_ __ ______ _ __ ' ) ) / ' ) ) /--' __. __ , --/ __ __. _. o ____ _, / / _ , , , _ / \_(_/|_/ (_/_ (_/ / (_(_/|_(__<_/ / <_(_)_ / (_ 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 > Maxdist ) return MISSED If ( T > Tnear ) Tnear = T Normal = plane.normal Else /* back face - T is a far point */ If ( T < 0.0 ) return MISSED If ( T < Tfar ) Tfar = T If ( Tnear > Tfar ) return MISSED endfor return HIT At the end, Tnear is the intersection distance and Normal is the surface normal. Tfar is the exit distance, if needed. 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. ------------------------------------------------------------------------------- New Radiosity Bibliography Available, by Eric Haines A bibliography of publications related to radiosity is now available at: 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. ------------------------------------------------------------------------------- A Suggestion for Speeding Up Shadow Testing Using Voxels, by Andrew Pearce 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%alias@csri.utoronto.ca | pearce@alias.UUCP ------------------------------------------------------------------------------- Real3d, passed on by Juhana Kouhia (jk87377@tut.fi) and "Zap" Andersson [This was an advertisement on some amiga board.] 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 ------------------------------------------------------------------------------- Utah Raster Toolkit Patch, by Spencer Thomas The first patch for the Utah Raster Toolkit version 3.0 is now available. The patch file is urt-3.0.patch1, and is currently available from cs.utah.edu and freebie.engin.umich.edu, and will soon be available from our other archive sites (depending on how quickly the archive maintainers grab the patch file). There are also slight changes to the files urt-img.tar and urt-doc.tar (in particular, if you had trouble printing doc/rle.ps, this is fixed). [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 spencer@eecs.umich.edu 313-936-2616 (8-6 E[SD]T M-F) ------------------------------------------------------------------------------- NFF Shell Database, by Thierry Leconte (Thierry.Leconte@irisa.fr) [Below is Thierry Leconte's code for an NFF version of the seashell generator I listed last issue. He added some reasonable lights and a view (which I was too lazy to do). I'll probably add it to the 3.0 version of the SPD. Setting "steps" is similar to an SPD SIZE_FACTOR type control. You'll need the SPD to compile and link this program. -- EAH] #include #include #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 ) ; } } ------------------------------------------------------------------------------- FTP list update and New Software, by Eric Haines, George Kyriazis I posted my FTP site list for ray tracing related stuff, and a few people were nice enough to write and update this list. The new list is posted after this note from George Kyriazis at RPI (his site has the friendliest login I've ever seen): -------- 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 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 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 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 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 life.pawl.rpi.edu [128.113.10.2]: /pub/ray - *Kyriazis stochastic Ray Tracer*. George Kyriazis xanth.cs.odu.edu [128.82.8.1]: /amiga/dbw.zoo - DBW Render for the Amiga (zoo format). Tad Guy munnari.oz.au [128.250.1.21]: */pub/graphics/vort.tar.Z - CSG and algebraic surface ray tracer*, /pub - DBW, pbmplus. David Hook cs.utah.edu [128.110.4.21]: /pub - *Utah raster toolkit*. Spencer Thomas gatekeeper.dec.com [16.1.0.2]: /pub/DEC/off.tar.Z - *OFF objects*, /pub/misc/graf-bib - *graphics bibliographies (incomplete)*. Randi Rost abcfd20.larc.nasa.gov [128.155.23.64]: /amiga - DBW, /usenet/comp.{sources|binaries}.amiga/volume90/applications - DKBTrace 2.01. Tad Guy expo.lcs.mit.edu [18.30.0.212]: contrib - *pbm.tar.Z portable bitmap package*, *poskbitmaptars bitmap collection*, *Raveling Img*, xloadimage. Jef Poskanzer 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 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 irisa.fr [131.254.2.3]: */iPSC2/VM_pRAY ray tracer*, /NFF - many non-SPD NFF format scenes. Didier Badouel 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 - netlib@ornl.gov. *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 ======== USENET cullings follow =============================================== Humorous Anecdotes, by J. Eric Townsend, Greg Richter, Michael McCool, Eric Haines from J. Eric Townsend (jet@uh.edu): 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 (mccool@dgp.toronto.edu) >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"?). ------------------------------------------------------------------------------- G r a p h i c s I n t e r f a c e ' 9 1 Calgary, Alberta, Canada 3-7 June 1991 CALL FOR PARTICIPATION 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: usersams@ualtamts.bitnet EMail: blob@cpsc.ucalgary.ca [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] ------------------------------------------------------------------------------- Parametric Surface Reference, by Spencer Thomas In article <3632.26f78d3f@cc.curtin.edu.au> Kessells_SR@cc.curtin.edu.au writes: > 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 spencer@eecs.umich.edu 313-936-2616 (8-6 E[SD]T M-F) ------------------------------------------------------------------------------- Solid Light Sources Reference, by Steve Hollasch, Philip Schneider from: comp.graphics Steve Hollasch (hollasch@enuxha.eas.asu.edu) writes: 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 (pjs@decwrl.dec.com) 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] ------------------------------------------------------------------------------- Graphics Gems Source Code Available, by Andrew Glassner, David Hook As many readers of the usenet are aware, at Siggraph '90 Academic Press released a new book, "Graphics Gems" (edited by Andrew Glassner, published by Academic Press, Cambridge MA, 864 pp, $49.95, ISBN 0-12-286165-5). The book is a compilation of many people's work, showing how they solved important problems in computer graphics. Many of the Gems are realized with ready-to-run C implementations, presented in two appendices. 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. ---------- header files ---------- GraphicsGems.h / Graphics Gems C Header File ---------- C code ---------- 2DClip / Two-Dimensional Clipping: A Vector-Based Approach AALines / Rendering Anti-Aliased Lines AAPolyScan.c / Fast Anti-Aliasing Polygon Scan Conversion Albers.c / Albers Equal-Area Conic Map Projection BinRec.c / Recording Animation in Binary Order For Progressive Temporal Refinement BoundSphere.c / An Efficient Bounding Sphere BoxSphere.c / A Simple Method for Box-Sphere Intersection Checking CircleRect.c / Fast Circle-Rectangle Intersection Checking ConcaveScan.c / Concave Polygon Scan Conversion DigitalLine.c / Digital Line Drawing Dissolve.c / A Digital "Dissolve" Effect DoubleLine.c / Symmetric Double Step Line Algorithm FastJitter.c / Efficient Generation of Sampling Jitter Using Look-up Tables FitCurves.c / An Algorithm for Automatically Fitting Digitized Curves FixedTrig.c / Fixed-Point Trigonometry with CORDIC Iterations Forms.c / Forms, Vectors, and Transforms GGVecLib.c / 2D And 3D Vector C Library HSLtoRGB.c / A Fast HSL-to-RGB Transform Hash3D.c / 3D Grid Hashing Function HypotApprox.c / A Fast Approximation to the Hypotenuse Interleave.c / Bit Interleaving for Quad- or Octrees Label.c / Nice Numbers for Graph Labels LineEdge.c / Fast Line-Edge Intersections On A Uniform Grid MatrixInvert.c / Matrix Inversion MatrixOrtho.c / Matrix Orthogonalization MatrixPost.c / Efficient Post-Concatenation of Transformation Matrices Median.c / Median Finding on a 3x3 Grid NearestPoint.c / Solving the Nearest-Point-On-Curve Problem and A Bezier Curve-Based Root-Finder OrderDither.c / Ordered Dithering PixelInteger.c / Proper Treatment of Pixels As Integers PntOnLine.c / A Fast 2D Point-On-Line Test PolyScan / Generic Convex Polygon Scan Conversion and Clipping Quaternions.c / Using Quaternions for Coding 3D Transformations RGBTo4Bits.c / Mapping RGB Triples Onto Four Bits RayBox.c / Fast Ray-Box Intersection RayPolygon.c / An Efficient Ray-Polygon Intersection Roots3And4.c / Cubic and Quartic Roots SeedFill.c / A Seed Fill Algorithm SquareRoot.c / A High-Speed, Low-Precision Square Root Sturm / Using Sturm Sequences to Bracket Real Roots of Polynomial Equations TransBox.c / Transforming Axis-Aligned Bounding Boxes TriPoints.c / Generating Random Points In Triangles ViewTrans.c / 3D Viewing and Rotation Using Orthonormal Bases ------------------------------------------------------------------------------- Graphics Gems Volume 2 CFP, by Sari Kalin This is a quick note to let everyone know that Academic Press will be publishing a sequel to the book GRAPHICS GEMS, edited by Andrew Glassner. Since Andrew decided to take a breather from editing books, I'll be doing the honors this time around. So, if you're interested in contributing a clever graphics algorithm or insight (i.e. a "Gem") to the new volume, contact Sari Kalin (the editor at Academic Press) and she'll send you an author's packet. Here's the address: Sari Kalin Academic Press 955 Massachusetts Ave. Cambridge, MA 02139 tel: (617) 876-3901 email: cdp!skalin@labrea.stanford.edu 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. ------------------------------------------------------------------------------- Foley, Van Dam, Feiner and Hughes "Computer Graphics" Bug Reports, by Steve Feiner Sender: feiner@cs.columbia.edu (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 feiner@cs.columbia.edu ------------------------------------------------------------------------------- Radiosity via Ray Tracing, by Pete Shirley (shirley@iuvax.cs.indiana.edu) from: comp.graphics kaufman@delta.eecs.nwu.edu (Michael L. Kaufman) writes: >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. ------------------------------------------------------------------------------- Algorithm Order Discussion, by Masataka Ohta, Pete Shirley In article <1150@mti.mti.com> adrian@mti.UUCP (Adrian McCarthy) writes: >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. ------------------------------------------------------------------------------- Point in Polygon, One More Time..., by Mark Vandewettering, Eric Haines, Edward John Kalenda, Richard Parent, Sam Uselton, "Zap" Andersson, and Bruce Holloway Mark VandeWettering writes about the point in polygon test: The solution proposed by rusmin@twinsun.com 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 (parent@cis.ohio-state.edu) 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 <1990Sep11.163420.13592@odin.corp.sgi.com> robert@sgi.com writes: > >In article , peter@ficc.ferranti.com (Peter >da Silva) writes: >|> In article <33619@cup.portal.com> ekalenda@cup.portal.com (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.) ------------------------------------------------------------------------------- Quadrant Counting Polygon In/Out Testing, by Craig Kolb, Ken McElvain from: comp.graphics [After all that, I thought it was worth posting some real live code, but instead for a quadrant counting method that is almost the same as the point in polygon ray test. The "infinite ray" test is really counting quadrants (in "An Intro to RT" I show how you can get the winding number using it), but does not bother to evaluate the exact quadrant unless need be. For example, if both endpoints of an edge are in the +Y space, we have no need to evaluate whether we're in +X or -X. -EAH] In article <1990Mar29.171010.28348@agate.berkeley.edu> raymond@sunkist.UUCP (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: kenm@sci.UUCP (Ken McElvain) Organization: Silicon Compilers Systems Corp. San Jose, Ca In article <5305@spool.cs.wisc.edu>, planting@speedy.cs.wisc.edu (W. Harry Plantinga) writes: > In article <7626@pur-ee.UUCP> beatyr@pur-ee.UUCP (Robert Beaty) writes: > >In article <20533@amdcad.AMD.COM> msprick@amdcad.UUCP (Rick Dorris) writes: > >>In article <971@ut-emx.UUCP> jezebel@ut-emx.UUCP (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 > >> > > > >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. > > > > >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 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 ------------------------------------------------------------------------------- Computer Graphics Journals, by Juhana Kouhia (jk87377@tut.fi) Here is a list, not as good as it could be. I would like to see a short descriptions about each journals on it. I would like to see more information about geometry related journals or journals that covers this newsgroup subjects. End of this list has list of journals, which was suggested to me, but I didn't find enough information about them or I was too lazy to find anything. If somebody has suggestions what to do with them, please let me know. Additions, corrections, etc. are welcome to the list. Thank you all who helped me. Computer Graphics, Geometry, Image Processing Journals ====================================================== ACM Transactions On Graphics ---------------------------- -Quarterly -Available from: Association For Computing Machinery 11 West 42 Street New York, NY 10036 USA Computer Aided Design --------------------- -10 issues / year -Available from: Butterworth Scientific Ltd. 88 Kingsway London WC2 6AB England Computer Graphics ----------------- -Includes SIGGRAPH conference proceeding -Includes SIGGRAPH panel proceeding -Available from: Association For Computing Machinery 11 West 42 Street New York, NY 10036 USA -Also available from: Academic Press Computer Graphics Forum ----------------------- -Journal of the European Association of Computer Graphics (EuroGraphics) -Available from: Elsevier Science Publishers B.V. Journals Department P.O. Box 211 1000 AE Amsterdam The Netherlands Computer Graphics World ----------------------- -Professional graphical application and industrial use -Monthly -Available from: PennWell Publishing Company 119 Russell Street P.O. Box 457 Littleton, Massachusetts 01460-0457 USA Computer Images International ----------------------------- -Professional graphical application and industrial use -Monthly -Available from: P.O. Box 109 Maclaren House Scarbrook Road Croydon CR9 1QH England Phone: 01-688 7788 Telex: 946665 Fax: 01-681 1672 Computers & Graphics -------------------- -Available from: Oxword Books (GB) Computer Vision, Graphics and Image Processing ---------------------------------------------- -Available from: Academic Press ---> [split 1991] Computer Vision, Graphics and Image Processing: Graphical Models and Image Processing ----------------------------------------------- -Available from: Academic Press Computer Vision, Graphics and Image Processing: Image Understanding ----------------------------------------------- -Available from: Academic Press Graphics Interface ------------------ -Proceedings of Canadian computer graphics convention -Available from in Canada: Canadian Information Processing Society 243 College Street, 5th Floor Toronto, Ontario M5T 2Y1 (416)-593-4040 -Available from in USA: Morgan Kaufmann Publishers Order Fulfillment Center PO Box 50490 Palo Alto, CA 94303 USA (415)-965-4081 IEEE Computer Graphics & Applications ------------------------------------- -Monthly -Available from: IEEE Computer Society Circulation Department P.O. Box 3014 Los Alamitos, CA 90720-9804 USA Image and Vision Computing -------------------------- -Image analysis -Available from: Butterworth Scientific Ltd. 88 Kingsway London WC2 6AB England Pixel ----- -Available from: Pixel Communications, Inc. 245 Henry St., Suite 2-G Brooklyn, NY 11201 USA Phone: (718) 624-3386 Signal Processing: Image Communication -------------------------------------- -A publication of the European Association for Signal Processing (EURASIP) EURASIP P.O. Box 134 CH-1000 Lausanne 13 Switzerland -Also available from: Elsevier Science Publishers B.V. Journals Department P.O. Box 211 1000 AE Amsterdam The Netherlands Visual Computer --------------- -Available from: Springer-Verlag Heidelberger Platz 3 D-1000 Berlin 33 Germany -Also available from: Springer-Verlag New York, Inc. Journal Fulfillment Services, Dept. J P.O. Box 2485 Secaucus, N.J. 07094 USA ****************************************************************************** Miscellaneous Journals ====================== Leonardo -------- -Journal of the International Society for the Arts, Sciences & Technology -SIGGRAPH art show catalogue -Available from: Pergamon ****************************************************************************** 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 ------------------------------------------------------------------------------- END OF RTNEWS