*"Light Makes Right"*

March 8, 1988

Volume 1, Number 4

Compiled by

All contents are copyright (c) 1988, all rights reserved by the individual authors

Archive locations: anonymous FTP at
ftp://ftp-graphics.stanford.edu/pub/Graphics/RTNews/,

wuarchive.wustl.edu:/graphics/graphics/RTNews, and many others.

You may also want to check out the Ray Tracing News issue guide and the Mother of all Ray Tracing Pages.

- Surface Acne, by Eric Haines and Jeff Goldsmith
- Goldsmith/Salmon Hierarchy Building, by Jeff Goldsmith
- Efficiency Tricks Followup, by Masataka Ohta, Jeff Goldsmith, Eric Haines
- Primitive/Box Overlap Testing (extracts from USENET news), by Ruud Waaj, Paul Heckbert, Andrew Glassner

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!

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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.)

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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!).

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These are comments generated by Jeff Goldsmith's note that Kay/Kajiya sorting is not needed for shadow rays.

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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?

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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.

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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?

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________________

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?

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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.

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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.

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Eric Haines / erich@eye.com