well as you can create single pictures, you can Support create series of pictures, animations. Real 3D includes also software for representing these animations interactively. Animation representation can be directed by a script language from ascii files or even from keyboard. Instead of looping animations you can define infinitely many ways to represent your pictures. Therefore you can create animations from a small number of pictures by displaying them various ways.

Rendering Real 3D includes several different rendering techniques: Techniques a real time wireframe model, a hidden line wireframe model, a high speed one light source ray tracing model, a non-shadow-casting ray tracing model and a perfect ray tracing model. You can select either a HAM display mode with 4096 colors or a grey scale display mode offering higher resolution. Also version with 16 million color rendering (24 bits output) will become available during November 1990.

Availability When writing this document (6.9.1990), marketing of Real 3D is already started in Europe with a little lower price than that of Sculpt 4D. The distribution in the USA is not yet arranged. For further information of Real 3D, please contact:

REALSOFT KY KP 9, SF-35700 VILPPULA FINLAND

Tel. +358-34-48390

________

from "Zap" Andersson:

REAL3d ('member that?) is available (in Sweden at least) from: KARLBERG & KARLBERG AB FLADIE KYRKOVAEG S-23700 BJARRED SWEDEN Phone: +46(0)46-47450 Phax: +46(0)46-47120

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[p.s. there was also a fix to a getx11 bug for the Sun 4, which is pub/urt-SUNOS4.1-patch.tar.Z on freebie and weedeater. --EAH]

Here is the description from the patch file:

Fixed core dump in rletogif, compile warnings in giftorle. Minor update bug in getx11 fixed. getx11 now exits if all its input files are bogus. New program: rlestereo, combines two images (left and right eye) into a red-blue (or green) stereo pair. Configuration file for Interactive Systems 386/ix. Minor fix to rleskel: ignore trailing garbage in an input image.

And the list of the current archive sites, from the urt.README file in the ftp directory:

North America East coast weedeater.math.yale.edu 130.132.23.17 (pub/*) Midwest freebie.engin.umich.edu 35.2.68.23 (pub/*) West cs.utah.edu 128.110.4.21 (pub/*) Europe Sweden alcazar.cd.chalmers.se 129.16.48.100 (pub/urt/urt-3.0.tar.Z) maeglin.mt.luth.se 130.240.0.25 (pub/Utah-raster/*) Australia ftp.adelaide.edu.au 129.127.40.3 (pub/URT/*) or, if you know what this means: Fetchfile: sirius.ua.oz in URT

=Spencer W. Thomas EECS Dept, U of Michigan, Ann Arbor, MI 48109 [email protected] 313-936-2616 (8-6 E[SD]T M-F)

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#include <stdio.h> #include <math.h> #include "def.h" #include "lib.h" main(argc,argv) int argc; char *argv[]; { static double gamma = 1.0 ; /* 0.01 to 3 */ static double alpha = 1.1 ; /* > 1 */ static double beta = -2.0 ; /* ~ -2 */ static int steps = 600 ; /* ~number of spheres generated */ static double a = 0.15 ; /* exponent constant */ static double k = 1.0 ; /* relative size */ double r,x,y,z,rad,angle ; int i ; COORD4 back_color, obj_color ; COORD4 center, light ; COORD4 from, at, up ; COORD4 sphere; #define OUTPUT_FORMAT OUTPUT_CURVES /* output viewpoint */ SET_COORD( from, 6, 60, 35 ) ; SET_COORD( at, 0.0, 8.0, -15.0 ) ; SET_COORD( up, 0.0, 0.0, 1.0 ) ; lib_output_viewpoint( &from, &at, &up, 45.0, 0.5, 512, 512 ) ; /* output background color - UNC sky blue */ SET_COORD( back_color, 0.078, 0.361, 0.753 ) ; lib_output_background_color( &back_color ) ; /* output light sources */ SET_COORD( light, -100.0, -100.0, 100.0 ) ; lib_output_light( &light ) ; /* set up sphere color */ SET_COORD( obj_color, 1.0, 0.8, 0.4 ) ; lib_output_color( &obj_color, 0.8, 0.2, 100.0, 0.0, 1.0 ) ; for ( i = -steps*2/3; i <= steps/3 ; ++i ) { angle = 3.0 * 6.0 * M_PI * (double)i / (double)steps ; r = k * exp( a * angle ) ; sphere.x = r * sin( angle ) ; sphere.y = r * cos( angle ) ; /* alternate formula: z = alpha * angle */ sphere.z = beta * r ; sphere.w = r / gamma ; lib_output_sphere( &sphere, OUTPUT_FORMAT ) ; } }

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________

iear.arts.rpi.edu [128.113.6.10]:

There was an article in IEEE CG&A a while ago from Sandia National Labs (the guy's name was Mareda I think) that uses fourier transforms and digital filters to create wave height fields from white noise. What I have in the directory is an implementation of this algorithm and a program that raytraces it on the AT&T Pixel Machine.

A list of what exists in there follows:

graphics-gems: source code to Glassner's Graphics Gems book. ray-tracing-news:What else? wave: Rendering of ocean waves using fft. (Mareda, et. al.) coldith: conversion from my image format to sun rasterfiles and dithering from 32 or 24 bit -> 8 bit rasterfiles. drt: A ray-tracer from the Netherlands by Marinko Laban gk: A distributed raytracer by me. microray: DBW_uRAY by David Wecker mtv: Well, you know what this is. It probably is an old version. non-completed-OO-modeler: Something I was working on. It barely works, but I put it out there just for the fun of it. ohta: Masataka Ohta's constant time ray-tracer; with a few improvements. pxm-and-vmpxm-ray.etc: Two raytracers for the AT&T Pixel Machine. The second one uses some virtual memory code to store more objects. The VM source is included also. qrt: Well, QRT! rayshade: Rayshade 2.21 by Craig Kolb.

I hope I'll have a few anonymous ftp sessions after this.. :-)

________

Corrected FTP site list for ray tracing related material:

weedeater.math.yale.edu [130.132.23.17]: /pub - *Rayshade 3.0 ray tracer*, *color quantization code*, RT News, *new Utah raster toolkit*, newer FBM, *Graphics Gems code*. Craig Kolb ([email protected])

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. Joe Dellinger ([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. [CURRENTLY NOT AVAILABLE]

alfred.ccs.carleton.ca [134.117.1.1]: /pub/dkbtrace - *DKB ray tracer*. David Buck ([email protected])

uunet.uu.net [192.48.96.2]: /graphics - RT News back issues (not complete), other graphics related material.

iear.arts.rpi.edu [128.113.6.10]: /pub - *Kyriazis stochastic Ray Tracer*. qrt, Ohta's ray tracer, other RT's (including one for the AT&T Pixel Machine), RT News, Graphics Gems, wave ray tracing using digital filter method. George Kyriazis ([email protected])

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

```
abcfd20.larc.nasa.gov [128.155.23.64]: /amiga - DBW,
/usenet/comp.{sources|binaries}.amiga/volume90/applications -
DKBTrace 2.01. Tad Guy ([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].isi.edu)

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])

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

surya.waterloo.edu [129.97.129.72]: /graphics - FBM, ray tracers

vega.hut.fi [128.214.3.82]: /graphics - RTN archive, ray tracers (MTV, QRT, others), NFF, some models

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])

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

from J. Eric Townsend ([email protected]):

Went to lunch with a good (but non-technical) friend of mine the other day. On the way home, we were talking about what a nice day it was for lying around and reading. She mentioned that she'd gotten a Joyce Carol Oates book I was looking for and was going to read it.

I said, "I wish I had time to read something fun, but I've got to read some more ray tracing today for my special problems class."

She said, "Ray Tracing? Who's that. I don't think I've heard of him."

She thought it was funny only after I stopped laughing and took a few minutes to explain it to her.

Tomorrow, I think I'm going to add a second name to my door (we have slots for two as most RA's share offices): "Ray Tracing".

________

from Greg Richter ({emory,gatech}!bluemtn!greg)

We had a similar incident with a new secretary who informed me that a salesman had called asking about our Gator Rays. She wanted to know if we were involved in animal testing.

________

from Michael McCool ([email protected])

>She said, "Ray Tracing? Who's that. I don't think I've heard of him."

For some reason the term seems to collect fun. At SIGGRAPH in Dallas this year the Ray-tracing course organizers [Glassner & Arvo] kept bringing up the "related fields" of rat-racing and tray-racing. Last SIGGRAPH there was a "tutorial video" on tray-racing that was shown; it involved sliding trays down stairs, and gave examples of acceleration techniques, etc. One wonders.

________

from Eric Haines:

And don't forget the t-shirt (a number of Canadians, Calgarians I think, had them on): There's a picture of a nerdy guy holding a pencil and kneeling over a man laying on the ground covered with a sheet of paper. The entire figure is labeled "Ray Tracing". The caption: "Okee dokee, Ray, here comes Mr. Pencil."

John Wallace also mentioned to me seeing a poster in Denver of jewels with the words "Ray Tracy" below, as this was the jeweller's name.

For those who've moved from graduate work to the world of business, a slogan: "Once I was a ray-tracer, now I'm a rat racer."

I received the "Spherical Aberration" award from Andrew Glassner & Jim Arvo for helping organize various ray tracing things. The award was a glass sphere on a wooden base. It sat on my office windowsill until I moved to a new office one day. Looking at the award, I noticed black marks at the base. The sphere had acted like a (crummy, luckily) magnifying glass and burnt grooves in the wood! It was interesting to see how the marks seemed to correspond to the movement of the sun and the seasons. Anyway, the moral is "Caustics can be dangerous" (after all, why do you think they call them "caustic"?).

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Graphics Interface '91 is the seventeenth Canadian Conference devoted to computer graphics and interactive techniques, and is the oldest regularly scheduled computer graphics conference in the world. Now an annual conference, film festival, and tutorials, Graphics Interface has established a reputation for a high-quality technical program. The 1991 conference will be held in Calgary, Alberta, June 3-7 1991 in conjunction with Vision Interface '91. Graphics Interface '91 is sponsored by the Canadian Man-Computer Communications Society.

IMPORTANT DATES:

Four copies of a Full Paper due: 31 Oct. 1990 *** N O T E *** Tutorial Proposals due: 15 Nov. 1990 Authors Notified: 1 Feb. 1991 Cover Submissions due: 1 Feb. 1991 Final Paper due: 29 Mar. 1991 Electronic Theatre Submissions due: 1 May 1991

TOPICS:

Contributions are solicited describing unpublished research results and applications experience in graphics, including but not restricted to the following areas:

Image Synthesis & Realism User Interface Shading & Rendering Algorithms Windowing Systems Geometric Modeling Computer Cartography Computer Animation Image Processing Interactive Techniques Medical Graphics Graphics for CAD/CAM Graphics in Education Computer-Aided Building Design Graphics & the Arts Industrial & Robotics Applications Visualization Graphics in Business Graphics in Simulation

Four copies of full papers should be submitted to the Program Chairman before Oct.31 1990. Include with the paper full names, addresses, phone numbers, fax numbers and electronic mail addresses of all the authors. One author should be designated "contact author"; all subsequent correspondence regarding the paper will be directed to the contact author. The other addresses are required for follow-up conference mailings, including the preliminary program.

FOR GENERAL INFORMATION: SUBMIT PAPERS TO:

Wayne A. Davis Brian Wyvill GI '91 General Chairman GI '91 Program Chairman Department of Computing Science Department of Computer Science University of Alberta University of Calgary Edmonton, Alberta, Canada Calgary, Alberta, Canada T6G 2H1 T2N 1N1

Tel: 403-492-3976 Tel: 403-220-6009 EMail: [email protected] EMail: [email protected]

[There are often a fair number of papers on ray tracing at this conference {vs. maybe one at SIGGRAPH}, so it is a good place to consider submitting RT research. --EAH]

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> Can someone please tell me where I can find an algorithm for

> finding the intersection of a ray and a Bezier and/or B-Spline

> patch.

You might look at

Lischinski and Gonczarowski, "Improved techniques for ray tracing parametric surfaces," Visual Computer, Vol 6, No 3, June 1990, pp 134-152.

Besides having an interesting technique, they refer to most of the other relevant work.

[This entire issue is dedicated to ray tracing, and is worth checking out. -EAH]

```
--
=Spencer W. Thomas EECS Dept, U of Michigan, Ann Arbor, MI 48109
[email protected] 313-936-2616 (8-6 E[SD]T M-F)
```

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How do raytracers make light sources out of arbitrary objects? I thought a while back that one approach would be to find the direction to the object from the illuminated point, fire a random cone of rays at the object, and assign some fraction of the object's light to the point for each unobstructed ray.

The main drawback of this approach, as I see it, is that it would yield a mottled illuminated area, and the mottling would vary in a random manner.

About five minutes ago I had an idea for another approach:

- Find the 2D bounding box (from the illuminated point's view) of the illuminating object.

- From this box, get the two orthogonal basis vectors.

- Now subdivide this bounding box (using the basis vectors), just as you would the original raytrace grid.

- For each light ray fired, determine if the ray intersects the illuminating object. If it does, increment the `silhouette' counter. If the light ray intersects no other object, then increment the `light' counter.

- Once done, the light that shines on the illuminated point is (light_counter/silhouette_counter) * object_light.

This technique would also lend itself to numerous optimizations. For example, if you assume that all light objects cast a convex silhouette, then you could use binary search techniques to locate the edges of the silhouette. That is, you can assume that all scan lines will be runs of space-silhouette-space intersections, hone in on the edges, and then multiply the resulting silhouette width by the scanline height to get the relative area.

Is there a better way to do this? I haven't come across this problem in any of the graphics texts I've read.

________

Philip Schneider ([email protected]) replies:

Get in touch with the University of Washington Department of Computer Science. Two or three years ago Dan O'Donnell wrote an M.S. thesis on what he called "solid light sources". (Sorry, my copy is in a box right now, so I don't recall the exact title :-(

Real nice work, as I recall, and the resulting pictures were pretty interesting -- one of them featured a coffee mug, with steam rising from it that turned into a glowing "neon sign" light formed into the shape of the word "Espresso" (of course, I'm biased from having worked alongside him at the UW graphics lab :-)

Philip J. Schneider DEC Advanced Technology Development

[Has anyone seen this thesis? Could you give me an exact reference (for the Ray Tracing Bibliography)? --EAH]

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The authors and the publisher are pleased to release this source code to the public domain: neither the authors nor publisher hold any copyright restrictions on any of these files. The code is freely available to the entire computer graphics community for study, use, and modification. We do request that the comment at the top of each file, identifying the original author and the program's original publication in the book Graphics Gems, be retained in all programs that use these files.

Each Gem is made available on an as-is basis; although considerable effort has been expended to check the programs as originally designed and their current release in electronic form, the authors and the publisher make no guarantees about the correctness of any of these programs or algorithms.

All source files in the book are now available via anonymous ftp from site 'weedeater.math.yale.edu'. To download the files, connect to this site with an ftp program. For user name type the word 'anonymous'; for password enter your last name. When you are logged in, type 'cd pub/GraphicsGems/src'. Each program from the book is stored in its own plaintext file. I suggest you first download the file README (type 'get README', then quit ftp and open the file with any text editor); among other things it describes how to download the rest of the directory, identifies the administrator of the site (who will collect bug reports, etc.), and provides a table of contents so you can identify the source files with their corresponding Gems.

We have enjoyed putting this book together. It was a pleasure for me to work with the many talented people who contributed to the success of this project. A central theme of the book's philosophy was for the results to be practical and useful - public release of the source code is a happy result of this philosophy, shared by the authors, editor, and publisher.

We all hope this free source code is a useful resource for programmers everywhere.

________

From David Hook:

AARnet/ACSnet sites can now obtain GraphicGems source code from gondwana.ecr.mu.oz.au (128.250.1.63) via anonymous ftp in pub/GraphicsGems or through fetchfile, (for a general info file do a "fetchfile -dgondwana.ecr.mu.oz pub/GraphicsGems/GEMS.INFO" and for a general listing "fetchfile -dgondwana.ecr.mu.oz -LV pub".

Please note this is a clone site of the GraphicsGems code at weedeater.math.yale.edu, and bug reports, etc... should still be forward to the administrators there. Their addresses are listed in the GEMS.INFO and README files.

________

[I felt the following was a good way to summarize much of what "Graphics Gems" has in it. It's excellent, highly recommended (no, I don't have anything in it). Andrew Woo's trick for a quick rejection test on polygons gave me a few percent speedup on intersecting these, for example. Oddly enough, I had tried his idea earlier (Kells Elmquist independently discovered it here), but didn't get much speedup. Seeing it in print made me try it again, but this time on a variety of databases. This time it gave some speed-up - the first time I tried it on a database particularly ill-suited for performance improvement! Finding out that someone else had used it successfully encouraged me to explore further. What's his trick? You'll have to see the book... - EAH]

The table below gives the correspondence between each source file in this directory and the name of the Gem it implements. Each implementation illustrates one way to realize the techniques described by the accompanying Gem in the book. The files here contain only the source code for that realization. For a more complete description of the algorithms and their applications see the Gems of the same name in the first 11 Chapters of the book.

[Original listing removed, you can see it (and the code) at http://www.graphicsgems.org. - EAH]

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Sari Kalin Academic Press 955 Massachusetts Ave. Cambridge, MA 02139

```
tel: (617) 876-3901
email: cdp![email protected]
```

AP wants to get the book out by SIGGRAPH `91, so that means the schedule is tight. The submission deadline for first drafts is November 1, 1990, so don't delay! Also, I'm sure AP would appreciate hearing any comments you might have about the first volume.

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```
Sender: [email protected] (Steven Feiner)
Organization: Columbia University Dept. of CS
```

We're in the process of setting up a separate email account to make it easy to report bugs, suggest changes, and obtain a copy of the bug list for Computer Graphics: Principles and Practice, 2nd Ed. by Foley, van Dam, Feiner, and Hughes. Since Dave Sklar, the person who is setting up the account, is also busting to get the versions of the book's SRGP and SPHIGS graphics packages ready for their SIGGRAPH demos, the email account won't be available until after SIGGRAPH. We'll post details as soon as it's up.

Meanwhile, here are fixes for some dangling references and a missing exercise, all of which had been devoured by a hungry gremlin:

1) Dangling references:

FIUM89 Fiume, E.L. The Mathematical Structure of Raster Graphics, Academic Press, San Diego, 1989.

FOUR88 Fournier, A. and D. Fussell, ``On the Power of the Frame Buffer,'' ACM TOG, 7(2), April 1988, 103-128.

HUBS82 Hubschman, H. and S.W. Zucker, ``Frame-To-Frame Coherence and the Hidden Surface Computation: Constraints for a Convex World,'' ACM TOG, 1(2), April 1982, 129-162. [The bibliography includes HUBS81, the SIGGRAPH 81 paper on which HUBS82 was based.]

SNYD87 Snyder, J.M. and A.H. Barr, ``Ray Tracing Complex Models Containing Surface Tessellations,'' SIGGRAPH 87, 119-128.

TAMM82 Tamminen, M. and R. Sulonen. ``The EXCELL Method for Efficient Geometric Access to Data,'' in Proc. 19th ACM IEEE Design Automation Conf., Las Vegas, June 14-16, 1982, 345-351.

2) A missing exercise:

15.25 If you have implemented the z-buffer algorithm, then add hit detection to it by extending the pick-window approach described in Section 7.12.2 to take visible-surface determination into account. You will need a SetPickMode procedure that is passed a mode flag, indicating whether objects are to be drawn (drawing mode) or instead tested for hits (pick mode). A SetPickWindow procedure will let the user set a rectangular pick window. The z-buffer must already have been filled (by drawing all objects) for pick mode to work. When in pick mode, neither the frame-buffer nor the z-buffer is updated, but the z-value of each of the primitive's pixels that falls inside the pick window is compared with the corresponding value in the z-buffer. If the new value would have caused the primitive to be drawn in drawing mode, then a flag is set. The flag can be inquired by calling InquirePick, which then resets the flag. If InquirePick is called after each primitive's routine is called in pick mode, picking can be done on a per-primitive basis. Show how you can use InquirePick to determine which object is actually visible at a pixel.

```
Steve Feiner
[email protected]
```

back to contents

>This may be a stupid question, but why can't radiosity be handled by ray

>tracers? Also, are there any archives that contain code/papers on radiosity

>that I can learn from?

>Michael

Ray Tracers can indeed do radiosity. Check out the Sillion and Puech paper or the Wallace et al. paper in Siggraph '89. Also the Airey et al. paper in proceedings of the symposium of Interactive 3D graphics (Computer Graphics 24 (2)), and my Graphics Interface 90 paper. Also Heckbert's Siggraph 90 paper.

If all you want is a brute force radiosity code (and this code works pretty well), then start with N polygons. Each polygon will have reflectivity Ri and will emit power Ei. Assume you want to send R rays on the first pass. We will now do what amounts to physical simulation:

T = 0 // T is total emitted power For i = 1 to N Ui = Ei // Ui is unsent power Pi = Ei // Pi is total power estimate T = T + Ei

dP = T / R // dP is the approximate power carried by each ray For b = 1 to NumReflections For i = 1 to N r = int(Ui / dP) // patch i will send power Ui in r rays dPi = Ui / r Ui = 0 for j = 1 to r choose random direction with cosine weighting and send ray with until it hits polygon p (see Ward et al. Siggraph 88 paper equation 2 p 87)

Up = Up + Rp * dPi Pp = Pp + Rp * dPi

// Once this is done, we will have the power Pi coming from each surface, // Now we should convert to radiance (see my GI 90 paper or Kajiya's // Course notes in Siggraph 90 Advanced RT notes)

For i = 1 to N Li = Pi / (pi * Ai) // Li is radiance, pi is 3.14..., Ai is area

This ignores interpolation to polygon vertices to give a smooth image (see Cohen & Greenberg siggraph 85 figure 8A).

You might also want to check out Ward et al.'s Siggraph 88 paper. Not true radiosity, but is ray tracing based and has some of the best features of ray tracing methods. If your scene is all diffuse, that method may be the way to go.

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>Rather than using recursive or hierarchical

>spatial subdivision techniques to reduce ray-object intersection tests

>(which are of O(log n) algorithms)

Can you prove it? I think (but can't prove) hierarchical spatial subdivision is only O(n**(1/3)).

>many instances can use a surface map for

>a single bounding volume as a lookup table to immediately determine a small

>subset of objects to test (which is truly of O(1)). (Small subset here is

>roughly equivalent to the set of objects in the smallest volume in a

>comparable hierarchical scheme.)

I already published an O(1) ray tracing algorithm (See "An introduction to RAY TRACING" edited by Andrew S. Glassner, Academic Press, 6.3 The Ray Coherence Algorithm, page 232-234, or, "Computer Graphics 1987 (Proc. of CG International '87)", page 303-314, Ray Coherence Theorem and constant time ray tracing algorithm).

Judging from the above brief description of your algorithm, it may be similar or identical to mine.

>It's *not* general,

Hmmm, mine is general.

________

Kaplan also has claimed a constant time algorithm. I don't believe that his is constant time - it (like an octree) is a divide and conquer search, so it will AT BEST be O(logN) (it takes O(logN) time to travel down the height of a tree).

I don't really see how we can even say what the big-O of a ray intersection is without precisely stating what rays are allowed on what geometry. For example, suppose I set up N epsilon radius spheres in random locations within a cube, where epsilon is small. In the typical case a ray might come close to many spheres. If an octree is used, the candidate sets of many leaves might be checked (worse than O(logN)). If all of the spheres have the same center, how can any scheme get a candidate set for a ray through the center that doesn't include all spheres? This would be O(NlogN) for an octree and O(N) optimally. How would your method be O(1)? It seems that often we have good algorithm behavior in practice with pathological cases giving terrible big-Os. Perhaps we can bound the set of scenes somehow?

________

Ohta replies:

>Kaplan also has claimed a constant time algorithm. I don't believe that

>his is constant time--

I agree with you. I know what is O(1).

>I don't really see how we can even say what the big-O of a ray intersection

>is without precisely stating what rays are allowed on what geometry.

Well, it is assumed that, ray object intersection calculation takes only constant time. That is, to ray trace a surface defined by N-th degree polynominal in constant time regardless to N, is just impossible.

>For example, suppose I set up N epsilon radius spheres in random locations

>within a cube, where epsilon is small. In the typical case a ray might

>come close to many spheres. If an octree is used, the candidate sets

>of many leaves might be checked (worse than O(logN)). If all of the spheres

>have the same center, how can any scheme get a candidate set for a ray

>through ythe center that doesn't include all spheres? This would be

>O(NlogN) for an octree and O(N) optimally. How would your method be O(1)?

Good question. But, first, we should make it clear what is constant time ray tracing. As for the per-scene complexity, no algorithm (including your first example) can be better than O(N) just because of input complexity (reading all the input takes O(N) time). So, we should talk about complexity to trace a single ray.

My algorithm may consume possibly long and computationally complex pre-processing time to analyze a scene. But, the important fact is that the time for pre-processing is dependent only on the scene and not on the number of rays.

And, after pre-precessing, all rays can be traced in constant time.

With your example of co-centric spheres (assuming epsilon radius is different on each sphere, or the problem is reduced to too trivial to trace a single sphere), each sphere should further be subdivided into smaller pieces to obtain constant time property. With such a finer subdivision, even octree method may be able to do better than O(NlogN).

>It seems that often we have good algorithm behavior in practice with

>pathological cases giving terrible big-Os. Perhaps we can bound the set

>of scenes somehow?

It may be reasonable to define complexity of a scene by the complexity of pre-processing to obtain constant-timeness.

________

In a separate note, Ohta writes:

>Can you prove it? I think (but can't prove) hierarchical spatial

>subdivision is only O(n**(1/3)).

I have found it is obvious. All spatial subdivision is at most O(n**(1/3)) if

1) Objects are tiny 2) Objects are uniformly scattered in space

1) means that the possibility of intersection is negligible. 2) means at least O(n**(1/3)) subspace must be traversed.

back to contents

The solution proposed by [email protected] was based upon the Jordan Curve theorem: any ray from inside a polygon crosses an odd number of edges on its way to infinity. He chose a random ray that began at the point in question, and counted the number of intersections. Problem: if you intersected a vertex you were kind of clueless. Solution, fire another ray.

You solve these problems by simplifying everything. The ray you shoot should go to the positive X axis. Assume without loss of generality that your point is the origin. Now: if you are going to intersect a vertex, its because the y component of an edge endpoint is == 0. Well, decide whether you want to count this as positive or negative. Assume positive (I always do). It turns out you get the right answer anyway. For example

origin ^ | o o counts as one intersection | v

origin ^ ^ |/ o o counts as zero or two intersections

origin

o o counts as zero or two intersections |\ v v

Voila! C'est explique!

[and in a later note:]

Hardly my own idea. It was shown to me by Eric Haines originally, but I don't think he claims credit for it either. Any takers? Is it patented by Unisys as well :-)?

________

Eric Haines [the crazy fool!] replies:

Anyway, having an ego and all that, I do indeed claim to be the inventor of the "consider all points on the line to be above the line" solution, which gets rid of those pesky special cases where vertices are on the test ray. I started with some very complicated special case code in 1986 which worried about whether the points were on the ray. Months went by... One day, looking at the code, I noticed another stupid special case that I didn't handle correctly (something like "if the last point is on the ray and the first point is on the ray..."). I looked at the problem again and realized that the only property of the ray that I really cared about was that it was a divider, not that it was a set of points forming a ray. Eureka, Arkansas! Get rid of those points, and so define away the problem - no points can lie on the ray, if we define the ray as having no points. O happy day, it even worked. Anyway, it's all written up in my section of "An Introduction to Ray Tracing", edited by Andrew Glassner, Academic Press.

Historical note: the earliest reference I have to the point in polygon test is the classic "A Characterization of Ten Hidden-Surface Algorithms" by Ivan Sutherland et al, 1974, ACM Computing Surveys v6 n1. This has both the ray crossing test and the sum of the angles test, plus the convex polygon test (check if the point is inside all lines by substitution into each edge's 2D line equation).

Computational geometry fiends noted that the method has the problem of being indeterminate on edges: if your intersection point is exactly on an edge, it's arbitrary whether the point is determined to be inside or outside the polygon (that is, do you consider an edge crossing the point to be to the right or left of the point, or do you want a third category, such as "on"?).

However, there is a general consistency to the ray crossing test for ray tracing. If the point being tested is along the edge joining two visible polygons (which both face the same general direction, i.e. not a silhouette edge) and the polygons are projected consistently upon the plane perpendicular to the ray, the point is guaranteed to be considered to be inside one and only one of the polygons. That is, no point will be considered within any two non-overlapping polygons, nor will it "fall in the crack" between polygons.

Think about it this way: if points on the left edges of the polygon are considered outside, then the points on the right edges will be considered inside. This is because we would then consider an edge crossing the x axis at exactly 0 as being to the right of the test point. Since one polygon's left edge is another's right edge, it all balances out to make each point be inside only one polygon in a polygon mesh. Horizontal edges are treated the same way: if a point is actually on such an edge, when tested, the point will be categorized as "below" the edge consistently. This will lead it to be inside one and only one polygon in a mesh.

In reality, when ray tracing you very rarely get points that are exactly on an edge, so this is something of a non-problem. But if you really really care about this possibility, make sure to always cast your polygons onto the plane perpendicular to the ray (this plane is also good for consistency if you want to get edges for Gouraud RGB interpolation, Phong normal interpolation, etc).

Finally, for you incredibly demonic CompGeom types: yes, indeed, points on silhouette edges are still inconsistent.

P.S. As our patent on the 90 degree angle was successful, the pending patent on the Jordan Curve Theorem should come through any day now... ;-)

________

Edward John Kalenda replies:

Sorry to be a poop Eric, but my boss at Calma, Steve Hoffman, told me about the "points on the ray are above the ray" thing in 1981. He claimed someone told HIM several years before.

I think it's one of those things that just need to be attributed to the anonymous coder.

________

I reply:

Oh, well, at least I can claim to be the first to publish! Sadly enough, the word still hasn't fully percolated out. The latest Foley & Van Dam (& Feiner & Hughes) says on page 34: "Next, choose a ray that starts at the test point and extends infinitely in any direction, and that does not pass through any vertices". Page 339 makes reference to "intersections at vertices" being a "special case". Passing through a vertex is still considered to be a problem (even though it isn't).

It's this kind of thing that makes me happy to see books like "Graphics Gems" come out. Letting the world know about the little tricks of the trade saves us all a lot of time and replication of effort (I sure wish I had known about the "above the ray" trick in 1986 - it would have saved me hours of struggle).

________

Richard Parent ([email protected]) writes:

With respect to 'consider all the points on the line to be above the line', both Steve Levine (Ph.D. from Stanford, I believe) and myself discussed this as a solution we used in our respective problems; mine was implementing Lourtrel's hidden line routine and I imagine his had to do with the hierarchical clipping he was doing. This was at one of the Siggraph's in the mid to late seventies, '76, if I had to guess. It's been around for awhile.

________

I reply:

I guess I could compare myself to Leibniz vs. Newton (both independently discovering calculus), but I'm probably more in the class of the guy that discovers that Wintergreen Life Savers give off sparks when chewed in the dark.

________

Sam Uselton writes:

I've been off news for a few days and just saw your posting of sept 6. Isn't the "consider all points on the line to be above the line" the same as "shortening an edge to prevent the vertex lying on the scan line" as suggested in Foley & Van Dam (the old one) when describing polygon scan conversion? That's not the first place I heard this idea either, it was just the easiest reference to grab off the shelf.

I think this is one of those solutions that is just subtle enough that most people don't think of it themselves and think it is neat when they see it but just obvious enough that a few people every year re-invent it, and go showing it around to others. Just the kind of thing IMHO that makes Glassner's collection and the RTNews such useful things, because it probably couldn't get published "traditionally" .

Trying VERY hard to pull up archival storage, I'm pretty sure I saw this first while still at UTD in grad school, which means Henry Fuchs was probably explaining it. Whether he is one of the many originators or he got it from a fellow Utah grad student, I couldn't guess. (Oh, yeah. Time? 1975-1979).

________

I note:

For scan conversion it is still a bit tricky: you have to think a bit about where edges begin and end (you want edges with vertices exactly on the scan line to be handled correctly, e.g. if the edge's maximum y ends on the scan line, delete this edge just before checking scan line). This kind of problem goes away for ray tracing, since you don't have to worry about active edges, etc.

________

Sam replies:

After a weekend of R&R old memory is more easily accessible. I seem to associate my first connection with point in polygon/ ray intersection/ Jordan curve theorem/etc etc to an informal seminar, led by Henry Fuchs and Zvi Kedem, attended by Alain Fournier, Don Fussell, Jose Barros, myself, and I think Bruce Naylor, in which we read and studied early Michael Shamos papers (Shamos & Hoey, Bentley & Shamos...). Must have been about 1978 or so.

________

I reply:

Thanks for the info. What I find amazing about all this is that somewhere, somewhere this was not mentioned in the ray tracing literature before "An Intro to RT". Until you (and others) pointed out that this problem and solution is analogous to the scan-line problem, I honestly hadn't made the connection! Nor, it seems, had anyone else in print. Sedgewick's "Algorithms" talks about this problem but doesn't give a "points above the ray" solution, Berlin in 1985 SIGGRAPH course notes gives a few solutions to the problem, but says that test rays through vertices are a special case & are very nasty. Certainly Cornell's ray tracer didn't solve this problem. Glassner used the sum of the angles method, so he didn't know about it, so UNC didn't know about it. Sounds like somewhere out west was the point of origin, but it never made it east of the Mississippi. Curious.

Sutherland et al's 1974 paper "A Characterization of Ten Hidden Surface Algorithms" mentions the problem as a problem ("care is required to get consistent results"). Anyway, sounds like there probably wasn't a solution before them (if anyone would know, I would think it would be them). Interesting puzzle to try to figure out the identity of this anonymous programmer.

________

From "Zap" Andersson:

As I think I posted earlier, this is somewhat similar to my own approach in getting rid of special cases: Assume we are testing for a ray along X axis... For all line segments, swap 'em, so it's "first" point is upwards (Have a lower Y coordinate). Then, for each segment, test if the point's Y > firstY. If not, discard (This, in essence, is a version of Eric's idea, only mine :-) then, check if Y <= lastY. If not, discard. IMPORTANT ISSUE HERE is that I actually CARE about the 'second' point of the line, and include it in the check, that's MY way of getting rid of problem of a corner pointing downwards: It will yield 2 intersections, Eric's method yields none. No big deal, really.... after this simple boundstest, it's time for the dreary math on checking if the intersection is on POSITIVE X, i.e. if X > firstX && X > lastX, discard, and last but not least, check the real intersection with some math (Left as an exercise for the reader :-).

OBTW, fr'got! FIRST, you check if (LastY - Y) * (FirstY - Y) is > 0. If so, discard.

________

Bruce Holloway posts:

In article ([email protected]) [email protected] writes:

>

>In article ([email protected]), [email protected] (Peter

>da Silva) writes:

>|> In article ([email protected]) [email protected] (Edward

>John Kalenda) writes:

>|> > Sorry to be a poop Eric, but my boss at Calma, Steve Hoffman, told me

>|> > about the "points on the ray are above the ray" thing in 1981. He claimed

>|> > someone told HIM several years before.

>|> >

>|> > I think it's one of those things that just need to be attributed to the

>|> > anonymous coder.

>|>

>|> Another of those obvious techniques like the XOR-cursor. Good thing nobody

>|> patented *this* one...

>

>I didn't see any smiley's after this one Peter. I'm sure that

>many readers don't realize that the XOR-cursor in hardware *IS* patented.

>

>... and that's not the only obvious technique that this particular

>company has a patent on.

This thread is a riot. My old boss at Calma, Joe Sukonick, patented the XOR-cursor technique based on work he did around 1974, when I went to work there. I remember meeting Jim Clark for the first time around 1979 in front of Stacey's bookstore in Palo Alto before he became famous for the Geometry Engine. He was married to a friend of mine from Calma (whom we were all in love with!) & said he didn't think Joe's patent was valid because it wasn't original. I agree with him.

One of the things the patent says is that XOR works because it is "idempotent". Joe had a Ph.D. in math from MIT & liked to use words like that, but I thought AND & OR were idempotent & XOR worked because it wasn't! What you need is any operation that can be undone, or inverted, like ADD, say. (What is XOR but an ADD without carry?) Anyway, the patent is now owned by Cadtrak, a corporate shell whose charter is to sue everyone under the sun over that patent. Last I heard, Western Digital was going to take them to court to overturn it.

Now as to the "points on the ray are above the ray", this is really the same as the idea of half-open intervals which has broad usage in computer graphics. When you point-sample a polygon, this is how you make sure that rectangles of area m*n hit exactly m*n pixels, even if they lie on your sample grid. When I was just a kid at Calma, I wrote two programs that used that idea. One was a program to cross-hatch concave (and convex) polygons for making plots of overlapping layers on ICs. Another was a program which intersected arbitrary closed polygons with each other. This was an application program written in Calma's GPL which was used to calculate the capacitance between layers of a chip, by finding the areas of all the overlaps. Both of these algorithms needed to use the half-open idea to take care of the corner cases.

I left Calma in 1976, too inexperienced to realize what a singular place it had been. After the ownership changed, most everyone scattered to the four corners of the globe. Later, I actually had a contract job working for Cal & Irma Hefte, the founders of Calma. Cal passed away some years ago-- he seemed to me to be a lot like Willy Loman in "Death of a Salesman". He told me "people are the most complicated & interesting things in the world". Mrs. Hefte and her daughters have a flower shop on Blossom Hill Rd. A genuine Silicon Valley story! (There's a lot more.)

*more discussion of topic* (there is also more below)

back to contents

In article ([email protected]) [email protected] (Raymond Chen) writes:

>Nobody yet has mentioned my favorite method for point-in-polygon

>detection: Using the winding number.

[...]

>/* Point in polygon detection. Original author unknown.

> * Except where noted, I have NOT edited the code in any way.

> * I didn't even fix the misspellings. (And no, I don't code

> * in this style.)

> */

[...]

> return(quad); /**rjc**/ /* for some reason, the original

> author left out this crucial line! */

>}

>--

>A remark: The whichquad function is not perfect. It doesn't handle

>the boundary cases right (but as I said, that's only a problem

>if the point lies on the polygon).

(After a long-overdue search through my archives...)

The code was posted to comp.graphics in February of '88 by Ken McElvain (decwrl!sci!kenm). Regarding the typos and the boundary cases, Ken wrote:

> I pulled this out of some other code and hopefully didn't break it in

> doing so. There is some ambiguity in this version as to whether a point

> lying on the polygon is inside or out. This can be fairly easily

> detected though, so you can do what you want in that case.

I once did a number of tests on Ken's winding number code and an implementation of the 'ray' algorithm, using a ray tracer (rayshade). For the test scenes I rendered, I found that the winding number method was approximately 10% faster than the ray method. Your mileage may vary.

[It surprises me that this algorithm is ever faster: the infinite ray solution is essentially the same idea as the quadrant idea, except that it avoids x compares when the signs of the y components are the same. Maybe I'll hack rayshade & prove it someday... -- EAH]

```
From: [email protected] (Ken McElvain)
Organization: Silicon Compilers Systems Corp. San Jose, Ca
```

In article ([email protected]), [email protected] (W. Harry Plantinga) writes:

> In article ([email protected]) [email protected] (Robert Beaty) writes:

> >In article ([email protected]) [email protected] (Rick Dorris) writes:

> >>In article ([email protected]) [email protected] (Jim @ MAC) writes:

> >>>Have a nice one here:

> >>>Have a boundary defined on the screen. Boundary is composed of points

> >>>joined by lines... Now some random points are generated and I want to check

> >>>if a given point is within or outside the existing boundary.. Any algorithm for

> >> <rick suggests the infinite ray/intersection counting algorithm>

> >

> >I have seen this type of algorithm before and the one I thought up

> >in an afternoon is FAR superior and vastly simpler to code up.

> >

> ><robert beaty suggests an algorithm that measures sums the angles of

> >the lines connecting the points and the test point>

>

> Haven't I seen this discussion of point-in-polygon algorithms about 15

> times before? :-)

>

> Robert, your algorithm is simpler only in the kind of problems it

> handles. It will only work for convex polygons, whereas the other

> works for any polygons. It's not even much simpler; measuring angles

> and determining whether line segments intersect are of comparable

> difficulty.

>

> Maybe you should have said that although your algorithm is far

> inferior, it's not any easier to code?

Robert's suggestion is a good one. The sum of the angles about the test point is known as the winding number. For non intersecting polygons if the winding number is non-zero then the test point is inside the polygon. It works just fine for convex and concave polygon's. Intersecting polygon's give reasonable results too. A figure 8 will give a negative winding number for a test point in one of the loops and a positive winding number for the other loop, with all points outside having a winding number of 0. Other advantages of the winding number calculation are that it does not suffer from the confusion of the infinite ray algorithm when the ray crosses a vertex or is colinear with an edge.

Here is my version of a point in poly routine using a quadrant granularity winding number. The basic idea is to total the angle changes for a wiper arm with its origin at the point and whos end follows the polygon points. If the angle change is 0 then you are outside, otherwise you are in some sense inside. It is not necessary to compute exact angles, resolution to a quadrant is sufficient, greatly simplifying the calculations.

I pulled this out of some other code and hopefully didn't break it in doing so. There is some ambiguity in this version as to whether a point lying on the polygon is inside or out. This can be fairly easily detected though, so you can do what you want in that case.

-------- /* * Quadrants: * 1 | 0 * ----- * 2 | 3 */

typedef struct { int x,y; } point;

pointinpoly(pt,cnt,polypts) point pt; /* point to check */ int cnt; /* number of points in poly */ point *polypts; /* array of points, */ /* last edge from polypts[cnt-1] to polypts[0] */ { int oldquad,newquad; point thispt,lastpt; int a,b; int wind; /* current winding number */

wind = 0; lastpt = polypts[cnt-1]; oldquad = whichquad(lastpt,pt); /* get starting angle */ for(i=0;i<cnt;i++) { /* for each point in the polygon */ thispt = polypts[i]; newquad = whichquad(thispt,pt); if(oldquad!=newquad) { /* adjust wind */ /* * use mod 4 comparisons to see if we have * advanced or backed up one quadrant */ if(((oldquad+1)&3)==newquad) wind++; else if((((newquad+1)&3)==oldquad) wind--; else { /* * upper left to lower right, or * upper right to lower left. Determine * direction of winding by intersection * with x==0. */ a = lastpt.y - thispt.y; a *= (pt.x - lastpt.x); b = lastpt.x - thispt.x; a += lastpt.y * b; b *= pt.y;

if(a > b) wind += 2; else wind -= 2; } } lastpt = thispt; } return(wind); /* non zero means point in poly */ }

/* * Figure out which quadrant pt is in with respect to orig */ int whichquad(pt,orig) point pt; point orig; { if(pt.x < orig.x) { if(pt.y < orig.y) quad = 2; else quad = 1; } else { if(pt.y < orig.y) quad = 3; else quad = 0; } return ( quad ) ; /* [I added the fix - EAH] */ }

Ken McElvain decwrl!sci!kenm

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Additions, corrections, etc. are welcome to the list. Thank you all who helped me.

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What? =====

IEEE Trans. on Pattern Analysis and Machine Intelligence,

IEEE Trans. on Systems, Man, and Cybernetics

Journal of the Discrete and Computational Geometry

Machine Vision and Applications

Pattern Recognition -Available from: Pergamon

Pattern Recognition Letters -Available from: North-Holland

Symposium on Computational Geometry

Symposium on Foundation of CS -One or two papers a year on geometry

Symposium on Theory of Computing

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Eric Haines / [email protected]