Inside Quake: Visible-Surface
Determination
by Michael Abrash
Years ago, I was working at Video
Seven, a now-vanished video adapter manufacturer, helping to develop a VGA clone.
The fellow who was designing Video Seven’s VGA chip, Tom Wilson, had worked
around the clock for months to make his VGA run as fast as possible, and was
confident he had pretty much maxed out its performance. As Tom was putting
the finishing touches on his chip design, however, news came fourth-hand that
a competitor, Paradise, had juiced up the performance of the clone they were
developing, by putting in a FIFO.
That was it; there was no information
about what sort of FIFO, or how much it helped, or anything else. Nonetheless,
Tom, normally an affable, laid-back sort, took on the wide-awake, haunted look
of a man with too much caffeine in him and no answers to show for it, as he
tried to figure out, from hopelessly thin information, what Paradise had done.
Finally, he concluded that Paradise must have put a write FIFO between the system
bus and the VGA, so that when the CPU wrote to video memory, the write immediately
went into the FIFO, allowing the CPU to keep on processing instead of stalling
each time it wrote to display memory.
Tom couldn’t spare the gates or
the time to do a full FIFO, but he could implement a one-deep FIFO, allowing
the CPU to get one write ahead of the VGA. He wasn’t sure how well it would
work, but it was all he could do, so he put it in and taped out the chip.
The one-deep FIFO turned out to
work astonishingly well; for a time, Video Seven’s VGAs were the fastest around,
a testament to Tom’s ingenuity and creativity under pressure. However, the
truly remarkable part of this story is that Paradise’s FIFO design turned out
to bear not the slightest resemblance to Tom’s, and didn’t work as well.
Paradise had stuck a read FIFO between display memory and the video output
stage of the VGA, allowing the video output to read ahead, so that when the
CPU wanted to access display memory, pixels could come from the FIFO while the
CPU was serviced immediately. That did indeed help performance--but not as
much as Tom’s write FIFO.
What we have here is as neat a parable
about the nature of creative design as one could hope to find. The scrap of
news about Paradise’s chip contained almost no actual information, but it forced
Tom to push past the limits he had unconsciously set in coming up with his original
design. And, in the end, I think that the single most important element of
great design, whether it be hardware or software or any creative endeavor, is
precisely what the Paradise news triggered in Tom: The ability to detect the
limits you have built into the way you think about your design, and transcend
those limits.
The problem, of course, is how to
go about transcending limits you don’t even know you’ve imposed. There’s no
formula for success, but two principles can stand you in good stead: simplify,
and keep on trying new things.
Generally, if you find your code
getting more complex, you’re fine-tuning a frozen design, and it’s likely you
can get more of a speed-up, with less code, by rethinking the design. A really
good design should bring with it a moment of immense satisfaction in which everything
falls into place, and you’re amazed at how little code is needed and how all
the boundary cases just work properly.
As for how to rethink the design,
do it by pursuing whatever ideas occur to you, no matter how off-the-wall they
seem. Many of the truly brilliant design ideas I’ve heard over the years sounded
like nonsense at first, because they didn’t fit my preconceived view of the
world. Often, such ideas are in fact off-the-wall, but just as the news about
Paradise’s chip sparked Tom’s imagination, aggressively pursuing seemingly-outlandish
ideas can open up new design possibilities for you.
Case in point: The evolution of
Quake’s 3-D graphics engine.
The toughest 3-D challenge of
all
I’ve spent most of my waking hours
for the last seven months working on Quake, id Software’s successor to DOOM,
and after spending the next three months in much the same way, I expect Quake
will be out as shareware around the time you read this.
In terms of graphics, Quake is to
DOOM as DOOM was to its predecessor, Wolfenstein 3D. Quake adds true, arbitrary
3-D (you can look up and down, lean, and even fall on your side), detailed lighting
and shadows, and 3-D monsters and players in place of DOOM’s sprites. Sometime
soon, I’ll talk about how all that works, but this month I want to talk about
what is, in my book, the toughest 3-D problem of all, visible surface determination
(drawing the proper surface at each pixel), and its close relative, culling
(discarding non-visible polygons as quickly as possible, a way of accelerating
visible surface determination). In the interests of brevity, I’ll use the abbreviation
VSD to mean both visible surface determination and culling from now on.
Why do I think VSD is the toughest
3-D challenge? Although rasterization issues such as texture mapping are fascinating
and important, they are tasks of relatively finite scope, and are being moved
into hardware as 3-D accelerators appear; also, they only scale with increases
in screen resolution, which are relatively modest.
In contrast, VSD is an open-ended
problem, and there are dozens of approaches currently in use. Even more significantly,
the performance of VSD, done in an unsophisticated fashion, scales directly
with scene complexity, which tends to increase as a square or cube function,
so this very rapidly becomes the limiting factor in doing realistic worlds.
I expect VSD increasingly to be the dominant issue in realtime PC 3-D over the
next few years, as 3-D worlds become increasingly detailed. Already, a good-sized
Quake level contains on the order of 10,000 polygons, about three times as many
polygons as a comparable DOOM level.
The structure of Quake levels
Before diving into VSD, let me note
that each Quake level is stored as a single huge 3-D BSP tree. This BSP tree,
like any BSP, subdivides space, in this case along the planes of the polygons.
However, unlike the BSP tree I presented last time, Quake’s BSP tree does not
store polygons in the tree nodes, as part of the splitting planes, but rather
in the empty (non-solid) leaves, as shown in overhead view in Figure 1.
 |
| Figure 1: In Quake, polygons are stored in the empty
leaves. Shaded areas are solid leaves (solid volumes, such as the insides
of walls). |
Correct drawing order
can be obtained by drawing the leaves in front-to-back or back-to-front BSP
order, again as discussed last time. Also, because BSP leaves are always
convex and the polygons are on the boundaries of the BSP leaves, facing inward,
the polygons in a given leaf can never obscure one another and can be drawn
in any order. (This is a general property of convex polyhedra.)
Culling and visible surface determination
The process of VSD would ideally
work as follows. First, you would cull all polygons that are completely outside
the view frustum (view pyramid), and would clip away the irrelevant portions
of any polygons that are partially outside. Then you would draw only those
pixels of each polygon that are actually visible from the current viewpoint,
as shown in overhead view in Figure 2, wasting no time overdrawing pixels multiple
times; note how little of the polygon set in Figure 2 actually need to be drawn.
Finally, in a perfect world, the tests to figure out what parts of which polygons
are visible would be free, and the processing time would be the same for all
possible viewpoints, giving the game a smooth visual flow.
 |
| Figure 2: An ideal VSD architecture would draw only visible
parts of visible polygons. |
As it happens, it is easy to determine
which polygons are outside the frustum or partially clipped, and it’s quite
possible to figure out precisely which pixels need to be drawn. Alas, the world
is far from perfect, and those tests are far from free, so the real trick is
how to accelerate or skip various tests and still produce the desired result.
As I discussed at length last time,
given a BSP, it’s easy and inexpensive to walk the world in front-to-back or
back-to-front order. The simplest VSD solution, which I in fact demonstrated
last time, is to simply walk the tree back-to-front, clip each polygon to the
frustum, and draw it if it’s facing forward and not entirely clipped (the painter’s
algorithm). Is that an adequate solution?
For relatively simple worlds, it
is perfectly acceptable. It doesn’t scale very well, though. One problem is
that as you add more polygons in the world, more transformations and tests have
to be performed to cull polygons that aren’t visible; at some point, that will
bog performance down considerably.
Happily, there’s a good workaround
for this particular problem. As discussed earlier, each leaf of a BSP tree
represents a convex subspace, with the nodes that bound the leaf delimiting
the space. Perhaps less obvious is that each node in a BSP tree also describes
a subspace--the subspace composed of all the node’s children, as shown in Figure
3. Another way of thinking of this is that each node splits into two pieces
the subspace created by the nodes above it in the tree, and the node’s children
then further carve that subspace into all the leaves that descend from the node.
 |
| Figure 3: Node E describes the shaded subspace, which
contains leaves 5, 6, and 7, and node F. |
Since a node’s subspace is bounded
and convex, it is possible to test whether it is entirely outside the frustum.
If it is, all of the node’s children are certain to be fully clipped,
and can be rejected without any additional processing. Since most of the world
is typically outside the frustum, many of the polygons in the world can be culled
almost for free, in huge, node-subspace chunks. It’s relatively expensive to
perform a perfect test for subspace clipping, so instead bounding spheres or
boxes are often maintained for each node, specifically for culling tests.
So culling to the frustum isn’t
a problem, and the BSP can be used to draw back to front. What’s the problem?
Overdraw
The problem John Carmack, the driving
technical force behind DOOM and Quake, faced when he designed Quake was that
in a complex world, many scenes have an awful lot of polygons in the frustum.
Most of those polygons are partially or entirely obscured by other polygons,
but the painter’s algorithm described above requires that every pixel of every
polygon in the frustum be drawn, often only to be overdrawn. In a 10,000-polygon
Quake level, it would be easy to get a worst-case overdraw level of 10 times
or more; that is, in some frames each pixel could be drawn 10 times or more,
on average. No rasterizer is fast enough to compensate for an order of magnitude
more work than is actually necessary to show a scene; worse still, the painter’s
algorithm will cause a vast difference between best-case and worst-case performance,
so the frame rate can vary wildly as the viewer moves around.
So the problem John faced was how
to keep overdraw down to a manageable level, preferably drawing each pixel exactly
once, but certainly no more than two or three times in the worst case. As with
frustum culling, it would be ideal if he could eliminate all invisible polygons
in the frustum with virtually no work. It would also be a plus if he could
manage to draw only the visible parts of partially-visible polygons, but that
was a balancing act, in that it had to be a lower-cost operation than the overdraw
that would otherwise result.
When I arrived at id at the beginning
of March, John already had an engine prototyped and a plan in mind, and I assumed
that our work was a simple matter of finishing and optimizing that engine.
If I had been aware of id’s history, however, I would have known better. John
had done not only DOOM, but also the engines for Wolf 3D and several earlier
games, and had actually done several different versions of each engine in the
course of development (once doing four engines in four weeks), for a total of
perhaps 20 distinct engines over a four-year period. John’s tireless pursuit
of new and better designs for Quake’s engine, from every angle he could think
of, would end only when we shipped.
By three months after I arrived,
only one element of the original VSD design was anywhere in sight, and John
had taken “try new things” farther than I’d ever seen it taken.
The beam tree
John’s original Quake design was
to draw front to back, using a second BSP tree to keep track of what parts of
the screen were already drawn and which were still empty and therefore drawable
by the remaining polygons. Logically, you can think of this BSP tree as being
a 2-D region describing solid and empty areas of the screen, as shown in Figure
4, but in fact it is a 3-D tree, of the sort known as a beam tree. A beam tree
is a collection of 3-D wedges (beams), bounded by planes, projecting out from
some center point, in this case the viewpoint, as shown in Figure 5.
 |
| Figure 4: Quake's beam tree effectively partitioned the
screen into 2-D regions. |
 |
| Figure 5: Quake's beam tree was composed of 3-D wedges,
or beams, projecting out from the viewpoint to polygon edges. |
In John’s design, the beam tree
started out consisting of a single beam describing the frustum; everything outside
that beam was marked solid (so nothing would draw there), and the inside of
the beam was marked empty. As each new polygon was reached while walking the
world BSP tree front to back, that polygon was converted to a beam by running
planes from its edges through the viewpoint, and any part of the beam that intersected
empty beams in the beam tree was considered drawable and added to the beam tree
as a solid beam. This continued until either there were no more polygons or
the beam tree became entirely solid. Once the beam tree was completed, the
visible portions of the polygons that had contributed to the beam tree were
drawn.
The advantage to working with a
3-D beam tree, rather than a 2-D region, is that determining which side of a
beam plane a polygon vertex is on involves only checking the sign of the dot
product of the ray to the vertex and the plane normal, because all beam planes
run through the origin (the viewpoint). Also, because a beam plane is completely
described by a single normal, generating a beam from a polygon edge requires
only a cross-product of the edge and a ray from the edge to the viewpoint.
Finally, bounding spheres of BSP nodes can be used to do the aforementioned
bulk culling to the frustum.
The early-out feature of the beam
tree--stopping when the beam tree becomes solid--seems appealing, because it
appears to cap worst-case performance. Unfortunately, there are still scenes
where it’s possible to see all the way to the sky or the back wall of the world,
so in the worst case, all polygons in the frustum will still have to be tested
against the beam tree. Similar problems can arise from tiny cracks due to numeric
precision limitations. Beam tree clipping is fairly time-consuming, and in
scenes with long view distances, such as views across the top of a level, the
total cost of beam processing slowed Quake’s frame rate to a crawl. So, in
the end, the beam-tree approach proved to suffer from much the same malady as
the painter’s algorithm: The worst case was much worse than the average case,
and it didn’t scale well with increasing level complexity.
3-D engine du jour
Once the beam tree was working,
John relentlessly worked at speeding up the 3-D engine, always trying to improve
the design, rather than tweaking the implementation. At least once a week,
and often every day, he would walk into my office and say “Last night I couldn’t
get to sleep, so I was thinking...” and I’d know that I was about to get my
mind stretched yet again. John tried many ways to improve the beam tree, with
some success, but more interesting was the profusion of wildly different approaches
that he generated, some of which were merely discussed, others of which were
implemented in overnight or weekend-long bursts of coding, in both cases ultimately
discarded or further evolved when they turned out not to meet the design criteria
well enough. Here are some of those approaches, presented in minimal detail
in the hopes that, like Tom Wilson with the Paradise FIFO, your imagination
will be sparked.
Subdividing raycast: Rays are cast
in an 8x8 screen-pixel grid; this is a highly efficient operation because the
first intersection with a surface can be found by simply clipping the ray into
the BSP tree, starting at the viewpoint, until a solid leaf is reached. If
adjacent rays don’t hit the same surface, then a ray is cast halfway between,
and so on until all adjacent rays either hit the same surface or are on adjacent
pixels; then the block around each ray is drawn from the polygon that was hit.
This scales very well, being limited by the number of pixels, with no overdraw.
The problem is dropouts; it’s quite possible for small polygons to fall between
rays and vanish.
Vertex-free surfaces: The world
is represented by a set of surface planes. The polygons are implicit in the
plane intersections, and are extracted from the planes as a final step before
drawing. This makes for fast clipping and a very small data set (planes are
far more compact than polygons), but it’s time-consuming to extract polygons
from planes.
Draw-buffer: Like a z-buffer, but
with 1 bit per pixel, indicating whether the pixel has been drawn yet. This
eliminates overdraw, but at the cost of an inner-loop buffer test, extra writes
and cache misses, and, worst of all, considerable complexity. Variations are
testing the draw-buffer a byte at a time and completely skipping fully-occluded
bytes, or branching off each draw-buffer byte to one of 256 unrolled inner loops
for drawing 0-8 pixels, in the process possibly taking advantage of the ability
of the x86 to do the perspective floating-point divide in parallel while 8 pixels
are processed.
Span-based drawing: Polygons are
rasterized into spans, which are added to a global span list and clipped against
that list so that only the nearest span at each pixel remains. Little sorting
is needed with front-to-back walking, because if there’s any overlap, the span
already in the list is nearer. This eliminates overdraw, but at the cost of
a lot of span arithmetic; also, every polygon still has to be turned into spans.
Portals: the holes where polygons
are missing on surfaces are tracked, because it’s only through such portals
that line-of-sight can extend. Drawing goes front-to-back, and when a portal
is encountered, polygons and portals behind it are clipped to its limits, until
no polygons or portals remain visible. Applied recursively, this allows drawing
only the visible portions of visible polygons, but at the cost of a considerable
amount of portal clipping.
Breakthrough
In the end, John decided that the
beam tree was a sort of second-order structure, reflecting information already
implicitly contained in the world BSP tree, so he tackled the problem of extracting
visibility information directly from the world BSP tree. He spent a week on
this, as a byproduct devising a perfect DOOM (2-D) visibility architecture,
whereby a single, linear walk of a DOOM BSP tree produces zero-overdraw 2-D
visibility. Doing the same in 3-D turned out to be a much more complex problem,
though, and by the end of the week John was frustrated by the increasing complexity
and persistent glitches in the visibility code. Although the direct-BSP approach
was getting closer to working, it was taking more and more tweaking, and a simple,
clean design didn’t seem to be falling out. When I left work one Friday, John
was preparing to try to get the direct-BSP approach working properly over the
weekend.
When I came in on Monday, John had
the look of a man who had broken through to the other side--and also the look
of a man who hadn’t had much sleep. He had worked all weekend on the direct-BSP
approach, and had gotten it working reasonably well, with insights into how
to finish it off. At 3:30 AM Monday morning, as he lay in bed, thinking about
portals, he thought of precalculating and storing in each leaf a list of all
leaves visible from that leaf, and then at runtime just drawing the visible
leaves back-to-front for whatever leaf the viewpoint happens to be in, ignoring
all other leaves entirely.
Size was a concern; initially, a
raw, uncompressed potentially visible set (PVS) was several megabytes in size.
However, the PVS could be stored as a bit vector, with 1 bit per leaf, a structure
that shrunk a great deal with simple zero-byte compression. Those steps, along
with changing the BSP heuristic to generate fewer leaves (contrary to what I
said a few months back, choosing as the next splitter the polygon that splits
the fewest other polygons is clearly the best heuristic, based on the latest
data) and sealing the outside of the levels so the BSPer can remove the outside
surfaces, which can never be seen, eventually brought the PVS down to about
20 Kb for a good-size level.
In exchange for that 20 Kb, culling
leaves outside the frustum is speeded up (because only leaves in the PVS are
considered), and culling inside the frustum costs nothing more than a little
overdraw (the PVS for a leaf includes all leaves visible from anywhere in the
leaf, so some overdraw, typically on the order of 50% but ranging up to 150%,
generally occurs). Better yet, precalculating the PVS results in a leveling
of performance; worst case is no longer much worse than best case, because there’s
no longer extra VSD processing--just more polygons and perhaps some extra overdraw--associated
with complex scenes. The first time John showed me his working prototype, I
went to the most complex scene I knew of, a place where the frame rate used
to grind down into the single digits, and spun around smoothly, with no perceptible
slowdown.
John says precalculating the PVS
was a logical evolution of the approaches he had been considering, that there
was no moment when he said “Eureka!”. Nonetheless, it was clearly a breakthrough
to a brand-new, superior design, a design that, together with a still-in-development
sorted-edge rasterizer that completely eliminates overdraw, comes remarkably
close to meeting the “perfect-world” specifications we laid out at the start.
Simplify, and keep on trying new
things
What does it all mean? Exactly
what I said up front: Simplify, and keep trying new things. The precalculated
PVS is simpler than any of the other schemes that had been considered (although
precalculating the PVS is an interesting task that I’ll discuss another time).
In fact, at runtime the precalculated PVS is just a constrained version of the
painter’s algorithm. Does that mean it’s not particularly profound?
Not at all. All really great designs
seem simple and even obvious--once they’ve been designed. But the process of
getting there requires incredible persistence, and a willingness to try lots
of different ideas until the right one falls into place, as happened here.
My friend Chris Hecker has a theory
that all approaches work out to the same thing in the end, since they all reflect
the same underlying state and functionality. In terms of underlying theory,
I’ve found that to be true; whether you do perspective texture mapping with
a divide or with incremental hyperbolic calculations, the numbers do exactly
the same thing. When it comes to implementation, however, my experience is
that simply time-shifting an approach, or matching hardware capabilities better,
or caching can make an astonishing difference. My friend Terje Mathisen likes
to say that “almost all programming can be viewed as an exercise in caching,”
and that’s exactly what John did. No matter how fast he made his VSD calculations,
they could never be as fast as precalculating and looking up the visibility,
and his most inspired move was to yank himself out of the “faster code” mindset
and realize that it was in fact possible to precalculate (in effect, cache)
and look up the PVS.
The hardest thing in the world is
to step outside a familiar, pretty good solution to a difficult problem and
look for a different, better solution. The best ways I know to do that are
to keep trying new, wacky things, and always, always, always try to simplify.
One of John’s goals is to have fewer lines of code in each 3-D game than in
the previous game, on the assumption that as he learns more, he should be able
to do things better with less code.
So far, it seems to have worked
out pretty well for him.
Learn now, pay forward
There’s one other thing I’d like
to mention before I close up shop for this month. As far back as I can remember,
DDJ has epitomized the attitude that sharing programming information
is A Good Thing. I know a lot of programmers who were able to leap ahead in
their development because of Hendrix’s Tiny C, or Stevens’ D-Flat, or simply
by browsing through DDJ’s annual collections. (Me, for one.) Most companies
understandably view sharing information in a very different way, as potential
profit lost--but that’s what makes DDJ so valuable to the programming
community.
It is in that spirit that id Software
is allowing me to describe in these pages how Quake works, even before Quake
has shipped. That’s also why id has placed the full source code for Wolfenstein
3D on ftp.idsoftware.com/idstuff/source; you can’t just recompile the code and
sell it, but you can learn how a full-blown, successful game works; check wolfsrc.txt
in the above-mentioned directory for details on how the code may be used.
So remember, when it’s legally possible,
sharing information benefits us all in the long run. You can pay forward the
debt for the information you gain here and elsewhere by sharing what you know
whenever you can, by writing an article or book or posting on the Net. None
of us learns in a vacuum; we all stand on the shoulders of giants such as Wirth
and Knuth and thousands of others. Lend your shoulders to building the future!
References
Foley, James D., et al., Computer
Graphics: Principles and Practice, Addison Wesley, 1990, ISBN 0-201-12110-7
(beams, BSP trees, VSD).
Teller, Seth, Visibility Computations
in Densely Occluded Polyhedral Environments (dissertation), available on
http://theory.lcs.mit.edu/~seth/
along with several other papers relevant
to visibility determination.
Teller, Seth, Visibility Preprocessing
for Interactive Walkthroughs, SIGGRAPH 91 proceedings, pp. 61-69.
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