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_ __ ______ _ __ ' ) ) / ' ) ) /--' __. __ , --/ __ __. _. o ____ _, / / _ , , , _ / \_(_/|_/ (_/_ (_/ / (_(_/|_(__<_/ / <_(_)_ / (_</_(_(_/_/_)_ / /| ' |/ Ray Tracing News, e-mail edition, 2/15/88 concatenated by Eric Haines, hpfcla!hpfcrs!eye!erich@hplabs.HP.COM So, now that the SIGGRAPH paper submission rush is over, the SIGGRAPH paper review process begins. Fortunately, it's generally easier to comment on someone else's deathless prose than write it yourself. It's also time to start procrastinating on writing up SIGGRAPH tutorial notes. So, all in all it's not been too busy, except for all the "real" work we've all (hopefully) been doing. Dore' ----- The only new news I've got is on the new product by Ardent, called Dore' (rhymes with "moray" - there should be an up-accent over that "e" in Dore). Ardent is the new name for Dana Computer Inc (i.e. the "single-user supercomputer/supergraphics" people. Their "Titan" minisupercomputer is due out realsoonnow). Dore' stands for "Dynamic Object-Rendering Environment". The places I've seen articles so far is "Electronics", February 4, 1988, on pages 69-70, and "Mini-Micro Systems", February 1988, pages 22-23. The first article offers more detail. I don't really want to rehash either article in full. The salient points (to me) about Dore' are: (1) Toolkit approach. (2) Can render using vectors, hidden surface, or ray tracing. (3) Hierarchical, object oriented system. (4) Five object classes: (a) primitives (including points, curves, polygons, meshes, cubic solids (?!), and NURBS (non-uniform rational B-splines), (b) appearance attributes (material properties, inc. solid texture maps and environmental reflection maps), (c) geometric attributes (modeling matrices), (d) studio objects (camera, lights) (I like this term!), (e) organizational objects (hierarchy, and evidentally the ability to define function calls inside the environment which call routines in the application program. No idea how this works). (5) Quoted times: 0.1 second for vector, 10 seconds for hidden surface, 100 seconds ray-traced (I assume on the Titan. No idea what kind of scene complexity or resolution). (6) Written in C. (7) "Open" system - source code sold in hopes of selling Dore' on other systems. The best part (for universities and research labs) is the price: $250 for a source code license - not sure what the cost is for source code maintenance (vs. $15000 for commercial users plus $5000/year after the first year). Per copy binary license is $200. I am teaching the ray-tracing section of "A Consumer's and Developer's Guide to Image Synthesis" at SIGGRAPH this year, so definitely want to know more. I would also like more information just out of curiosity. So, you university people, please go out there and get one - seems like a real bargain. The contact info for Ardent is: Ardent Computer Corp 550 Del Rey Ave Sunnyvale, CA 94086 408-732-2806 That's all, folks, Eric _ __ ______ _ __ ' ) ) / ' ) ) /--' __. __ , --/ __ __. _. o ____ _, / / _ , , , _ / \_(_/|_/ (_/_ (_/ / (_(_/|_(__<_/ / <_(_)_ / (_</_(_(_/_/_)_ / /| ' |/ "Light Makes Right" March 1, 1988 I just receive Andrew's note that the hardcopy RTN is in the mail, which inspired me to flush the buffer and send on the latest offerings. Special thanks to Jeff Goldsmith for submissions. - Eric -------------------------------------------------- Mailing list updates -------------------- First, an address change. John Peterson is now with Apple, who writes: 'I'm currently hanging out at Apple thinking about "3D graphics for the rest of us" and how to keep the jaggies away from personal computers. (But there is this Cray sitting about 50 feet away. Hmmm...)' # # John Peterson - bicubic splines, texturing # Apple Computer (graduated University of Utah, 1988) alias john_peterson hpfcrs!hpfcla!jp%apple.apple.com@RELAY.CS.NET I asked him for ray tracers at the University of Utah. So, Tom Malley and Rod Bogart (whose initials are 'RGB') are now subscribers. From Tom: My thesis research was similar to what John Wallace described, being a two pass approach to radiosity to include specular reflection and transparency. Form factors were all calculated via ray tracing, however. I did some brief examination of different ray intersection methods along the way (Rubin-Whitted, Kay-Kajiya, and Glassner). # # Tom Malley - blending ray tracing and radiosity # Evans & Sutherland (graduated University of Utah, 1988) # (malley@cs.utah.edu, cs.utah.edu!esunix!tmalley) alias tom_malley hpfcrs!hpfcla!hplabs!malley@cs.utah.edu To quote John Peterson about Rod Bogart: Rod developed a really neat method for using ray tracing to integrate computer generated pictures with real world images (coming soon to a SIGGRAPH near you...). # # Rod Bogart - blending ray tracing and images # University of Utah alias rod_bogart hpfcrs!hpfcla!hplabs!bogart%gr@cs.utah.edu ----------------------------------- Another Dore' Article In case you have not been able to track down the two articles previously mentioned about Dore', Ardent's new rendering system, there's now a third (that I know of): it's in "Computer Design", Feb 15, 1988, pages 30-31. Pretty much like the other articles (i.e. cast from the same press release). ----------------------------------- Responses to the "teapot in a football stadium" problem: From: Andrew Glassner Just a quick response to your football stadium/teapot example. When you subdivide a node, look at its children. If only one child is non-empty, replace the original node with its non-null child. Do this recursively until the subdivision criterion is satisfied. I do this in my spacetime ray tracer, and the results can be big. The ray propagation can get just a bit more complex, but there are clever rays to keep it simple (see John Amanatide's article in Eurographics '87, plus I have a scheme that I hope to write up soon...). Better yet, go with a hybrid space subdivision/bounding volume scheme, such as the one described in my spacetime paper (poorly described in the Intro to RT notes, but better described in the version slated for the March issue of CG&A; I'd be happy to mail you a preprint). I think this hybrid scheme gives the best of both worlds, and you can use whatever space subdivision and bounding volume techniques that you like in the two distinct phases of the algorithm. I use adaptive space subdivision and Kay's bounding slabs, and that combination seems to work pretty well. And now I have to get back to moving into my office! ------------------------------------------ Comments on Jim Arvo's Efficiency Article From: Eric Haines (with a few extra comments than my original letter to Jim) Your article on efficiency is fascinating. I hope to read it more carefully tonight and (eventually--we just came under a crunch of work) comment on it. Sounds like you've done a lot of serious thought and speculation on the possibilities. I agree with the philosophy of objects each having their own private hierarchies, and having the ability to hook these hierarchies up however you want. We've done that on a small scale with our tesselated spline surfaces: automatic hierarchy a la Goldsmith & Salmon (IEEE CG&A, May 1987) for everything, but then octrees for the spline surfaces themselves. A nice feature of Goldsmith is that you can weight the cost of each primitive into the algorithm: multiply its area by some intersection cost (which you'll probably have to figure out through experimentation) to give it a weighting. In this way a torus surface which has the same size bounding volume as a quadrilateral can be given a higher weighting factor. A higher cost has the effect of making the hierarchical tree less horizontal near the complicated object, i.e. there are more bounding volumes overall, with a few complicated objects in each. This is what you want, since you'd rather spend a little extra time on intersecting bounding volumes than wasting a lot of time intersecting the empty space around costly objects. Response from: Jim Arvo I'm glad you found my article interesting. All your interesting mail finally motivated me to contribute to the discussion. I thought I would toss out a pet idea of mine and see if it sparked any debate. It turns out that Jeff Goldsmith also looked at simulated annealing for bounding box hierarchies. One day one of us will get some results. Hopefully not negative results! With all the talk about octrees and such, it's clear that there are a number of potential papers "waiting in the wings". I've been thinking that by getting the right collaborations going, we (the ray tracing group) could easily "hand" IEEE several related papers, effectively defining a theme issue. What do you think? My reply: The efficiency article collection sounds possible. Another idea which someone (Mike Kaplan, maybe? I forget) mentioned at last SIGGRAPH was "A Characterization of Ten Ray Tracing Efficiency Algorithms". If well done, this would be a classic. There are probably entirely new schemes still to be found, and certainly trying to optimize and figure out good hybrid methods is an area ripe for development. But right now many of the structures and algorithms are in place, and still have not been fully compared. Timings are unconvincing, and statistics are worthwhile but don't tell the whole story. An in-depth comparison of the major algorithms and techniques to improve these would be wonderful. Someday, someday ... well, my hope is that a few of us could do some writing along these lines, even if it's just brainstorming on how to compare particular algorithms in a rigorous fashion (e.g. How can we simulate a scene mathematically? OK, idealize each object as a box or sphere for simplicity. Now, how do we distribute the points to get realistic clustering? Once we have a "scene generator" which could create various typical distributions of objects in a scene, then we have to analyze how this generator would interact with each algorithm, and be able to predict how each efficiency scheme deals with the scenes generated. Or there might be simpler ways to isolate and analyze each factor which affects the efficiency of a scheme. Anyway, whatever, but this stuff looks fun!). Understanding the strengths of the various techniques seems vital to being able to do any kind of "annealing" process for optimization. ------------------------------------------------------------ Efficiency Tricks ----------------- From Jeff Goldsmith: Here's a good hack for Ray Tracing News: When using Tim Kay's heapsort on bounding volumes in order to get the closest, don't bother to do that for illumination rays. I know it seems obvious, but I never thought to do it. The obvious corollary to that idea has a little more reach to it. Since illumination rays form the bulk of the rays we trace, getting the nearest intersection is of limited value. In addition, if CSG is used, more times occur when the nearest intersection is of less value. This seems to indicate that space tracing techniques are doing some amount of needless work. Since it doesn't really cost that much, perhaps it is not a flaw, but maybe space tracers should consider approaches that don't worry about where along the path we are and optimize that problem instead. --------------------------------------------- More Book Recommendations ------------------------- From: Jeff Goldsmith I agree completely with your comment about libraries. Mine is a crucial resource for me. Here are some of my favorite books that are in my office: Geometry: Computational Geometry for Design and Manufacture Faux & Pratt --an early CAD text. It has lots of good stuff on splines and 3D math. Differential Geometry of Curves and Surfaces DoCarmo --A super text on classical differential geometry. (Not quite the same as analytic geometry.) CRC Standard Math Tables --This has an awesome section on analytic geometry. Calculus, too. Can't live without it. It is not the same as the first part of the Chemistry and Physics one. Analytic Geometry Steen and Ballou --Once was the standard college text on the subject. That was a long time ago, but it is very easy to read and it covers the fundamentals. Computing: Data Structures and Algorithms --Aho, Hopcroft and Ullman Read anything by these guys. Data Structure Techniques --Standish More How-to than AHU's tome. Numerical Analysis --Burden, Faires, and Reynolds I have the other two, as well. This is the least complete of the three, but the algorithms inside are childishly easy to implement. They always seem to work, too. Best of all, for many cases, they have test data and solutions. Software Tools --Kernighan and Plauger How to write command line interpreters, editors, macro expanders, the works. Great reading. Fundamentals of Computer Algorithms --Horowitz and Sahni Less technical than AHU, but pretty technical. Thicker. It may very well answer the problem you can't figure out straight off. The Art of Computer Programming --Knuth The "Encyclopedia" Physics: (Seem awfully useful sometimes) Gravitation --Misner, Thorne, and Wheeler The thickest book on my shelf. It's a paperback, too. (It's bent three bookends permanently. Cheap JPL ones.) Truly a tome on modern physics. Modern Physics --Tippler Much easier to read than MTW. Has lots of good appendices. University Astronomy --Pasachoff and Kuttner I read this book for fun. I wonder why I didn't read it while I was taking Kuttner's course? The Feynman Lectures on Physics Awesome first course. Most of my needs are problems in the text. Graphics, etc: Raster Graphics Handbook --Conrac All about fundamentals of the craft. Light and Color in Nature and Art --Williamson and Cummings Much easier to read than Hall's thesis, but less technical as well. Etc, Etc: The Random House Dictionary of the English Language, College Edition The best collegiate sized dictionary around. By far. The Chicago Manual of Style Has most of the answers. Did you know that to recreate is to have fun, but to re-create is computer graphics? The Elements of Style The one that came before computers. ----------------------------------------------- Bug for the Day by Eric Haines --------------- {This will be pretty unexciting for those who never intend to implement an octree subdivision scheme. For future implementers, I hope you find it of use: it took me quite a few hours to track this one down, so I think it is worth going into.} This bug was one I had when implementing octree subdivision for ray tracing. The basic algorithm used was Glassner's: once you intersect the octree structure, move the intersection point in one half of the smallest cube's dimension in the direction normal to the wall hit. In other words, find out what cube is the next cube by finding a point that should be well inside of it, then translating this point into integer octree coordinates and traversing the octree downwards until a leaf node is found. However, there are some subtle errors that can occur with moving to the next octree cube. My favorite is almost hitting the edge of a cube, moving into the next cube, then getting caught moving to the cube diagonal to this cube, i.e. moving from cube 1 to 2 to 3 ... X--> +---+---+ ^ | 2 | $ | Numbers are the order of cubes moved through. | +---#---+ Y | 1 | 3 | +---+---+ ^________ray started here, and hit almost at the "#". (ray is in +X, +Y direction) This went into an infinite loop, going between 2 and 3 forever. The reason was that when I hit the boundary 1&2 I would add a Y increment (half minimum box size) to the intersection point, then convert this to find that I was now in box 2. I would then shoot the ray again and it would hit the wall at 2&$. To this intersection point I would add an X increment. However, what would happen is that the Y intersection point would actually be ever so slightly low - earlier when I hit the 1&2 wall adding the increment pushed us into box 2. But now when the Y intersection point was converted it would put us in the 1+3 boxes, and X would then put us in box 3. Basically, the precision of the machine made the mapping between world space and octree space be ever so slightly off. The infinite loop occurred when we shot the ray again at box 3. It would hit the 3/$ wall, get Y incremented, and because X was ever so slightly less than what was truly needed to put the intersection point in the 3+$ boxes, we would go back to box 2, ad infinitum. Another way to look at this is that when we would intersect the ray against any of the walls near the "#" point, the intersection point (due to roundoff) was always mapping to box 1 if not incremented. Incrementing in Y would move it to box 2, and in X would move it to box 3, but then the next intersection test would yield another point that would be in box 1. Since we couldn't increment in both directions at once, we could never get past 2 and 3 simultaneously. This bug occurs very rarely because of this: the intersection points all have to be such that they are very near a corner, and the mapping of the points must all land within box 1. This problem occurred for me once in a few million rays, which of course made it all that much more fun to search for it. My solution was to check the distance of the intersections generated each time: if the closest intersection was a smaller distance from the origin than the closest distance for the previous cube move, then this intersection point would not be used, but rather the next higher would be. In this way forward progress along the ray would always be made. By the way, I found that it was worthwhile to always use the original ray origin for testing ray/cube intersections - doing this avoids any cumulative precision errors which could occur by successively starting from each new intersection point. To simulate the origin starting within the cube I would simply test only the 3 cube faces which faced away from the ray direction (this was also faster to test). Anyway, hope this made sense - has anyone else run into this bug? Any other solutions? --------------------------------------------- A Pet Peeve (by Jeff Goldsmith) ----------- Don't ever refer to pixels as rows and columns. It makes it hard to get the order (row,column)? (column,row)? right. Refer to pixels as (x,y) coordinates. Not only is that the natural system to do math on them, but it is much easier to visualize in a debugging environment, as well as running the thing. I use the -x and -y npix switches on the tracer command line to override any settings and have found them to be much easier to deal with than the -r and -c that seem to be everywhere. Note that C's normal array order is (I think. I always get these things wrong.) (y,x). [I agree: my problem now is that Y=0 is the bottom edge of the screen when dealing with the graphics package (HP's Starbase), and Y=0 is the top when directly accessing the frame buffer (HP's SRX). -- EAH] --------------------------------------------- Next "RT News" issue I'll include a write-up of Goldsmith/Salmon which should hopefully make the algorithm clearer, plus some little additions I've made. I've found Goldsmith/Salmon to be a worthwhile, robust efficiency scheme which hasn't received much attention. It embodies an odd way of thinking (I have to reread my notes about it when I want to change the code), as there are a number of costs which must be taken into account and inherited. It's not immediately intuitive, but has a certain sense to it once all the pieces are in place. Hopefully I'll be able to shed some more light on it. All for now, Eric _ __ ______ _ __ ' ) ) / ' ) ) /--' __. __ , --/ __ __. _. o ____ _, / / _ , , , _ / \_(_/|_/ (_/_ (_/ / (_(_/|_(__<_/ / <_(_)_ / (_</_(_(_/_/_)_ / /| ' |/ "Light Makes Right" March 8, 1988 ------------------------------------------------- Surface Acne ------------ From Eric Haines: A problem which just about every ray tracer has run into, and which has rarely appeared in the literature (and even more rarely been solved in any way) is what I call "surface acne". An easy way to explain this problem is with an example. Say you are looking at a double sided (i.e. no culling) cylinder primitive. You shoot an eye ray, hitting the outside. Now you look at a light. As it turns out, the intersection point truly is bathed by the light, and so should see it. What actually may happen is that the shadow test ray hits the cylinder. In images this will show up as black dots or other anomalous shadings - "surface acne". I've seen this left in some images to give an interesting textured effect, but normally it's a real problem. How did this happen? Well, theoretically it can't. However, due to precision error the following happens. When you hit the cylinder and calculated the intersection point in world space, the point computed was actually ever so slightly inside the cylinder. Now, when the shadow ray is sent out, it is tested against the cylinder's surface, and an intersection is found at some tiny distance from the origin. A common solution is to just assign an epsilon to each intersector and cross your fingers. In other words, what you really do is move the ray origin ever so slightly along the shadow (or reflection or refraction) ray direction and hope this was far enough that the new origin is 'outside' of the object (in actuality, what you want is for the new origin to be on the same side of the object as the parent ray, except for refraction rays, which want to start on the opposite side). This works fairly well for test systems, but is pretty scary stuff for software used by anyone who didn't design it (e.g. some user decides to input his molecular database in meters, causing all his data to be much smaller in radius than my fudge factor. When I add my fudge factor distance to the ray, I find that my new ray origin is way outside the scene). Another solution is to not test the item intersected if it is not self-shadowing. For example, a polygon cannot cast a shadow on itself, so should not be tested for intersection when a ray originates on its surface. This works fine for some primitives, but falls apart when self-shadowing objects (cylinders, tori, spline surfaces, etc) are used. I have also experimented with some root polishing techniques, which help to solve some problems, but I'll leave it at this for now. Has anyone any better solutions for surface acne (ideally foolproof ones)? I suspect that the best solution is a combination of the above techniques, but hopefully I'm missing some concept that might make this problem easy to solve. Hope to hear from you all on this! ------------- Addenda from Jeff Goldsmith: Al [Barr] and I have used a technical term for "surface acne," too. We called it "black dots" or more often "black shit." (Zbuffers have similar problems. The results are called "zbuffer shit" or "zippers". Mostly the cruder term is used since the artifacts are not particularly desirable.) -------------------------------------------------- Goldsmith/Salmon Hierarchy Building ----------------------------------- Well, I was going to write up some info on the Goldsmith/Salmon hierarchy building algorithm, but the RT News buffer was filled almost immediately and I haven't done it yet. However, there was this from Jeff Goldsmith, about his earlier paper (IEEE CG&A, May 1987): If you are going to spend some time and effort on automatic tree generation stuff (Note: paper 2 is almost done--mostly talks about parallelism and hypercubes, but some stuff on trees as well--mostly work heuristics that include primitives and so on) I'd like to hear some thinking about the evaluation function. Firstly, it's optimized for primary rays. That turns out to be an unfortunate choice, since most rays are secondary rays. We've come up with a second order correction that is good for evaluating trees, but turns the generation algorithm into O(n log^2 n). We've not played around with it enough to tell whether it works. If you have some thoughts/solutions, that would be nice. Another finding on the same vein that is much more important is: the mean (see next note) seems to be reasonably close, but sigma is very high for the predictions vs. actual tries. This wasn't important (actually, wasn't detected) on a sequential machine, but became crucial on a parallel machine. Some of the variation is due to our assumption/ attempt at view direction independence. (Clearly, stuff in back is not checked for intersection much.) I don't know whether that is all of it--we get bizarre plots of this data. If you have any thoughts on how to make a better or more precise evaluation function, I'd really like to hear the reasoning and perhaps steal and use the results. Oh, the promised note: The mean is only correct if the highest level bounding volume (root node) is contained completely within the view volume. If it isn't, the actual results end up proportional to the predicted ones, but I haven't worked out the constant. (It shows up on our graphs pretty clearly, though.) The second part of the algorithm is the builder. I'm not convinced that it is a very good method at all, but it met the criteria I set up when trying to decompose trees--O(below n^2) and reasonably local (I was trying to use simulated annealing at the time.) Some other features were environmental; some were because I couldn't think of a better way. In no sense am I convinced that the incremental approach or the specific one chosen is best. I'd like to hear about that, too. The only part I really like about the whole thing is the general approach of using heuristics to guess at some value (rated in flops eventually) and then trying to optimize that value. Beyond that, I think there is a whole realm of computational techniques waiting to be used to approximately solve optimization problems. I'm really interested in other work done in that direction and especially results regarding graphics. Thanks for the good words; I seem to have been mentioned in most of the last issue. I bet that has something to do with my having acquired a network terminal on my desk less than a month ago (yay!). ----------------------------------------------------- Efficiency Tricks followup -------------------------- These are comments generated by Jeff Goldsmith's note that Kay/Kajiya sorting is not needed for shadow rays. ----------- Comments from Masataka Ohta: In the latest ray tracing news, you write: >Efficiency Tricks >Since illumination rays form the bulk of the rays we >trace. If so, instead of space tracing, you should use ray coherence at least for the illumination rays. The ray coherent approaches are found in CG&A vol. 6, no. 9 "The Light Buffer: A Shadow-Testing Accelerator" and in my paper "ray coherence theorem and constant time ray tracing algorithm" in proceedings of CG International '87. >In addition, if CSG is used, more times occur when the nearest >intersection is of less value. This seems to indicate that >space tracing techniques are doing some amount of needless work. How about tracing illumination rays from light sources, instead of from object surface? It will be faster for your CSG case, if the surface point lies in the shadow, though if the surface point is illuminated, there will be no speed improvement. The problem is interesting to me because my research on coherent ray tracer also suggests that it is much better to trace illumination rays from the light source. Do you have any other reasons to determine from where illumination rays are fired? ---------------------------------------------------------------------- Jeff Goldsmith's reply: Actually, I believe you, though I won't say with certainty that we know the best way to do shadow testing. However, I'm interested in fundamentally understanding the ray tracing algorithm and determining what computation MUST be done, so the realization that space tracing illumination rays still seems meaningful. In fact, it is my opinion that space tracing is not the right way to go and "backwards" (classical) ray tracing will eventually be closer to what will be used 30 years from now. I won't even try to defend that position; no one knows the answers. What we are trying to do is shed a little "light" on the subject. Thanks for your comments. ----------------- From Eric Haines: I just got from Ohta the same note Ohta sent to you, plus your reply. Your reply is so short that I've lost the sense of it. So, if you don't mind, a quick explanation would be useful. > However, > I'm interested in fundamentally understanding the ray tracing > algorithm and determining what computation MUST be done, so > the realization that space tracing illumination rays still > seems meaningful. What is "the realization that space tracing illumination rays"? I'm missing something here - which realization? > In fact, it is my opinion that space tracing > is not the right way to go and "backwards" (classical) ray > tracing will eventually be closer to what will be used 30 > years from now. Do you mean by "space tracing" Ohta's method? Basically, it looks like I should reread Ohta's article, but I thought I'd check first. -------------- Further explanation from Jeff Goldsmith: I think that a word got dropped from the sentence, either when I typed it in or later. (Who knows--I do that about as often as computers do.) I meant: Since distance order is not needed for illumination rays, space tracing methods in general (not Ohta's in particular) do extra work. It's not always clear that extra information costs extra computation, but they usually go hand in hand. (It was just a rehash of the original message.) Anyway, if extra computation is being done, perhaps then there is an algorithm that does not do this computation, yet does all the others (or some others...) that is of lower asymptotic time complexity. Basically, this all boils down to my response to various claims that people have "constant time" ray tracers. It is just not true. It can't be true if they are using a method that will yield the first intersection along a path since we know that that computation cannot be done in less than O(n log n) without a discretized distance measurement. I don't think that space tracers discretize distance in the sense of a bucket sort, but I could be convinced, I suppose. Anyway, that's what the ramblings are all about. If you have some insights, I'd like to start an argument (sorry, discussion) on the net about the topic. What do you think? ------------------------------------------------------------ Extracts from USENET news ------------------------- There was recently some interesting interchange about octree building on USENET. Some people don't read or don't receive comp.graphics, so the rest of this issue consists of these messages. ---------------- From Ruud Waij (who is not on the RT News e-mail mailing list): In article <198@dutrun.UUCP> winffhp@dutrun.UUCP (ruud waij) writes: My ray tracing program, which can display the primitives block, sphere cone and cylinder, uses spatial enumeration of the object space (subdivision in regularly located cubical cells (voxels)) to speed up computation. The voxels each have a list of primitives. If the surface of a primitive is inside a voxel, this primitive will be put in the list of the voxel. I am currently using bounding boxes around the primitives: if part of the bounding box is inside the voxel, the surface of the primitive is said to be inside the voxel. This is a very easy method but also very s-l-o-w. I am trying to find a better way of determining whether the surface of a primitive is in a voxel or not, but I am not very succesful. Does anyone out there have any suggestions ? --------------- Response from Paul Heckbert: Yes, interesting problem! Fitting a bounding box around the object and listing that object in all voxels intersected by the bounding box will be inefficient as it can list the object in many voxels not intersected by the object itself. Imagine a long, thin cylinder at an angle to the voxel grid. I've never implemented this, but I think it would solve your problem for general quadrics: find zmin and zmax for the object. loop over z from zmin to zmax, stepping from grid plane to grid plane. find the conic curve of the intersection of the quadric with the plane. this will be a second degree equation in x and y (an ellipse, parabola, hyperbola, or line). note that you'll have to deal with the end caps of your cylinders and similar details. find ymin and ymax for the conic curve. loop over y from ymin to ymax, stepping from grid line to grid line within the current z-plane find the intersection points of the current y line with the conic. this will be zero, one, or two points. find xmin and xmax of these points. loop over x from xmin to xmax. the voxel at (x, y, z) intersects the object Perhaps others out there have actually implemented stuff like this and will enlighten us with their experience. ----------------- Response from Andrew Glassner: Ruud and I have discussed this in person, but I thought I'd respond anyway - both to summarize our discussions and offer some comments on the technique. The central question of the posting was how to assign the surfaces of various objects to volume cells, in order to use some form spatial subdivision to accelerate ray tracing. Notice that there are at least two assumptions underlying this method. The first assumes that the interior of each object is homogeneous in all respects, and thus uninteresting from a ray-tracing point of view. As a counterexample, if we have smoke swirling around inside a crystal ball, then this "homogeneous-contents" assumption breaks down fast. To compensate, we either must include the volume inside each object to each cell's object list (and support a more complex object description encompassing both the surface and the contents), or include as new objects the stuff within the original. The other assumption is that objects have hard edges; otherwise we have to revise our definition of "surface" in this context. This can begin to be a problem with implicit surfaces, though I haven't seen this really discussed yet in print. But so as long as we're using hard-edged objects with homogeneous interiors, the "surface in a cell" approach is still attractive. From here on I'll assume that cells are rectangular boxes. So to which cells do we attach a particular surface? Ruud's current technique (gathered from his posting) finds the bounding box of the surface and marks every cell that is even partly within the bounding volume. Sure, this marks a lot of cells that need not be marked. One way to reduce the marked cell count is to notice that if the object is convex, we can unmark any cell that is completely within the object; we test the 8 corners with an inside/outside test (fast and simple for quadrics; only slightly slower and harder for polyhedra). If all 8 corners are "inside", unmark the cell. Of course, this assumes convex cells - like boxes. Note that some quadrics are not convex (e.g. hyperboloid of one sheet) so you must be at least a little careful here. The opposite doesn't hold - just because all 8 corners are outside does NOT mean a cell may be unmarked. Consider the end of a cylinder poking into one side of a box, like an ice-cream bar on a stick, where the ice-cream bar itself is our cell. The stick is within the ice cream, but all the corners of the ice cream bar are outside the stick. Since this box contains some of the stick's surface, the box should still be marked. So our final cells have either some inside and some outside corners, or all outside corners. What do we lose by having lots of extra cells marked? Probably not much. By storing the ray intersection parameter with each object after an intersection has been computed, we don't ever need to actually repeat an intersection. If the ray id# that is being traced matches the ray id# for which the object holds the intersection parameter, we simply return the intersection value. This requires getting access to the object's description and then a comparison - probably the object access is the most expensive step. But most objects are locally coherent (if you hit a cell containing object A, the next time you need object A again will probably be pretty soon). So "false positives" - cells who claim to contain an object they really don't - aren't so bad, since the pages containing an object will probably still be resident when we need it again. We do need to protect ourselves, though, against a little gotcha that I neglected to discuss in my '84 CG&A paper. If you enter a cell and find that you hit an object it claims to contain, you must check that the intersection you computed actually resides within that cell. It's possible that the cell is a false positive, so the object itself isn't even in the cell. It's also possible that the object is something like a boomerang, where it really is within the current cell but the actual intersection is in another cell. The loss comes in when the intersection is actually in the next cell, but another surface in the next cell (but not in this one) is actually in front. Even worse, if you're doing CSG, that phony intersection can distort your entire precious CSG status tree! The moral is not to be fooled just because you hit an object in a cell; check to be sure that the intersection itself is also within the cell. How to find the bounding box of a quadric? A really simple way is to find the bounding box of the quadric in its canonical space, and then transform the box into the object's position. Fit a new bounding box around the eight transformed corners of the original bounding box. This will not make a very tight volume at all, (imagine a slanted, tilted cylinder and its bounding box), but it's quick and dirty and I use it for getting code debugged and at least running. If you have a convex hull program, you can compute the hull for concave polyhedra and use its bounding box; obviously you needn't bother for convex polyhedra. For parametric curved surfaces you can try to find a polyhedral shell the is guaranteed to enclose the surface; again you can find the shell's convex hull and then find the extreme values along each co-ordinate. If your boxes don't have to be axis-aligned, then the problem changes significantly. Consider a sphere: an infinite number of equally-sized boxes at different orientation will enclose the sphere minimally. More complicated shapes appear more formidable. An O(n^3) algorithm for non-aligned bounding boxes can be found in "Finding Minimal Enclosing Boxes" by O'Rourke (International Journal of Computer and Information Sciences, Vol 14, No 3, 1985, pp. 183-199). Other approaches include traditional 3-d scan conversion, which I think should be easily convertable into an adaptive octree environment. Or you can grab the bull by the horns and go for raw octree encoding, approximating the surface with lots of little sugar cubes. Then mark any cell in your space subdivision tree that encloses (some or all of) any of these cubes. _ __ ______ _ __ ' ) ) / ' ) ) /--' __. __ , --/ __ __. _. o ____ _, / / _ , , , _ / \_(_/|_/ (_/_ (_/ / (_(_/|_(__<_/ / <_(_)_ / (_</_(_(_/_/_)_ / /| ' |/ "Light Makes Right" March 26, 1988 Table of Contents: Intro, Eric Haines Mailing list changes and additions: Kuchkuda, Lorig, Rekola More on shadow testing, efficiency, etc., Jeff Goldsmith More comments on tight fitting octrees for quadrics, Jeff Goldsmith LINEAR-TIME VOXEL WALKING FOR OCTREES, Jim Arvo Efficiency Tricks, Eric Haines A Rendering Trick and a Puzzle, Eric Haines PECG correction, David Rogers --------------------------------------------------------------- Well, NCGA was pretty uninspiring, as it rapidly becomes more and more PC oriented. It was great to see people, though, and nice to escape the Ithaca snow and rain. As far as ray tracing goes, a few companies announced products. The AT&T Pixel Machine now has two rendering packages, PICLIB and RAYLIB (these may be merged into one package someday - I would guess that separate development efforts caused the split [any comments, Leonard?]). With the addition of some sort of VM capability, this machine becomes pretty astounding in its ray tracing performance (in case you didn't get to SIGGRAPH last year, they had a demo of moving by mouse a shiny ball on top of the mandrill texture map: about a frame per second ray trace on a small part of the screen). HP announced its new graphics accelerator, the TurboSRX, and with it the eventual availability of a ray tracing and (the first!) radiosity package as an extension to their Starbase graphics library. Ardent and their Dore' package were sadly missing. Apollo was also noticeable for their non-appearance. Sun TAAC was there, showing off some ray traced pictures but seemingly not planning to release a ray tracer (the salesman claiming that whoever bought a TAAC would simply write their own). Stellar was there with their supercomputer workstation - interesting, but no ray-tracing in sight. Anyone else note anything of ray-tracing (or other) interest? ------------------------------------------------------------------------- Some mailing list changes and additions Changed address: # Roman Kuchkuda # Megatek alias roman_kuchkuda \ hpfcrs!hpfcla!hplabs!ucbvax!ucsd!megatek!kuchkuda@rutgers.edu New people: I saw Gray at NCGA and got his email address. He worked on ray tracing at RPI and is at Cray: # Gray Lorig - volumetric data rendering, sci-vi, and parallel & vector # architectures. # Cray Research, Inc. # 1333 Northland Drive # Mendota Heights, MN 55120 # (612)-681-3645 alias gray_lorig hpfcrs!hpfcla!hplabs!gray%rhea.CRAY.COM@uc.msc.umn.edu By way of introduction, this from Erik Jansen: I visited the Helsinki University of Technology last week and found there a lot of ray tracing activities going on. They are even reviving their old EXCELL system (Markku Tamminen did a PhD work on a spatial index based on an adaptive binary space subdivision in '81-'82, I met him in '81 and '82 and we talked at these occasions about ray tracing and spatial subdivision. In his PhD thesis (1982) there is a ray tracing algorithm given for the EXCELL method (EXtendible CELL method). I decided to implement the algorithm for ray tracing polygon models. That implementation failed because I could only use our PDP-11 at that time and I could have about ten cells in internal memory - too less for effective coherence. The program spend 95% of its time on swapping. So far the history). I told them about the RT-news and they are very interested to receive it. I will mail them (Charles Woodward, Panu Rekola, e.o.) your address, so that they can introduce themselves to the others. # # Panu Rekola - spline intersection, illumination models, textures # Helsinki University of Technology # Laboratory of Information Processing Science # Room Y229A # SF-02150 Espoo # Finland # pre@kiuas.hut.fi (or pre@hutcs.hut.fi) alias panu_rekola hpfcrs!hpfcla!hpda!uunet!mcvax!hutcs!pre Panu Rekola writes: I just received a message from Erik Jansen (Delft) in which he told me that you take care of a mailing list called "Ray Tracing News". (I already sent a message to Andrew Glassner on the same topic because Erik told me to contact him when he visited us some weeks ago.) Now, I would like to join the discussion; I promise to ask no stupid questions. I have previously worked here in a CAD project (where I wrote my MSc thesis on FEM elements) and since about a year I have been responsible of our graphics. Even though my experience in the field is quite short I suppose I have learned a lot while all people want to see their models in color and with glass etc., visualization has been the bottleneck in our CAD projects. As an introduction to the critical members of the mailing list you could tell that I am a filter who read unstandard input from the models created by other people, manipulates the data with the normal graphics methods, and outpus images. The special features of our ray tracer are the EXCELL spatial directory (which has been optimized for ray tracing during the last few weeks), a new B-spline (and Bezier) algorithm, methods to display BR models with curved surfaces (even blend surfaces, although this part yet unfinished). The system will be semi-commercially used in a couple of companies soon (e.g. car and tableware industry). ------------------------------------------------------------------------ More on shadow testing, efficiency, etc. (followup to Ohta/Goldsmith correspondence): From Jeff Goldsmith: Sorry I haven't responded sooner, but movie-making has taken up all my time recently. With respect to pre-sorting, etc. It is important to note that the preprocessing time must be MUCH smaller than the typical rendering time. So far this has been true, and even more so for animation. O(n) in my writing (explicitly in print) means linear in the number of objects in the scene. Obviously, it is quite likely that the asymptotic time complexity (a.t.c.) of any ray tracing algorithm will be different for the number of rays. Excluding ray coherence methods and hybrid z-buffer/ray tracing methods, the current a.t.c. is O(n) in the number of rays for ray tracing. Actually, I think it is the same for these other methods because the hybrid methods just eliminate some of the rays from consideration and leave the rest to be just as hard and the coherence methods don't eliminate more than, say, 1/2 of the rays, I think. In any event, for the a.t.c. to become sub-linear, there can be no such fraction, right? About space tracing: I think that I said that finding the closest intersection is an O(log n) problem. I agree, though, that that statement is not completely correct. Bucket sort methods, for example, can reduce the a.t.c. below log n. Also, global sort time (preprocessing) can distribute some of the computation across all rays, which can reduce the time complexity. What about the subdivide on the fly methods? (e.g: Arvo and Kirk) How do they fit in the scheme of things? I think your evaluation of the space tracing methods is correct, though the space complexity becomes important here, too. Also, given a "full" space (like Fujimoto's demos,) the time complexity is smaller. That leads to the question, "What if the time complexity of an algorithm depends on its input data?" Standard procedure is to evaluate "worst case" complexity, but we are probably interested in "average case" or more likely, "typical case." Also, it would be worthwhile and interesting to understand which algorithms do better with which type of data. We need to quantify this answer when trying to find good hybrid schemes. (The next generation?) At SIGGRAPH '87 we had a round table and each answered the question, "what would you like to see happen to ray tracing in the next year." My choice was to see something proven about ray tracing. It sounds like you are interested in that too. Any takers? -------------------------------------------------------------------- More comments on tight fitting octrees for quadrics {followup to Ruud Waij's question last issue} From Jeff Goldsmith: With respect to the conversation about octree testing, I've only done one try at that. I just tested 9 points against the implicit representation of the surface. (8 corners and the middle.) I didn't use it for ray tracing (I even forget what for) but I suspect that antialiasing will hide most errors generated that way. Jim Blinn came up with a clever way to do edges and minima/ maxima of quadric surfaces using (surprise) homogeneous coordinates. I don't think there ever was a real paper out of it, but he published a tutorial paper in the Siggraph '84 tutorial notes on "The Mathematics of Computer Graphics." That technique works for any quadric surface (cylinders aren't bounded, though) under any homogeneous transform (including perspective!) He also talks about how to render these things using his method. I tried it; it works great and is incredibly fast. I didn't implement many of his optimizations and can draw a texture mapped cylinder (no end caps) that fills the screen (512x512) on a VAX 780 in under a minute. As to how this applies to ray tracing, he gives a method for finding the silhouette of a quadric as well as minima and maxima. It allows for easy use of forward differencing, so should be fast enough to "render" quadrics into an octree. Bob Conley did a volume-oriented ray tracer for his thesis. I don't remember the details, but there'll be a long note about it that I'll pass on. He mentions that his code can do index of refraction varying over position. He uses a grid technique similar to Fujimoto's. --------------------------------------------------------------- From Jim Arvo: Just when you thought we had moved from octrees on to other things... This just occurred to me yesterday. (Actually, that was several days ago. This mail got bounced back to me twice now. More e-mail gremlins I guess.) LINEAR-TIME VOXEL WALKING FOR OCTREES ------------------------------------- Here is a new way to attack the problem of "voxel walking" in octrees (at least I think it's new). By voxel walking I mean identifying the successive voxels along the path of a ray. This is more for theoretical interest than anything else, though the algorithm described below may actually be practical in some situations. I make no claims about the practicality, however, and stick to theoretical time complexity for the most part. For this discussion assume that we have recursively subdivided a cubical volume of space into a collection of equal-sized voxels using a BSP tree -- i.e. each level imposes a single axis-orthogonal partitioning plane. The algorithm is much easier to describe using BSP trees, and from the point of view of computational complexity, there is basically no difference between BSP trees and octrees. Also, assuming that the subdivision has been carried out to uniform depth throughout simplifies the discussion, but is by no means a prerequisite. This would defeat the whole purpose because we all know how to efficiently walk the voxels along a ray in the context of uniform subdivision -- i.e. use a 3DDDA. Assuming that the leaf nodes form an NxNxN array of voxels, any given ray will pierce at most O(N) voxels. The actual bound is something like 3N, but the point is that it's linear in N. Now, suppose that we use a "re-traversal" technique to move from one voxel to the next along the ray. That is, we create a point that is guaranteed to lie within the next voxel and then traverse the hierarchy from the root node until we find the leaf node, or voxel, containing this point. This requires O( log N ) operations. In real life this is quite insignificant, but here we are talking about the actual time complexity. Therefore, in the worst case situation of following a ray through O( N ) voxels, the "re-traversal" scheme requires O( N log N ) operations just to do the "voxel walking." Assuming that there is an upper bound on the number of objects in any voxel (i.e. independent of N), this is also the worst case time complexity for intersecting a ray with the environment. In this note I propose a new "voxel walking" algorithm for octrees (call it the "partitioning" algorithm for now) which has a worst case time complexity of O( N ) under the conditions outlined above. In the best case of finding a hit "right away" (after O(1) voxels), both "re-traversal" and "partitioning" have a time complexity of O( log N ). That is: BEST CASE: O(1) voxels WORST CASE: O(N) voxels searched before a hit. searched before a hit. +---------------------------------------------------+ | | Re-traveral | O( log N ) O( N Log N ) | | | Partitioning | O( log N ) O( N ) | | | +---------------------------------------------------+ The new algorithm proceeds by recursively partitioning the ray into little line segments which intersect the leaf voxels. The top-down nature of the recursive search ensures that partition nodes are only considered ONCE PER RAY. In addition, the voxels will be visited in the correct order, thereby retaining the O( log N ) best case behavior. Below is a pseudo code description of the "partitioning" algorithm. It is the routine for intersecting a ray with an environment which has been subdivided using a BSP tree. Little things like checking to make sure the intersection is within the appropriate interval have been omitted. The input arguments to this routine are: Node : A BSP tree node which comes in two flavors -- a partition node or a leaf node. A partition node defines a plane and points to two child nodes which further partition the "positive" and "negative" half-spaces. A leaf node points to a list of candidate objects. P : The ray origin. Actually, think of this as an endpoint of a 3D line segment, since we are constraining the "ray" to be of finite length. D : A unit vector indicating the ray direction. len : The length of the "ray" -- or, more appropriately, the line segment. This is measured from the origin, P, along the direction vector, D. The function "Intersect" is initially passed the root node of the BSP tree, the origin and direction of the ray, and a length, "len", indicating the maximum distance to intersections which are to be considered. This starts out being the distance to the far end of the original bounding cube. ============================================================================ FUNCTION Intersect( Node, P, D, len ) RETURNING "results of intersection" IF Node is NIL THEN RETURN( "no intersection" ) IF Node is a leaf THEN BEGIN intersect ray (P,D) with objects in the candidate list RETURN( "the closest resulting intersection" ) END IF dist := signed distance along ray (P,D) to plane defined by Node near := child of Node in half-space which contains P IF 0 < dist < len THEN BEGIN /* the interval intersects the plane */ hit_data := Intersect( near, P, D, dist ) IF hit_data <> "no intersection" THEN RETURN( hit_data ) Q := P + dist * D /* 3D coords of point of intersection */ far := child of Node in half-space which does NOT contain P RETURN( Intersect( far, Q, D, len - dist ) ) END IF ELSE RETURN( Intersect( near, P, D, len ) ) END ============================================================================ As the BSP tree is traversed, the line segments are chopped up by the partitioning nodes. The "shrinking" of the line segments is critical to ensure that only relevent branches of the tree will be traversed. The actual encodings of the intersection data, the partitioning planes, and the nodes of the tree are all irrelevant to this discussion. These are "constant time" details. Granted, they become exceedingly important when considering whether the algorithm is really practial. Let's save this for later. A naive (and incorrect) proof of the claim that the time complexity of this algorithm is O(N) would go something like this: The voxel walking that we perform on behalf of a single ray is really just a search of a binary tree with voxels at the leaves. Since each node is only processed once, and since a binary tree with k leaves has k - 1 internal nodes, the total number of nodes which are processed in the entire operation must be of the same order as the number of leaves. We know that there are O( N ) leaves. Therefore, the time complexity is O( N ). But wait! The tree that we search is not truly binary since many of the internal nodes have one NIL branch. This happens when we discover that the entire current line segment is on one side of a partitioning plane and we prune off the branch on the other side. This is essential because there are really N**3 leaves and we need to discard branches leading to all but O( N ) of them. Thus, k leaves does not imply that there are only k - 1 internal nodes. The quention is, "Can there be more than O( k ) internal nodes?". Suppose we were to pick N random voxels from the N**3 possible choices, then walk up the BSP tree marking all the nodes in the tree which eventually lead to these N leaves. Let's call this the subtree "generated" by the original N voxels. Clearly this is a tree and it's uniquely determined by the leaves. A very simple argument shows that the generated subtree can have as many as 2 * ( N - 1 ) * log N nodes. This puts us right back where we started from, with a time complexity of O( N log N ), even if we visit these nodes only once. This makes sense, because the "re-traversal" method, which is also O( N log N ), treats the nodes as though they were unrelated. That is, it does not take advantage of the fact that paths leading to neighboring voxels are likely to be almost identical, diverging only very near the leaves. Therefore, if the "partitioning" scheme really does visit only O( N ) nodes, it does so because the voxels along a ray are far from random. It must implicitly take advantage of the fact that the voxels are much more likely to be brothers than distant cousins. This is in fact the case. To prove it I found that all I needed to assume about the voxels was connectedness -- provided I made some assumptions about the "niceness" of the BSP tree. To give a careful proof of this is very tedious, so I'll just outline the strategy (which I *think* is correct). But first let's define a couple of convenient terms: 1) Two voxels are "connected" (actually "26-connected") if they meet at a face, an edge, or a corner. We will say that a collection of voxels is connected if there is a path of connected voxels between any two of them. 2) A "regular" BSP tree is one in which each axis-orthogonal partition divides the parent volume in half, and the partitions cycle: X, Y, Z, X, Y, Z, etc. (Actually, we can weaken both of these requirements considerably and still make the proof work. If we're dealing with "standard" octrees, the regularity is automatic.) Here is a sequence of little theorems which leads to the main result: THEOREM 1: A ray pierces O(N) voxels. THEOREM 2: The voxels pierced by a ray form a connected set. THEOREM 3: Given a collection of voxels defined by a "regular" BSP tree, any connected subset of K voxels generates a unique subtree with O( K ) nodes. THEOREM 4: The "partitioning" algorithm visits exactly the nodes of the subtree generated by the voxels pierced by a ray. Furthermore, each of these nodes is visited exaclty once per ray. THEOREM 5: The "partitioning" algorithm has a worst case complexity of O( N ) for walking the voxels pierced by a ray. Theorems 1 and 2 are trivial. With the exception of the "uniqueness" part, theorem 3 is a little tricky to prove. I found that if I completely removed either of the "regularity" properties of the BSP tree (as opposed to just weakening them), I could construct a counterexample. I think that theorem 3 is true as stated, but I don't like my "proof" yet. I'm looking for an easy and intuitive proof. Theorem 4 is not hard to prove at all. All the facts become fairly clear if you see what the algorithm is doing. Finally, theorem 5, the main result, follows immediately from theorems 1 through 4. SOME PRACTICAL MATTERS: Since log N is typically going to be very small -- bounded by 10, say -- this whole discussion may be purely academic. However, just for the heck of it, I'll mention some things which could make this a (maybe) competative algorithm for real-life situations (in as much as ray tracing can ever be considered to be "real life"). First of all, it would probably be advisable to avoid recursive procedure calls in the "inner loop" of a voxel walker. This means maintaining an explicit stack. At the very least one should "longjump" out of the recursion once an intersection is found. The calculation of "dist" is very simple for axis-orthogonal planes, consisting of a subtract and a multiply (assuming that the reciprocals of the direction components are computed once up front, before the recursion begins). A nice thing which falls out for free is that arbitrary partitioning planes can be used if desired. The only penalty is a more costly distance calculation. The rest of the algorithm works without modification. There may be some situations in which this extra cost is justified. Sigh. This turned out to be much longer than I had planned... >>>>>> A followup message: Here is a slightly improved version of the algorithm in my previous mail. It turns out that you never need to explicitly compute the points of intersection with the partitioning planes. This makes it a little more attractive. -- Jim FUNCTION BSP_Intersect( Ray, Node, min, max ) RETURNING "intersection results" BEGIN IF Node is NIL THEN RETURN( "no intersection" ) IF Node is a leaf THEN BEGIN /* Do the real intersection checking */ intersect Ray with each object in the candidate list discarding those farther away than "max." RETURN( "the closest resulting intersection" ) END IF dist := signed distance along Ray to plane defined by Node near := child of Node for half-space containing the origin of Ray far := the "other" child of Node -- i.e. not equal to near. IF dist > max OR dist < 0 THEN /* Whole interval is on near side. */ RETURN( BSP_Intersect( Ray, near, min, max ) ) ELSE IF dist < min THEN /* Whole interval is on far side. */ RETURN( BSP_Intersect( Ray, far , min, max ) ) ELSE BEGIN /* the interval intersects the plane */ hit_data := BSP_Intersect( Ray, near, min, dist ) /* Test near side */ IF hit_data indicates that there was a hit THEN RETURN( hit_data ) RETURN( BSP_Intersect( Ray, far, dist, max ) ) /* Test far side. */ END IF END ------------------------------------------------------------------------ Some people turn out to be on the e-mail mailing list but not the hardcopy list for the RT News. In case you don't get the RT News in hardcopy form, I'm including the Efficiency Tricks article & the puzzle from it in this issue. Efficiency Tricks, by Eric Haines --------------------------------- Given a ray-tracer which has some basic efficiency scheme in use, how can we make it faster? Some of my tricks are below - what are yours? [HBV stands for Hierarchical Bounding Volumes] Speed-up #1: [HBV and probably Octree] Keep track of the closest intersection distance. Whenever a primitive (i.e. something that exists - not a bounding volume) is hit, keep its distance as the maximum distance to search. During further intersection testing use this distance to cut short the intersection calculations. Speed-up #2: [HBV and possibly Octree] When building the ray tree, keep the ray-tree around which was previously built. For each ray-tree node, intersect the object in the old ray tree, then proceed to intersect the new ray tree. By intersecting the old object first you can usually obtain a maximum distance immediately, which can then be used to aid Speed-up #1. Speed-up #3: When shadow testing, keep the opaque object (if any) which shadowed each light for each ray-tree node. Try these objects immediately during the next shadow testing at that ray-tree node. Odds are that whatever shadowed your last intersection point will shadow again. If the object is hit you can immediately stop testing because the light is not seen. Speed-up #4: When shadow testing, save transparent objects for later intersection. Only if no opaque object is hit should the transparent objects be tested. Speed-up #5: Don't calculate the normal for each intersection. Get the normal only after all intersection calculations are done and the closest object for each node is know: after all, each ray can have only one intersection point and one normal. (Saving intermediate results is recommended for some intersection calculations.) Speed-up #6: [HBV only] When shooting rays from a surface (e.g. reflection, refraction, or shadow rays), get the initial list of objects to intersect from the bounding volume hierarchy. For example, a ray beginning on a sphere must hit the sphere's bounding volume, so include all other objects in this bounding volume in the immediate test list. The bounding volume which is the father of the sphere's bounding volume must also automatically be hit, and its other sons should automatically be added to the test list, and so on up the object tree. Note also that this list can be calculated once for any object, and so could be created and kept around under a least-recently-used storage scheme. ------------------------------------------ A Rendering Trick and a Puzzle, by Eric Haines ---------------------------------------------- One common trick is to put a light at the eye to do better ambient lighting. Normally if a surface is lit by only ambient light, its shading is pretty crummy. For example, a non-reflective cube totally in shadow will have all of its faces shaded the exact same shade - very unrealistic. The light at the eye gives the cube definition. Note that a light at the eye does not need shadow testing - wherever the eye can see, the light can see, and vice versa. The puzzle: Actually, I lied. This technique can cause a subtle error. Do you know what shading error the above technique would cause? [hint: assume the Hall model is used for shading]. --------------------------------------------------------------------------- USENET roundup: Other than a hilarious set of messages begun when Paul Heckbert's Jell-O (TM) article was posted to USENET, and the perennial question "How do I find if a point is inside a polygon?", not much of interest. However, I did get a copy of the errata in _Procedural Elements for Computer Graphics_ from David Rogers. I updated my edition (the Second) with these corrections, which was generally a time drain: my advice is to keep the errata sheets in this edition, checking them only if you are planning to use an algorithm. However, the third edition corrections are mercifully short. From: "David F. Rogers" <rochester!harvard!USNA.MIL!dfr@cornell.UUCP> From: David F. Rogers <dfr@USNA.MIL> Subject: PECG correction Date: Thu, 10 Mar 88 13:21:11 EST Correction list for PECG 2/26/86 David F. Rogers There have been 3 printings of this book to date. The 3rd printing occurred in approximately March 85. To see if you have the 3rd printing look on page 386, 3rd line down and see if the word magenta is spelled correctly. If it is, you have the 3rd printing. If not, then you have the 2nd or 1st printing. To see if you have the 2nd printing look on page 90. If the 15th printed line in the algorithm is while Pixel(x,y) <> Boundary value you have the 2nd printing. If not you have the 1st printing. Please send any additional corrections to me at Professor David F. Rogers Aerospace Engineering Department United States Naval Academy Annapolis, Maryland 21402 uucp:decvax!brl-bmd!usna!dfr arpa:dfr@usna _____________________________________________________________ Known corrections to the third printing: Page Para./Eq. Line Was Should be 72 2 11 (5,5) (5,1) 82 1 example 4 (8,5) delete 100 5th equation upper limit on integral should be 2 vice 1 143 Fig. 3-14 yes branch of t < 0 and t > 1 decision blocks should extend down to Exit-line invisible 144 Cyrus-Beck algorithm 7 then 3 then 4 11 then 3 then 4 145 Table 3-7 1 value for w [2 1] [-2 1] 147 1st eq. 23 V sub e sub x j V sub e sub y j ______________________________________________________________ Known corrections to the second printing: (above plus) text: 19 2 5 Britian Britain 36 Eq. 3 10 replace 2nd + with = 47 4 6 delta' > 0 delta'< = 0 82 1 6 set complement 99 1 6 multipled multiplied 100 1 6 Fig. 2-50a Fig. 2-57a 100 1 8 Fig. 2-50b Fig. 2-57b 122 write for new page 186 2 6 Fig. 3-37a Fig. 3-38a 186 2 9 Fig. 3-38 Fig. 3-38b 187 Ref. 3-5 to appear Vol. 3, pp. 1-23, 1984 194 Eq. 1 xn + xn - 224 14 lines from bottom t = 1/4 t = 3/4 329 last eq. -0.04 -0.13 next to last eq. -0.04 twice -0.13 twice 3rd from bottom 0.14 -0.14 330 1st eq. -0.09 -0.14 2nd eq. -0.09 -0.14 3rd eq. -0.17 -0.27 4th eq. 0.36 0.30 5.25 4.65 last eq. 5.25 4.65 332 4 beta < beta > 6 beta < beta > 355 2nd eq. w = s(u,w) w = s(theta,phi) 385 2 5 magneta magenta 386 3 magneta magenta algorithms: (send self-addressed long stamped envelope for xeroxed corrections) 97 Bresenham 1 insert words first quadrant after modified 10 remove () 12 1/2 I/2 14 delta x x sub 2 117 Explicit 18 Icount = 0 delete clipping 18 insert m = Large 120 9 P'2 P'1 12 insert after Icount = 0 end if 13 insert after 1 if Icount <> 0 then neither end P' = P0 14 removed statement label 1 15 >= > 17 delete 18 delete 43 y> yT> 122-124 Sutherland- write for new pages Cohen 128 midpoint 4 insert after initialize i i = 1 129 6 i = 1 delete 6 insert save original p1 Temp = P1 8 i = 2 i > 2 11,12 save original.. delete Temp = P1 14 add statement label 2 130 19-22 delete 24 i = 2 i = i + 1 29 <> <> 0 33 P1 P 143 3 wdotn Wdotn 144 20 >= > 176 Sutherland- 1 then 5 then 4 Hodgman 177 9 4 x 4 2 x 2 198 floating 21,22 x,y Xprev,Yprev horizon 199 4 Lower Upper 200 11-19 rewrite as if y < Upper(x) and y > Lower(x) then Cflag = 0 if y> = Upper(x) then Cflag = 1 if y< = Lower(x) then Cflag = -1 29 delete 31 Xinc (x2-x1) 36 step Xinc step 1 201 4 delete 6 Xinc = 0 (x2-x1) = 0 12 Y1 - Y1 + Slope - 12 insert after Csign = Ysign 13 Yi = Y1 Yi = Y1 + Slope 13 insert after Xi = X1 + 1 14-end rewrite as while(Csign = Ysign) Yi = Yi + Slope Xi = Xi + 1 Csign = Sign(Yi - Array(Xi)) end while select nearest integer value if |Yi -Slope -Array(Xi - 1)| <= |Yi - Array(Xi)| then Yi = Yi - Slope Xi = Xi -1 end if end if return 258 subroutine Compute N i 402 HSV to Rgb 12 insert after end if 25 end if delete 404 HLS to RGB 2 M1 = L*(1 - S) M2 = L*(1 + S) 4 M1 M2 6 M2 = 2*L - M1 M1 = 2*L - M2 10-12 =1 =L 18 H H + 120 19 Value + 120 Value 22 H H - 120 23 Value - 120 Value 405 RGB to HLS 22 M1 + M2 M1 - M2 figures: 77 Fig. 2-39a interchange Edge labels for scanlines 5 & 6 Fig. 2-39b interchange information for lists 1 & 3, 2 & 4 96 Fig. 2-57a,b y sub i + 1 y sub(i+1) 99 Fig. 2-59 abcissa of lowest plot should be xi vice x 118 Fig. 3-4 first initialization block - add m = Large add F entry point just above IFLAG = -1 decision block 119 to both IFLAG=-1 blocks add exit points to F 125 Fig. 3-5 line f - interchange Pm1 & Pm2 128 Fig. 3-6a add initialization block immediately after Start initialize i, i=1 immediately below new initialization block add entry point C in Look for the farthest vissible point from P1 block - delete i=1 in decision block i = 2 - change to i > 2 129 Fig. 3-6b move return to below Save P1 , T = P1 block remove Switch end point codes block in Reset counter block replace i=2 with i=i + 1 180 Fig. 3-34b Reverse direction of arrows of box surrounding word Start. 330 Fig. 5-16a add P where rays meet surface 374 Fig. 5-42 delete unlabelled third exit from decision box r ray? 377 Fig. 5-44 in lowest box I=I+I sub(l (sub j)) replace S with S sub(j) _________________________________________________________________________ Known corrections to the first printing: 90,91 scan line seed write for xeroxed corrections fill algorithm ________________________________________________________________________ END OF RTNEWS