"Light Makes Right"
January 27, 1993
Volume 6, Number 1
All contents are copyright (c) 1992,1993, all rights reserved by the individual authors
Archive locations: anonymous FTP at
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.
On a related note, recently I received a note from Ken Sykes at Microsoft. He had sped up the rgbvary.c code in Graphics Gems III by using integers instead of floating point. Doing this reduced filtering time by a factor of 8 on his PC. He wished more publicly available code used integer arithmetic when possible.
The ray tracing roundup in this issue shows that people are quite busy out there. I've broadened the bounds of the column a bit to include other rendering related releases, since the dividing line between ray tracing and other algorithms is not particularly sharp nor important (for example, you may preview a ray trace with a z-buffer algorithm, or use scanline methods to accelerate your ray tracer).
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George Simiakakis SYS PG University of East Anglia Norwich NR4 7TJ England A118@CPC865.EAST-ANGLIA.AC.UK
Interests : subdivision techniques, radiosity
For the moment I am investigating 5D subdivision techniques for ray tracing. Starting from the Ray Classification algorithm I am trying to come up with a more efficient algorithm with less variance in it's performance. The main ways of doing that are adaptive choice of subdivision parameters and degeneration of 5D subdivision to spatial subdivision where this is appropriate.
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Grids and octrees are certainly the most popular, and they do quite an effective job at speeding up intersections by reducing the number of candidate objects that the ray might hit. More speed is always better, of course, so there are always variants of these methods usually with a time speedup at the expense of storage, preprocessing, and/or programming complexity.
I've thought up a small, quick, trick that can be included in almost any grid-type sorting algorithm. It trades off storage space for a decent speedup, but its biggest charm is very easy implementation. Modification of your favorite grid-sorting algorithm is probably only an hour or two of work.
The trick is based on the observation that the number of "cubes" that a ray passes through per unit length is a function of the direction of the ray. A uniform unit-sized grid aligned along the world axes is the easiest demonstration of this, though it works for non-uniform grids and octrees too. If a ray is pointed straight along the X axis, it will obviously "skewer" an entire row of cubes. At a distance of n units, the ray has passed through n unit cubes.
If the ray's direction is different, though, it passes through MORE cubes. At a 45 degree angle ( the unit vector is xn=0.707 yn=0.707 zn=0.0), the ray will have moved an x distance of 0.707*n units and a y distance of 0.707*n units. It has passed through a total of 1.414*n cubes! [This is correct: A ray will only pass from one cube to a cube that it shares a face with. Most algorithms never even check for a diagonal step, since this has a vanishingly small probability when you're dealing with floating point numbers. For example, a ray going from cube 0,0 to cube 1,1 might go from 0,0 to 0,1 to 1,1 and not straight from 0,0 to 1,1.]
The number of unit cubes a ray passes through (at the limit of n large) is just the sum of the absolute x,y,and z distances the ray traverses. The important thing to notice is that the volume of space that contains objects that need to be tested for intersection with the ray is directly proportional to this number of cubes. The more cubes the ray passes through, the more intersections you'll probably have to do. It is therefore "cheaper" to test a ray that moves right along an axis, which passes through one cube per unit length, than one that moves at a perfect diagonal along the lattice (from 0 0 0 to the direction 1 1 1 ) which passes through 1.703 cubes per unit length. THIS WORST CASE HAS TO TEST 70% MORE VOLUME (AND OBJECTS) THAN THE BEST CASE. This is all due simply to the direction of the ray as compared to the coordinate system of the grid. I wrote a quick program to find the "average" case, which was about 1.3 cubes per unit length, assuming all ray directions were equally likely.
My algorithm enhancement is based on this grid orientation dependency. The basic idea is simple: just make one (or more) EXTRA grids with the same objects, but with the grids at an angle to the original grid. To test a ray with the objects in the world, you just choose which grid is most "aligned" with the ray along any axis. This "best" alignment can be determined quickly and simply by looking at the (normalized) ray direction in each grid's coordinate system. The function [fabs(xn)+fabs(yn)+fabs(zn)] tells you the number of cubes per unit length that the ray will pass through. The smaller this number the better, since less volume (and on the average less objects) will have to be tested.
Storage requirements are obviously increased: two grids take twice the room of one. [Always a trade off!] But usually the grids aren't THAT large, since they just store lists of object ID's and not the actual objects themselves. The time to assemble the grid is obviously increased but I found that it was easy to modify the loop that decides what box(es) each object goes into so that it did all of the grids simultaneously with the same loop. For two grids, it increased preprocessing time by about 70%.
What kind of overall speedup is expected? Well, the more grids (at different angles) that are used, the better your ray-alignment will be on average, meaning fewer cubes will have to be tested. The testing to determine which set of boxes to use takes a trivial amount of extra time, but the extra preprocessing to make the grids IS significant. Also, there will STILL be inefficiency: every ray can't always be directly along an axis of one of the grids. I implemented a two grid and a four grid model. Though I didn't spend a whole lot of time in optimization, the four grid method was horrible: the preprocessing step took far too long for a scene with about 1000 objects, slowing down the overall render time. For two grids (the second grid rotated at a 45, 45, 45 degree angle, you know what I mean), the speedup was evident: Preprocessing was about 170% of the old time, but actual rendering was about 25% faster. Depending on how many objects were being traced, the overall speedup was from 0% to 20%. This is in no way a revolutionary speedup, but for about two hours of programming it is not bad! Also, these numbers are based on a non-optimized program, and can only get better if I do a more careful implementation.
Why wasn't the rendering speedup more than 25%? A couple of reasons. The biggest is that when a ray passes though more volume, there TENDS to be more objects that need to be intersected. But there's often many objects that span adjacent boxes, and these (in a good implementation!) are not re-tested so it doesn't matter much that the extra volume was passed though. It depends on the object density and size: if most objects were small compared to the box size and roughly uniformly distributed in space, the number of objects tested would correlate better with the volume of the cubes that the ray passes through. [Which is really what we're reducing with this algorithm.] But even when most grids are empty or have objects that span many cells, using the more "aligned" grid is never going to hurt: testing less cells is going to be easier.
Anyway, there might be some improvements to this idea (it's only about a week old!) but it is so simple to implement that I thought I'd pass it along. I've implemented it for uniform grids (very simple but not necessarily the best!) and octrees. I have not tried to make a non-uniform grid yet, but you'd probably have to make a modification of the cost function based on the AVERAGE x, y, and z sizes of the boxes.
If anyone implements this idea or has any new ideas, I'd like to hear about it. Meanwhile I'll hopefully get some time to run some more accurate benchmarks.
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Jim Callahan (firstname.lastname@example.org) writes: I understand that Radiance stores images as 32-Bit RGB. How does an adjustment of exposure effect the colors displayed. Obviously it affects the brightness of the image, but what are the differences between exposure and gamma correction? Are both needed? If a light source is too dim, I want to know in absolute terms.
This is a bit confusing to me because I realize that the eye is constantly readjusting its exposure. I would like to be able to say that the image is a "realistic" simulation of a scene, but can this really be done?
You've touched on a very complicated issue. The 32-bit format used in Radiance stores a common 1-byte exponent and linear (uncorrected gamma) values. This provides better than 1% accuracy over a dynamic range of about 10^30:1, compared to about 3% accuracy over a 100:1 dynamic range for 24-bit gamma-corrected color.
Changing the exposure of a Radiance image changes only the relative brightness of the image. Gamma correction is meaningful only in the presence of a monitor or display device with a power law response function. Gamma correction is an imperfect attempt to compensate for this response function to get back linear radiances. Thus, applying the proper gamma correction for your monitor merely gives you a linear correlation between CRT radiance and the radiance value calculated. (Radiance is named after the value it calculates, in case you didn't already know.)
However, as you correctly pointed out, linear radiances are not necessarily what you want to have displayed. Since the dynamic range of a CRT is limited to less than 100:1 in most environments, mapping calculated radiances to such a small range of dispayable values does not necessarily evoke the same response from the viewer that the actual scene would. The film industry has known this for many years, and has a host of processing and exposure techniques for dealing with the problem. Even though computer graphics provides us with much greater flexibility in designing our input to output radiance mapping, we have only just begun to consider the problem, and it has not gotten nearly the attention it deserves. (If you are interested in learning more on the topic, I suggest you check out the excellent CG+A article [not out yet, should be good. - EAH] and longer Georgia Tech technical report by Jack Tumblin and Holly Rushmeier.)
Color is an even stickier problem. Gary Meyer and others have explored a little the problem of mapping out-of-gamut colors to a CRT, but offhand I don't know what work has been done on handling clipped (over-bright) values. This is another interesting perceptual issue ripe for exploration.
The best you can currently claim for a computer graphics rendering is that photography would produce similar results. Combined with accurate luminance calculations, this should be enough to convince most people. In absolute terms, the only way to know is by understanding lighting design and luminance/illuminance levels appropriate to the task. It will be many years before we will have displays capable of SHOWING us unambiguously whether or not a given lighting level is adequate.
[Graphics Gems II has an article "Real Pixels" and code by Greg Ward for using 32 bit format for RGB. The on-line distribution has more code than the book, as I recall. - EAH]
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One particularly useful trick if you do have a bounding volume around the polygon (say an axis-aligned cube) is to check the ray/plane intersection POINT with the bounding volume. The point in volume test is very cheap (6 compares) and provides a way to trivially reject hits that are far from the polygon. This quick rejection method has been developed by several people independently, and Andrew Woo has a nice description in Graphics Gems I on page 394. The only possible danger of using this extra rejection is that that a polygon laying on an axis-aligned plane will have a bounding box with no depth, and the "ray hits box?" and/or "point in box?" algorithms need to be robust enough to correctly handle it.
The method is therefore:
1) Test to see if plane's normal is facing you (50% culling right here!) 2) Test to see if ray intersects bounding cube at all 3) Intersect the ray with polygon's plane 4) Test intersection POINT with bounding cube 5) Test intersection point for in/out polygon
But what if you eliminated the ray/bounding cube test (#2) completely and for ALL (facing) polygons you computed the ray/plane intersection and tested that point with the bounds? If you count up the ray/bounding box test's costs, you need 3 adds, 3 divides, and 13 compares (This is from Woo's algorithm in GG I.) But intersection with a plane only costs 5 adds, 5 mults, and 2 compares, since you already computed the dot product to test whether the plane was facing you or not. So basically you can skip right ahead to the "is the ray/plane intersection POINT in the bounding box" (which provides better rejection than the ray/cube intersection) and you'll be ahead speed-wise.
Now here's a neat trick: if you're now JUST using the bounding volume to provide point rejection (not ray rejection) we might as well do it ONLY in the 2D projected plane we also do our in-out tests in. We don't even have to compute that third component (the one we don't use for testing polygon in/out anyway,) saving a mult or two. We basically have a 2D bounding AREA and not a bounding volume. The third coordinate did provide some additional rejection, but how effective it is depends on the plane's angle: the Z coordinate is a linear function of X and Y. This also avoids any ugliness from a zero-height bounding box.
The bounding AREA will do a fast rejection of trivial points far away from the center of interest. RTNv5n3 had several discussions of different test methods, but all of them might be helped by this trivial rejection depending on the complexity of the polygon. (Any bounding for a triangle is probably a waste, but if you have a 500 sided polygon, doing at least a gross rejection of far off points is going to be a severe win.)
NOTE: This does not mean that a bounding volume is necessarily a bad idea for a polygonal object! It DOES mean that a bounding volume for a SINGLE polygon is definitely slower than doing a 2D point rejection instead.
The question is for these complex-enough polygons, what type of rejection to use? (The rest of this discussion assumes the XY plane is the plane being used for the polygon test, but XZ or YZ are obviously just the same.) The bounding square (max/min X,Y) is by far the most obvious and useful, since it only costs 4 compares and will reject all of the way-off hits. A tighter bound might be useful for a more complex figure, however. One logical further test would be to measure the maximum extents of the polygon along other directions such as the 45 and 135 degree angles: you sort of get a tight shrink-wrapped octagon bounding your polygon.
If you want to check the 45 degree angles, you do a separate min/max test on the value sqrt(1/2)*X+sqrt(1/2)*Y, which is just a coordinate rotation of the point by 45 degrees. The 135 degree rotation is done by testing sqrt(1/2)*X-sqrt(1/2)*Y. The extra 4 rejections therefore cost 2 adds, 4 mults, and 2 compares.
Now here's a really sneaky trick: What if you change to an *UNNORMALIZED* coordinate system. Don't check sqrt(1/2)*X+sqrt(1/2)*Y, check instead X+Y! The maximum extent you're checking against absorbs that normalization constant, but that is the only thing you ever use these min/max numbers for so it is not a problem.
So to evaluate the shrink wrapped octagon, you:
1) Check min/max X span 2 compares 2) Check min/max Y span 2 compares 3) Compute A=X+Y 1 add 4) Check min/max A span 2 compares 5) Compute B=X-Y 1 add 6) Check min/max B span 2 compares
You could continue into 16 sided shrinkwrapped hulls if you really need to (C=A+X D=B+X E=A+Y F=B-Y) but this is probably tight enough for anybody.
This type of bounding box is useful for other types of point sampling as well; solid texturing evaluates functions of a single point and they often have a region where a color or pattern is applied to a central location and outlying areas are left alone or colored with a background. A 16 sided bounding volume (this time in 3D) only takes 16 compares and 6 adds (by coincidence, the same as 2D.) This has been implemented in several textures, in particular one that renders Bezier outline fonts on an object's surface.
A very different method for trivial rejection of 2D points takes much more precomputation but has the additional benefit of trivial ACCEPTANCE. Basically, you impose a uniform grid onto the XY plane and classify each box in the grid as inside, outside, or indeterminate. Only when a point lies in an "indeterminate" box does the full point-in-polygon routine need to be called. Any point that falls outside the grid is automatically rejected. (The grid is sized to just fit over the polygon.) This method is especially effective for many-sided but simple polygons that have a lot of "empty" inner area since any hits on the inside away from the edges are quickly accepted.
This grid isn't too hard to make. You "render" each polygon segment into the grid, marking any boxes the line touches with an ID meaning "indeterminate." Flood fill any untouched boxes that lie along the outside edge of the grid (using the N S E W neighbors) with a flag saying "outside." Then use the "point in polygon" routine in the center of each of the remaining untouched squares to determine its state, inside or outside. When you determine a new square, you can flood fill its unchecked neighbors. This all works since the only indeterminate boxes are the ones that edges pass through, and an edge (and therefore an "indeterminate" box) will always separate any transition between inside and outside. This will work for either winding number or even-odd methods of point-in-polygon definition.
The lookup grid is expensive in terms of memory, but the speedup can be significant especially for large or complex polygons. Each box in the grid needs two bits of storage since there are three possibilities to choose from. A cheaper but slower alternative is to use only one bit to encode the in/out/indeterminate state. During precompute, count up the number of boxes for acceptance and rejection, and encode the less common state as indeterminate.
[I have implemented this algorithm and it works very well, giving you near O(1) performance for "reasonable" data. I used the outlines of continents for my polygons (from 164 to 1152 points) and had good results. This algorithm would probably be good for GIS applications. The indeterminate cells can be evaluated much faster by noting which edges actually pass through the cell. Since you know the state of the corners of the cell (i.e. each corner is in or out), you draw a line segment from your test point to the nearest cell corner (or any corner, but the nearest should have less crossings). Using the ideas of Mukesh Prasad in Graphics Gems II for line segment intersection testing, you can quickly find how many crossings occur between the test point and the cell corner and so know the test point's status. - EAH]
One implementation danger is in ROBUSTLY identifying each square in the lookup grid that any edge passes though. A vertical or horizontal polygon edge might lie right along the borders of a square in the lookup grid, or less commonly, a line might pass diagonally through a corner of one of the squares of the grid. In both cases it is probably best to be conservative and identify the adjoining square(s) as indeterminate.
One modification of this algorithm can speed it up further. Instead of recording just three states in the look-up grid, a fourth state meaning "unprocessed" is added. During precomputation, you mark all of the "indeterminate" squares as before, but you don't do anything else. (Your grid after pre-computation will therefore be filled only with "indeterminate" and "unprocessed" squares.) When you begin rendering, you use the grid as before, but when you hit an "unprocessed" square, you do the point-in-polygon test, record the answer in the grid, do the flood-fill of the neighbors, and return the correct answer. This method is a little bit more complex to implement, but you'll only end up doing the minimum amount of work building the grid since you set it up partially "on demand."
These bounding area methods are useful complements to the point-in-polygon test. They provide quick rejections (or acceptances) the number of times that the (relatively) slow point in polygon routine is called, exactly the same way that a bounding volume can provide quick rejection of ray/object intersections.
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I am always surprised to see articles advocating angle tests, intersection counting, or Barycentric coordinates for determining if an intersection point is inside of a 3d dimensional triangle, when the simple way of determining this is also the fastest, if you can live with a few more bytes stored per triangle.
Store with each triangle 2 indices, i1 and i2. These are the coordinate offsets for the two axes that will be considered in the test. (the axis with the largest component in the normal vector is dropped, as usual). Store the 2 coefficients and the 1 constant of the "inside-outside" equation of each edge.
To test for intersection, calculate C*X[i1]+C*X[i2]+C (X is the intersection coordinate, and C are the 3 constants for the linear equation calculated at setup time) over all 3 edges. If any of them have a negative (or positive depending upon which convention you choose) result, return NO_INTERSECTION.
Assuming hardware multiply, this can be coded extremely efficiently, and can take advantage of multiply-accumulate instructions if they are available. In fact, with a fast MAC instruction, it might be more efficient to skip the coordinate indexing all together and just use the 3d equation of the plane passing through the edge perpendicular to the triangle on some architectures.
The only further optimization I take is that I store the edge equations sorted by the area of the 2d bounding volume of the triangle which is outside of that edge.
In 68040 code, this all boils down to: move.l 0(a5,d6.w),d4 ; d6=i1, a5 = &intersection point move.l 0(a5,d7.w),d3 ; d7=i2 muls.l (a4)+,d0:d4 ; C0*X1 muls.l (a4)+,d1:d3 ; C1*X2 add.l d3,d4 addx.l d1,d0 ; C0*X1+c1*x2 movem.l (a4)+,d1/d3 ; fetch 64 bit constant term add.l d3,d4 addx.l d1,d0 ; c0*x1+c1*x2+c2 bmi.s no_hit3 ; outside? repeated 3 times.
Reply from Eric Haines:
I'll put your note in the next RTN - thanks. Berlin, in the truly obscure reference
%A E.P. Berlin, Jr. %T Efficiency Considerations in Image Synthesis %B SIGGRAPH '85 course notes, volume 11 %D July 1985 %K polygon intersection
gives the same method you do (he thinks of it as three planes). I assume that your method works for convex polygons only, unless you test all triangles within the polygon and check the parity [see RTNv5n3 for more information].
The catch is, most people don't code in assembler (the counting crossings test is darned fast in assembler). However, your test is darned fast anyway, at least for simple polygons. The extra memory is something of a drawback, but who can complain?
I coded it up (looked pretty efficient) and tried it in my test suite. Here are the results:
For random polygons:
Number of vertices 3 4 5 3-7 20 100 plane 1.15 1.88 2.81 2.91 16.10 87.02 macmartin 1.90 2.33 2.76 2.67 10.63 51.47 inside % 6.78 11.78 13.11 12.22 26.22 35.67
For regular polygons:
Number of vertices 3 4 5 3-7 20 100 plane 1.22 2.23 3.25 3.36 16.67 86.51 macmartin 2.33 2.80 3.03 3.10 6.31 23.78 inside % 33.22 51.00 60.22 55.22 77.44 80.22
Admittedly, for the regular polygons I could do the test for the plane set based on "first hit means quit", since the regular polygons are convex. This will result in faster timings for it (as it would for the macmartin tests: if two crossings are found while doing the macmartin test for convex polygons, then you can quit). It's cool that your test is better for 3 and 4 vertex polygons, since these are real common.
Thinking about my method applied to polygons with large (>4) numbers of sides, I realized that the edge equations should be stored in bit-reversed order, assuming some bounding volume that reduces PIP tests to only those points which are somewhat near the polygon, and also assuming most polygons are relatively regular.
Imagine an octagon surrounded by a rough bounding box. If the first side didn't clip off the point, the 2nd isn't that likely to if it is at a similar angle to the first one. But the opposite side is more likely to. The optimal thing to do is to calculate the area which is inside the bounding box which has not yet been clipped off by one of the previous edges, but this would involve calculating intersections of the edges with each other, which is probably too much work to do on a polygon which might only cover 10 pixels on the output image.
The algorithm is to check the point against the edge equations of each edge of the convex polygon (the "inside-outside" equation of the edge). i.e:
if v0 is one vertex and v1 is another, and v2 is another point on the polygon,
a=v1.x-v0.x b=-(v1.y-v0.y) c=-(a*v1.x+b*v1.y)
if (a*v2.x+b*v2.y+c>0) then negate a,b,c to make the inside-outside sense correct.
Which coordinate x and y are depends, of course, upon the surface normal of the triangle.
x,y=intersection point of ray and plane projected onto the correct axis.
for(each edge) if (x*a[i]+y*b[i]+c[i] >0) then no_intersection
All the abc[i]'s are sorted in such a way (based upon the bounding volume) so as to make the probability high that the first test will reject the point. For a many-sided (roughly regular) convex polygon, storing the sides in bit reversed order (for an 8 sided polygon this is 0,4,2,6,1,5,3,7) causes the loop above to test the point against a bounding volume which "homes-in" on the actual shape of the polygon. For a triangle, I store the sides based upon the area of the triangle cut out by the intersection of the edge and the bounding box.
Steve Worley (email@example.com) had some independent observations, also realizing that half-plane testing should be fast:
In RTNv5n3, Peter Shirley wrote about a fast triangle test using barycentric coordinates. It seems to me that the fastest method (by far!) to test whether a point is in a 2D triangle is to just do three half-plane tests. Represent each of the lines that make up the triangle with two real numbers A and B such that the line is described by the formula Ax+By=1. If the triangle lies below that line, a point on the "wrong" side of the line will satisfy the inequality Ax+By>1. If the triangle is "above" the line, you just test Ax+By<1 instead. You do this test for each of the three triangle sides, and immediately return if it fails at any time. If it passes all three tests, the point is in the triangle. The computational cost is two multiplies, an add, and two compares for each test, so worst case cost is 6 mults, 3 adds, 6 compares. However, you're more likely to get rejected on the first tests, and the mean amount of computation for a completely random triangle turns out to be exactly 3.5 mults, 1.75 adds, and 3.5 compares.
A slightly faster method would be to write each line in the form Cx+y=D instead, which would save a multiply on each test. However this causes a problem because of perfectly vertical lines which would make C and D become infinite. An extra compare would be needed to check for this case so that the more general Ax+By=1 test could be substituted.
While this method is probably about as fast as a 2D point in triangle test can get, Shirley's barycentric method has one big advantage in that AFTER a hit, the computed coordinates can be immediately used for Gouraud or Phong shading. Depending on the percentages of tests versus hits your application gets, it might be cheaper to use only barycentric if typical tests have a high enough hit rate. Note also that both the barycentric and the half-plane rejection methods will work on any convex polygon.
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The February 1993 issue of National Geographic has a fold-out image of Venus on page 37. This image was rendered by David Anderson at SMU using Craig Kolb's Rayshade software. Also, the computer firm Santa Cruz Operation is evidently using/going to use images made from public scene files by Rayshade in showing off their SCO Open Desktop.
A new book on ray-tracing has come out, and comes with a disk of code for "Bob", a ray tracer (of at least 8K lines of code). Note that Stephen Coy is also the creator of the VIVID ray tracer. I hope to review this book for the next issue of the RTN - EAH. It's at least 8k lines of code.
Photorealism & Ray Tracing in C Christopher D. Watkins, Stephen B. Coy, and Mark Finlay M&T Books, a division of M&T Publishing, Inc. 411 Borel Avenue, Suite 100 San Mateo, CA 94402 (C) 1992 ISBN 1-55851-247-0
Some comments from Stephen Coy:
Bob, the raytracer in the book, is basically Vivid with a few, minor changes. The changes tend to center around the parser. I didn't want to use flex and byacc for the book so I spent a long day writing the parser from scratch in C. Everything works except allowing the user to perform math functions in the input files. I'd like to see some benchmarks with Bob vs some of the other tracers out there. Even though it is distantly derived from MTV I think it will generally beat MTV by quite a bit.
Before you ask, the name Bob just sort of happened. When I was working on the code I got tired of talking to Chris and calling it "the ray tracer for the book." I suggested that we just call it Bob until we came up with a better name. The deadlines came first.
Another new book is _Practical Ray Tracing in C_ by Craig A. Lindley. It contains a disk for the IBM PC and the ray tracer is DKB Trace. I assume it has the same features as the PD one on the net (and vice versa). The book is evidently a $49.95 paperback (with disk of course). (Tom Wilson, firstname.lastname@example.org)
[Does anyone know anything about this book? I haven't seen it and am unwilling to blow bucks on it. Any review (biased or no) is appreciated! - EAH]
For those of you who still believe free software is worthless, a comment from a guy at NASA on Radiance [an "industrial strength" lighting simulator free from Greg Ward - a ray tracer and much more]:
By the way, your package is a very good one, in just 2 weeks we were able to trace complex space shuttle lighting very easily. Nice work.
The source code from the notes of Siggraph '92 Course 23 (Procedural Modeling and Rendering Techniques) is now available for anonymous ftp from archive.cis.ohio-state.edu as pub/siggraph92/siggraph92_C23.shar . Without a copy of the course notes, these files may not make sense. (David Ebert, email@example.com)
Human heads and an anatomically correct human skull data are available. The data is a mesh and the demo contains convert utilities to translate into various other formats, eg. ASCII, Wavefront, IGES, etc. The demo runs on a SGI IRIS workstation. Ftp from taurus.cs.nps.navy.mil, login anonymous, password guest, file pub/dabro/cyberware_demo.tar.Z . (George Dabrowski, Cyberware Labs, firstname.lastname@example.org)
A simple public-domain radiosity package is available at ftp.yorku.ca (was: nexus.yorku.ca) (126.96.36.199) in /pub/reports/Radiosity_code.tar.Z (also mirrored at wuarchive.wustl.edu). The package contains C code for a progressive refinement solution using the following algorithms:
Wallace (Ray-traced form-factors), Haines (Shaft Culling), using automatic hierarchical bounding creation (Salmon 87) Chen (Progressive refinement with jitter hemicubes) A partial implementation of Hanrahan's BF-Refinement algorithm.
Additionally, there are model preprocessors for conversion from QuickModel and OFF formats, with geometric constraints of Baum's 91 Siggraph paper partially included; and a scene walk through program with simple Gouraud shading. The solution can be run stand-alone on any Unix box, but the walk-through requires a SGI 4D. (Bernard Kwok, email@example.com)
Version 2.2 of x3d, a 3D wireframe / hidden line / hidden surface viewer that runs under X11, is now available via anonymous ftp at castlab.engr.wisc.edu (188.8.131.52) and is found as /pub/x3d.2.2.tar.Z. (Mark Spychalla, firstname.lastname@example.org)
If you use AutoCAD 11 Advanced Modelling Extensions (AME) software to build 3D objects, it is now possible to convert these models to a raytracer compatible scene file format (SCN), which is used by the RTrace package (raytracer plus utilities). The converter code is available at asterix.inescn.pt [184.108.40.206] in directory pub/RTrace/scene-conv/acad (files scn.h and sol2scn.h).
A MAC version of RTrace 1.0 version (beta) is available in directory pub/RTrace/Macintosh at asterix.inescn.pt [220.127.116.11] The code was made by me; Reid Judd (email@example.com) and Greg Ferrar (firstname.lastname@example.org) made the Mac port. (Antonio Costa, email@example.com)
A new release of Tcl-SIPP is available from:
and should be available soon from:
Tcl-SIPP is a 3D image specification and rendering toolkit for use with Tcl and Tk.
It provides a Tcl command interface to SIPP, the SImple Polygon Processor library. This is used for creating 3-dimensional scenes and rendering them using a scanline z-buffer algorithm. The Tcl interpretive programming language is used to provide a powerful, yet simple interface to this library. The scene may be written to either a PPM format file, as defined by the PBMPlus toolkit or a RLE file, as defined by the Utah Raster Toolkit.
An interface to render to the photo widget in the Tk X11 toolkit is also provided. Events such as button presses may take place while rendering is in progress. (markd@NeoSoft.com, Mark Diekhans)
Under princeton.edu:pub/Graphics/rayshade.4.0, you'll find several new directories, including:
Contrib User-contributed enhancements, header files, etc. Amiga/DOS/MAC/OS2 Ports to various strange operating systems. Pix Rayshade-generated images, texture maps, etc.
There have been other changes to the archive; poke around and you'll undoubtedly discover them.
I've placed all of the old rayshade-users messages on the princeton archive: princeton.edu:pub/Graphics/rayshade-users/Feb-Sep92.Z.
This file is completely unedited -- if it was sent to the list between February and September 28th, it appears here. If some brave soul wants to edit out the chaff, I'd be happy to replace the file with something more appropriate.
Utah RLE viewers for the IBM PC are available at firstname.lastname@example.org)
NCSA Polyview 3.0 is now available via anonymous FTP to ftp.ncsa.uiuc.edu (18.104.22.168) in /SGI/Polyview3.0. Polyview 3.0 is a software tool for interactive visualization and analysis of 3D geometrical structures. Polyview 3.0 reads data files in NCSA HDF Vset format and automatically derives animation sequences based on available information. Script-based and graphical user interfaces complement each other in a seamless fashion to allow the easy creation of movie-style animations. Rayshade users on SGIs may be interested in this; among other things, it generates scene files in rayshade 4.0 format (and also in Pixar's RenderMan format). (Marc Andreessen, email@example.com)
POLYRAY is a ray tracer that is "more difficult to use but substantially faster". Version 1.4 is available at faramir(or ftp).informatik.uni-oldenburg.de (22.214.171.124) in pub/dkbtrace/incoming/polyray. Note that the file has probably moved somewhere by now. This site also contains a number of POV & DKBtrace scene files and images, as well as 3d fonts for POV and Vivid (Andy Haveland, firstname.lastname@example.org)
If you're on (or have access to) an Amiga system, then you may want to check out Vertex, a shareware ($40) 3D object editor/converter. It will read Wavefront .obj files and save them in Imagine, Sculpt 3D, Lightwave RayShade, GEO and 3D Professional file formats. While not perfect, it does correctly read the Wavefront geometry from the file, and you can modify smoothing and face colors right in Vertex. (Alex_-_DeBurie@cup.portal.com)
White Sands Missile Range (126.96.36.199) in pd1:(msdos.graphics) carries Thunder, a ray tracer from Germany.
A 512x512x24 bit Mandrill is available in PPM and JPEG formats from popeye.genie.uottawa.ca, in /pub/pics. (Dominic Richens, email@example.com)
The cameraman image is available via anonymous ftp from eedsp.gatech.edu in database/images/camera.256. The file is unformatted byte format with image dimensions 256x256. (Stan Reeves, firstname.lastname@example.org)
Graphtal is a L-system interpreter, and includes a number of features, including animation support, X11 previewer, z-buffer preview, and output for rayshade. It is in C++, and currently works on SparcStations, RS/6000's, and DEC Stations. The first public release of graphtal is now available via anonymous ftp at iamsun.unibe.ch (188.8.131.52) and is found as /Graphics/graphtal-1.0.tar.Z or /Graphics/graphtal_no_bison_no_flex-1.0.tar.Z. (Christoph Streit, email@example.com)
The Dr. Dobb's Journal's FTP directory ftp.mv.com /pub/ddj/packages has Xsharp, a fairly fast hidden surface displayer for the IBM PC. Source code in C and assembler is included, and Xsharp now has some simple texture mapping capabilities.
The GRAPHIC CONNECTION can be reached at the following numbers:
by modem: 503-591-8412 voice: 503-591-0134 FAX: 503-244-0919V.32bis/V.42.bis MNP, 24 hours a day.
This BBS is owned and operated by Vertech Design, is located in Portland, Oregon. TGC specializes in material/texture files, custom bitmap design, graphics utilities and programs, and specialized scanning services. There will also be a large message base with topic specific areas for all areas of CAD and graphics support.
[I tried this BBS out some time ago, but had trouble getting any material texture samples - the directory which was supposed to have these publicly available was inaccessible, for some reason. I paged the sysop, but he didn't seem to know what was wrong, either. - EAH]
For 3D stereo supplies, one source is Reel 3D's mail order catalog: Reel 3-D Enterprises, Inc. P.O. Box 2368 Culver City CA 90231 Phone (310)837-2368 Fax (310)558-1653 (Alexander Klein, editor of 3D-MAGAZIN, firstname.lastname@example.org)
ftp.rahul.net [184.108.40.206]:/pub/bryanw has a number of programs related to JPEG and MPEG generation and display. (Bryan Woodworth, email@example.com)
VIS-5D is a system for interactive visualization of 5-D gridded data sets such as those made by numeric weather models. One can make isosurfaces, contour line slices, colored slices, wind vector slices, wind trajectories, etc. of data in a 3-D grid and then rotate and animate the image in realtime. There are also features for text annotation and video production. Systems supported: SGI, IBM RS/6000, Stardent/Stellar. FTP from iris.ssec.wisc.edu (220.127.116.11). It is also available on wuarchive.wustl.edu in the directory graphics/graphics/packages. (firstname.lastname@example.org, Brian Paul)
Disc-1 Graphics- is a collection of more than 426 MegaBytes of popular public domain, shareware, and freeware graphics programs and data files. The disc contains more than 1200 programs, 16,000 files. The cost of the disc is $24.95 plus $5 to cover shipping and handling ($15 overseas). Orders may be FAXed to (916)-872-3826. Prepaid orders may be mailed to : Knowledge Media 436 Nunnelley Rd. Suite B Paradise,CA 95969, USA (Paul Benson, email@example.com)
The Copyright Guide from the ASMP (American Society of Media Photographers) is available in digital form now. FTP from ftp.eff.org: pub/cud/papers/asmp-guide, or ftp.ee.mu.oz.au: pub/text/CuD/papers/asmp-guide.Z, or ftp.moink.nmsu.edu. Although written from a photographers perspective the Guide might help to clear up a few points of confusion about copyright protection of images. (Don Smith, firstname.lastname@example.org)
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"... the architecture supports the following features:
o Standard radiosity and distribution ray tracing features (energy balancing, soft shadows, depth of field, motion blur, spectral sampling, etc.)
o User control of most rendering parameters (with defaults)
o Programmable shaders, selected by the user in run time (including textures)
o Programmable sampling techniques. Any sampling strategy may be used, including (bu not limited to) staticc or adaptive, uniform or noisy. Any sampler may be used to draw samples on any two-dimensional distribution. Higher-dimensional samplers may be used as well.
[nfotis: I think that would be a better idea to separate rendering and reconstruction, as G.Ward does with Radiance]
o Programmable reconstruction techniques, appropriate for any two- dimensional signal, such as illumination spheres and screen images.
o Programmable radiation patterns for light emitters.
o Programmable cameras, selected by the user at run time.
o Easily-extended object and meta-object classes.
o Still and animated sequence rendering.
o Any geometric object may be a light emitter.
o Sampling and reconstruction are techniques unified across screen and object domains. All sampling procedures are interchangeable, whether they are sampling the image plane, the illumination arriving at an object surface, the texture of a region, etc. Similarly, reconstruction techniques, are equally, generic and applicable to all domains. A sampler is simply considered a technique for gathering information on a two-dimensional distribution. Callback procedures are used to control a sampler for the different purposes of screen sampling, shading, texturing, etc.
o Shaders receive as input a description of the illumination sphere. They are not responsible for determining the incident illumination at a point, and they may reconstruct a sampled illumination signal before processing.
o The incident illumination sphere is described as a collection of samples of the incident light. Typically, one determines this sphere by first building a set of samples that are directed to light-emitting objects; they return the color of the light foud along the ray, whether it actually reached a light emitter or not. Then this set may be passed to an adaptive sampler as a "seed", or starting signal. This increases the likelihood that light emitters are sampled, and allows the incident illumination sphere to be adaptively sampled until the sampled signal meets the criteria for that sampler. This illumination sphere is then passed to a shader for modulation vy the bidirectional reflectance distribution function of the surface at this point.
o Objects may be queried by a shader for information. This contrasts with the Renderman model, where a shader may expect a number of variables to be precomputed and available. Since the shaders in this system are not precompiled from a special-purpose language, if is difficult to determine a priori what information a shader requires from an object. Thus each object contains a procedure that accepts a request from a shader in the form of a list of requested geometric values, and returns the relevant information. There is a performance penalty for this process, but it only occurs once per shading point. I consider that the extra overhead to parse the request list is compensated by the time saved by not calculating unnecessary values.
o Colors may be specified in a variety of formats, including spectral distributions.
o Meta-objects (accelerators, CSG trees, abstract structures, etc.) are considered "first-class".
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You're right in that part of the problem is that he's using point lights. However, Phong's highlights are basically a way to simulate surface shininess. After all, a true point light would never reflect (well, except at one single point) in a surface if the surface was perfectly reflective, with no "spread" in the reflection. Essentially, Phong's trick is to spread out the reflected light in a cosine to a power distribution, and note the value of this distribution from the eye's view angle - a wider distribution gives a duller looking surface. When you have area lights, you can't use this easily: you either have to reflect the lights directly (in which case the lights are seen in the reflection as if the surface were perfectly reflective) or you have to sample the area a sufficient amount to get the phong highlights and sum and scale these.
In theory, what works for lights should work for light reflectors in the environment. In other words, you could sample the environment (i.e. ray trace) from the view of the surface and use Phong highlighting on these sample rays and so get a shiny or dull looking surface. If you're smart, you'll simply use the Phong distribution itself to determine where the rays are shot, shooting more rays in the higher contribution areas. This has been done, and looks pretty good with enough reflection samples.
The problem with Phong's trick is that it is not energy conserving at all: a low cosine power gives a lot more total energy (light) reflected from a surface than a high cosine power. Phong kept peak intensity constant, which is important for making it easy for a user to adjust the specular highlight's look, but is lousy from any physically based standpoint.
This lack of energy conservation hit home when I tried doing texture mapping of the cosine exponent. Say you texture this exponent and it varies from 0 to 10. The weird effect is that the surface brightness is brightest around 1 (or less, if you allow < 1 exponents) and drops off as you go to 10. So at 0 you get no specular highlight, at 1 the overall brightness is at its height, then it drops off as you go to 10.
>The thresholding trick is a neat trick, that I didn't know about, and it'll
>save a lot of rendering time when you *do* use point light sources and still
>want a large shiny spot on your objects.
Yes - essentially, you're saying you want the surface to look perfectly reflective (i.e. mirrorlike, not like brushed aluminum) and for the light to have a finite radius. The only problem I see is that the thresholding trick does not take into account the distance the object is from the light, so that the light will always be reflected as the same relative size no matter what the distance the light is from the object.
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======== Net cullings follow =========================
We've decided to bring out Gems IV in 1994, not 1993, to keep the quality of the series high. The deadline for contributions is in the late Spring of 1993. Write to Academic Press (not me) for more detailed information about how to contribute:
Graphics Gems Editor Academic Press 955 Massachusetts Ave Cambridge MA 02139
or email email@example.com .
And if you've got ideas for contributions and you'd like to discuss their appropriateness with me, email me at firstname.lastname@example.org . Suggestions and criticisms of the previous volumes are also welcome.
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The project started with the DEC online computer graphics bibliography, which covered the years 1976 through 1986, and added the contributed bibliographic databases of a number of individuals, expanding the years covered as well as the sources of information.
This database includes references from conferences and workshops worldwide and from a variety of publications, from magazines and journals to books dating back as far as the late 19th century. The majority of the major journals and conference proceedings between the mid-1970's and 1992 are listed here.
The database is formatted in the BibTeX bibliography entry format, an easy-to-read and understand ASCII format. It is organized into files by year (except for the entries prior to 1975, which are collected into one file by themselves).
A set of tools for manipulating and searching the bibliography database is also available for downloading.
The database is available for anonymous FTP from "siggraph.org" "(18.104.22.168)" in the "publications/bibliography" directory. Use "anonymous" as the username and your electronic mail address as the password to gain entry to the FTP area on this machine. Please download and examine the file "READ_ME" contained in the "publications/bibliography" directory for more specific information concerning the database.
This project is an ongoing concern: We plan to expand the bibliography, both keeping it up-to-date as well as filling in missing pieces, large or small, and polishing and refining the format of the existing database. In addition, plans to provide interactive online searching of the database are underway. Alternative distribution channels are also being considered.
Volunteers are always welcome. Contact "email@example.com" for more information on what needs to be done.
Questions, corrections, suggestions, and contributions of material to the database can be directed to: "firstname.lastname@example.org" on the Internet.
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People have known for a long time that if you have two implicit surfaces f(x,y,z)=0 and g(x,y,z)=0 that are fairly continuous, with a common sign convention (f and g positive on the inside, negative on the outside, say) then the implicit surface defined by f+g=0 is a blend of the shapes. See [Ricci 1983] for a variant of this.
The van der Waals surfaces of molecules (roughly speaking, iso-potentials of the electron density) are described in Chemistry and Physics books and [Max 1983]. To create animation of DNA for Carl Sagan's COSMOS TV Series, Jim Blinn proposed approximating each atom by a Gaussian potential, and using superposition of these potentials to define a surface. He ray traced these [Blinn 1982], and called them "blobby models".
Shortly thereafter, people at Osaka University and at Toyo Links in Japan began using blobby models also. They called theirs "metaballs" (or, when misspelled, "meatballs"). Yoichiro Kawaguchi became a big user of their software and their Links parallel processor machine to create his "Growth" animations which have appeared in the SIGGRAPH film show over the years. The graduate students implementing the metaball software under Koichi Omura at Osaka used a piecewise quadratic approximation to the Gaussian, however, for faster ray-surface intersection testing (no need for iterative root finders; you just solve a quadratic). I don't know of any papers by the Japanese on their blobby modeling work, which is too bad, because they have probably pushed the technique further than anyone.
Bloomenthal has discussed techniques for modeling organic forms (trees, leaves, arms) using blobby techniques [Bloomenthal 1991] (though he prefers the term "implicit modeling") and for polygonizing these using adaptive, surface-tracking octrees [Bloomenthal 1988]. The latter algorithm is not limited to blobby models, but works for any implicit model, not just blobs. Polygonization allows fast z-buffer renderers to be used instead of ray tracers, for interactive previewing of shapes. A less general variant of this algorithm was described in the "marching cubes" paper by [Lorensen 87] and some bugs in this paper have been discussed in the scientific visualization community in the years since. In the sci-vis community, people call them "iso-surfaces" not "implicit surfaces".
Meanwhile, in Canada and New Zealand, the Wyvill brothers, and grad students, were doing investigating many of the same ideas: approximations of Gaussians, animation, and other ideas. See their papers listed below. Rather than "blobbies" or "metaballs", they called their creations "soft objects". But it's really the same idea.
Bloomenthal and Wyvill collected many good papers on blobby and implicit modeling for a recent SIGGRAPH tutorial (1991?).
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At Compugraphics 92, M. Beigbeder and V. Bourgin presented a paper titled "New Perspectives for Image Synthesis" in which they used artistic perspective projections, instead of the usual one. They had a "fishbone" perspective and a circular perspective. These perspectives broke a lot of the fundamental assumptions. Straight lines weren't always straight after they were projected and light didn't always travel in a straight line.
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I don't know POV................BUT
If it is in the tradition of the standard ray tracers, it starts at the eye, shooting rays through pixels into a scene. Essentially this is tracing ray paths in reverse. Generally speaking, ray paths are reversible, so this is fine. There are, however, difficulties. When a ray hits an object, in addition to reflected and refracted rays, rays to the light sources must be generated to determine shadows, intensity of illumination, etc. If one of these light source rays hits a refractive object, it may no longer be headed for the light source once the refraction is done.
What one would LIKE to do is shoot the light source ray in a direction (there may be several correct choices) which will result in a ray pointed at the light AFTER the refraction. Guessing what direction(s) this might be is HARD. One solution is to shoot lots of illumination rays in various directions (especially from a surface that is not perfectly specular, use the BRDF as the distribution being randomly sampled => distribution ("distributed") ray tracing).
Another solution is to do the ray tracing from the light, but then most of the rays won't get to the screen so the effort is wasted. There are various schemes in the literature for getting around the difficulties, but my guess is that they are not in most public domain code.
Another difficulty probably ignored in most PD code, is that in order to break out the spectrum, the refraction angle must be calculated on a wavelength dependent basis, generally with a single ray turning into several rays to properly sample the spectrum.
We (Redner, Lee & Uselton ++)have done an image of the experiment I believe you are describing. It was accepted into the SIGGRAPH slide set and distributed last summer at the conference. It does involve a forward ray tracing phase, and some stuff to remember these results in a way that can be used in a traditional backward ray tracer. Harder than it looks.
[Also see Mitchell & Hanrahan's article in SIGGRAPH '92 about this topic. -EAH]
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One of the best reference books for map projections is Map Projections --- A Working Manual by John P. Snyder USGS Professional Paper 1395 US Gov't Printing Office, 1987 (383 pages)
It's available directly from USGS, and was $20 a few years ago. In the USA, call 1-800-USA-MAPS (1-800-872-6277) for ordering info. Snyder covers all the projections used by USGS, and a few others. For each one he gives a bit of history, some explanatory material, detailed formulas, and examples.
There is also some source code available for anonymous FTP at spectrum.xerox.com, under directory /pub/map/source (I haven't used it, but I've seen it there).
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BTW, Will Vinton has had nothing to do with the software other than lending it his name. The program has been in development on the Amiga for several years as Animation Apprentice, then as Animation Journeyman. It's still available on the Amiga, and Mac and SGI versions are supposed to be in the works.
[and in a later post:]
If you are familiar with patch-based modeling, it is a fairly powerful modeling interface. It (IMHO) gives Alias a run for the money at a tiny fraction of the cost. I consider it the "poor person's Alias."
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First and foremost the most current version of PV3D is v.0.50. I did download it from The Graphics Alternative BBS (510 524-2165/2780) before I received my copy in the mail. I do not have ftp status from the mail site I use, so I cannot suggest a location for those so inclined. I would suspect that You Can Call Me Ray BBS (708 358-8721/5611) will have a copy available of v.0.50. I mention this because YCCMR is a free access board, while TGA is subscriber based. I highly recommend *both* systems for anyone interested in PC based raytracing.
The features included within the shareware version are identical to those in the registered version, save the following:
- you can save a created scene file for future manipulation.
- the registered version includes two additional utilities, of which one I have found to be most handy (a screen capture to texture map facility - very nice). *Source* code is included for both.
- larger screen previews of the online texture maps included with the product. The preview screens certainly help in picking an appropriate texture for that object, especially when you forget what the 'ell GRNT9 is supposed to look like =]. As per the point above there are simple instructions on how to incorporate your "designed" textures to this online library.
- a host of sample "triangled" DXF files - something I certainly appreciate given the sweat I've had creating them. Their integration is seamless, BTW.
For those who do not know what PV3D is, here's a brief review.
PV3D is a wireframe modeler for those PC based raytracers using Persistence of Vision. It is something more oriented towards the novice PoV user and for even the advanced, experienced souls, who just want to get on with creating (hopefully) interesting raytraced artworks. Beyond providing the basic primitives (sphere, quad sphere, cylinders, cones, cubes, pyramids, positive and negative blobs, planes and torii) PV3D can also generate spline based objects. You can incorporate "triangled" DXF files. Multiple lights can be positioned, as well as the look_at and camera locations, very easily. You can preview the textures used and the colours applied (corresponding surface "highlights") to individual objects. It is reasonably priced (250 Frebch Francs) and although still in a beta stage, extremely promising. It has cut down my "code" time dramatically, increasing my creative time ten fold. I'm a computer based artist and the goal is to produce art - PV3D is a major benefit in that pursuit.
Back to the latest version...
The biggest change in v.0.50 as far as I'm concerned is the new View 3D option. This will give you a world view of your scene from the perspective of the camera location. This is a major advantage, especially when you get up close to the maximum of 150 objects and you are, quite simply, lost. I know, I certainly have been in the past =]. Very nice addition.
The documentation is still hurting from a lack of a suitable French to English translation, but I intend to offer my assistance in that regard. Mind you if the author's English is bad, my French is a lot worse. I will be seeking a good translation program in this effort - any suggestions for a bi-directional program would be much appreciated.
[unfortunately, I didn't receive the second part of the review at our site, so this is all there is! - EAH]
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email@example.com (Darren Burns) wrote:
>I had been under the impression that it was quicker to intersect
>a line with a sphere than with a box. I just did a timing test.
>Basically I had a bunch of spheres or boxes sitting there and I
>ray-traced the scene, once using spheres and once using boxes.
>I found that the boxes were faster (not a lot, 11 seconds for
>spheres vs 9 for boxes). The volumes were about the same for
>both types of objects; actually the spheres were a little smaller.
You must be careful when drawing your conclusion. I've found 3D boxes faster too, but it is very dependent upon what's inside as to whether or not it will be. Depending on how optimized your code is, the sphere BV may be faster to intersect with a ray, but the comparison doesn't end there. When a ray hits an object inside the BV, both the sphere and the box are a waste of time. When the object inside the BV is missed, it is up to the BV to cull as many rays as possible. You want to perform the ray-object intersection code as few times as possible when it will miss the object (you obviously must execute the code when there is a hit).
Also you must take into account the relative execution times of (1) ray-sphere (as BV) int., (2) ray-box int., and (3) ray-object int. If (3) is much greater than both (1) and (2), you may get a better answer from your test. Suppose you have 2 BVs: BV #1 is the slower of the two, but culls more misses, BV #2 is the faster of the two, but culls fewer misses. Which is better? That depends on how many rays are actually involved in the comparison, but let's be sloppy and just say: if the time saved by using the faster BV #2 is lost by executing the slower ray-object routine more times, BV #1 may actually be the better choice. Too many tests involve spheres or boxes around simple triangles.
Basically, you are introducing yourself to an old, but difficult-to-fully- -solve problem. Much work has been done on the choice of BVs. Couple that with a construction of a hierarchy of BVs and you really have a mess. Find some of the bibliographies at ftp sites to see the work that has already been done (also you might find my collection of ray tracing abstracts which might give you a clue about what is discussed before you actively seek the papers -- send me e-mail for more details if you'd like, I don't want to bother at the moment). The text _An Introduction to Ray Tracing_ has a sufficient explanation of the background material.
The only strong conclusion I can make is that boxes work best for the scene(s) you tested. They may be a good choice in general, but that's a dangerous statement.
I hope I made some helpful comments. Others are appreciated.
[Me, I've given up bounding volume spheres and even ellipsoids: boxes seem to almost always have tighter bounds and having only one bounding volume throughout your program saves a lot of messing around in the code. - EAH]
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I've implemented an object for rayshade a couple of years ago which is pretty similar to what you've described(I call it cubicspin). You take any curve described by a 3rd degree polynomial and rotate it about an arbitrary axis. End points are also specified.
A third degree polynomial rotated like that becomes a 6th degree polynomial and then you can substitute in the ray equations to find the point of intersection. Throw in some checking for the end points and there ya go. This is the brute force method.
I use natural cubic splines to specify the curve.
Now if you started with a 4th degree curve, you would have to solve 8th degree equations, etc. But for the most uses, the extra degrees don't buy you much.
[My favorite article on this topic is still: %A Jarke J. van Wijk %T Ray Tracing Objects Defined by Sweeping Planar Cubic Splines %J ACM Trans. on Graphics %V 3 %N 3 %D July 1984 %P 223-37 - EAH]
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>firstname.lastname@example.org (Frank Belme) writes:
>I was wondering what a good way is to calculate the direction of each ray
>for ray tracing a scene given an eyepoint, eye direction, and field of view
>angle. Any help would be appreciated. Thanks.
There is actually a better way of doing this, that can take into account aspect ratio and fields of view prior to actually computing the ray direction (the speedup in this routine are generally not that noticeable, but it is nice to have something elegant!).
The first step is to compute two vectors, one in the direction of increasing x coordinates for the image, and one for increasing y coords, that are scaled to be the length of a pixel in each respective direction (aspect ratio calcs go in here). Then compute a vector that points towards the upper left corner of the screen (I will give pseudo code later).
When you have this information, you can quickly create any ray to fire by simply adding appropriately scaled versions of the x and y direction vectors to the vector pointing to the first pixel (of course you want to normalise the final vector :-):
xdir = (2 * lookDistance * tan(hfov / 2)) / xres ydir = (2 * lookDistance * tan(vfov / 2)) / yres ydir *= aspect // Adjust y pixel size given aspect ratio LLdir = camera.dir - (xdir * xres)/2 - (ydir * yres)/2
Computing the ray to fire:
dir = LLdir + xdir * x + ydir * y dir = dir normalised
and you are done - not rotations, just simply vector additions and scales (this is almost directly taken from my C++ ray tracer).
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