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---
title: Michael Abrash's Graphics Programming Black Book, Special Edition
author: Michael Abrash
date: '1997-07-01'
identifier:
- scheme: ISBN
text: 1576101746
publisher: The Coriolis Group
category: 'Web and Software Development: Game Development,Web and Software Development:
Graphics and Multimedia Development'
chapter: '68'
pages: 1243-1256
---
## Chapter 68 -- Quake's Lighting Model
### A Radically Different Approach to Lighting Polygons
It was during my senior year in college that I discovered computer
games. Not Wizardry, or Choplifter, or Ultima, because none of those
existed yet—the game that hooked me was the original Star Trek game, in
which you navigated from one 8x8 quadrant to another in search of
starbases, occasionally firing phasers or photon torpedoes. This was
less exciting than it sounds; after each move, the current quadrant had
to be reprinted from scratch, along with the current stats—and the
output device was a 10 cps printball console. A typical game took over
an hour, during which nothing particularly stimulating ever happened
(Klingons appeared periodically, but they politely waited for your next
move before attacking, and your photon torpedoes never missed, so the
outcome was never in doubt), but none of that mattered; nothing could
detract from the sheer thrill of being in a computer-simulated universe.
Then the college got a PDP-11 with four CRT terminals, and suddenly Star
Trek could redraw in a second instead of a minute. Better yet, I found
the source code for the Star Trek program in the recesses of the new
system, the first time I'd ever seen any real-world code other than my
own, and excitedly dove into it. One evening, as I was looking through
the code, a really cute girl at the next terminal asked me for help
getting a program to run. After I had helped her, eager to get to know
her better, I said, "Want to see something? This is the actual source
for the Star Trek game!" and proceeded to page through the code,
describing each subroutine. We got to talking, and eventually I worked
up the nerve to ask her out. She said sure, and we ended up having a
good time, although things soon fell apart because of her two or three
other boyfriends (I never did get an exact count). The interesting
thing, though, was her response when I finally got around to asking her
out. She said, "It's about time!" When I asked what she meant, she said,
"I've been trying to get you to ask me out all evening—but it took you
forever! You didn't actually think I was interested in that Star Trek
program, did you?"
Actually, yes, I had thought that, because *I* was interested in it. One
thing I learned from that experience, and have had reinforced countless
times since, is that we—you, me, anyone who programs because they love
it, who would do it for free if necessary—are a breed apart. We're
different, and luckily so; while everyone else is worrying about
downsizing, we're in one of the hottest industries in the world. And, so
far as I can see, the biggest reason we're in such a good situation
isn't intelligence, or hard work, or education, although those help;
it's that we actually *like* this stuff.
It's important to keep it that way. I've seen far too many people start
to treat programming like a job, forgetting the joy of doing it, and
burn out. So keep an eye on how you feel about the programming you're
doing, and if it's getting stale, it's time to learn something new;
there's plenty of interesting programming of all sorts to be done.
Follow your interests—and don't forget to have fun!
### The Lighting Conundrum
I spent about two years working with John Carmack on Quake's 3-D
graphics engine. John faced several fundamental design issues while
architecting Quake. I've written in earlier chapters about some of those
issues, including eliminating non-visible polygons quickly via a
precalculated potentially visible set (PVS), and improving performance
by inserting potentially visible polygons into a global edge list and
scanning out only the nearest polygon at each pixel.
In this chapter, I'm going to talk about another, equally crucial design
issue: how we developed our lighting approach for the part of the Quake
engine that draws the world itself, the static walls and floors and
ceilings. Monsters and players are drawn using completely different
rendering code, with speed the overriding factor. A primary goal for the
world, on the other hand, was to be as precise as possible, getting
everything right so that polygons, textures, and sophisticated lighting
would be pegged in place, with no visible shifting or distortion under
all viewing conditions, for maximum player immersion—all with good
performance, of course. As I'll discuss, the twin goals of performance
and rock-solid, complex lighting proved to be difficult to achieve with
traditional lighting approaches; ultimately, a dramatically different
approach was required.
### Gouraud Shading
The traditional way to do realistic lighting in polygon pipelines is
Gouraud shading (also known as *smooth shading*). Gouraud shading
involves generating a lighting value at each polygon vertex by applying
all relevant world lighting, linearly interpolating between lighting
values down the edges of the polygon, and then linearly interpolating
between the edges of the polygon across each span. If texture mapping is
desired (and all polygons are texture mapped in Quake), then at each
pixel in each span, the pixel's corresponding texture map location
(texel) is determined, and the interpolated lighting is applied to the
texel to generate a final, lit pixel. Texels are generally taken from a
32x32 or 64x64 texture that's tiled repeatedly across the polygon, for
several reasons: performance (a 64x64 texture sits nicely in the 486 or
Pentium cache), database size, and less artwork.
The interpolated lighting can consist of either a color intensity value
or three separate red, green, and blue values. RGB lighting produces
more sophisticated results, such as colored lights, but is slower and
best suited to RGB modes. Games like Quake that are targeted at
palettized 256-color modes generally use intensity lighting; each pixel
is lit by looking up the pixel color in a table, using the texel color
and the lighting intensity as the look-up indices.
Gouraud shading allows for decent lighting effects with a relatively
small amount of calculation and a compact data set that's a simple
extension of the basic polygon model. However, there are several
important drawbacks to Gouraud shading, as well.
#### Problems with Gouraud Shading
The quality of Gouraud shading depends heavily on the average size of
the polygons being drawn. Linear interpolation is used, so highlights
can only occur at vertices, and color gradients are monotonic across the
face of each polygon. This can make for bland lighting effects if
polygons are large, and makes it difficult to do spotlights and other
detailed or dramatic lighting effects. After John brought the initial,
primitive Quake engine up using Gouraud shading for lighting, the first
thing he tried to improve lighting quality was adding a single vertex
and creating new polygons wherever a spotlight was directly overhead a
polygon, with the new vertex added directly underneath the light, as
shown in Figure 68.1. This produced fairly attractive highlights, but
simultaneously made evident several problems.
A primary problem with Gouraud shading is that it requires the vertices
used for world geometry to serve as lighting sample points as well, even
though there isn't necessarily a close relationship between lighting and
geometry. This artificial coupling often forces the subdivision of a
single polygon into several polygons purely for lighting reasons, as
with the spotlights mentioned above; these extra polygons increase the
world database size, and the extra transformations and projections that
they induce can harm performance considerably.
Similar problems occur with overlapping lights, and with shadows, where
additional polygons are required in order to approximate lighting detail
well. In particular, good shadow edges need small polygons, because
otherwise the gradient between light and dark gets spread across too
wide an area. Worse still, the rate of lighting change across a shadow
edge can vary considerably as a function of the geometry the edge
crosses; wider polygons stretch and diffuse the transition between light
and shadow. A related problem is that lighting discontinuities can be
very visible at t-junctions (although ultimately we had to add edges to
eliminate t-junctions anyway, because otherwise dropouts can occur along
polygon edges). These problems can be eased by adding extra edges, but
that increases the rasterization load.
![**Figure 68.1**  *Adding an extra vertex directly beneath a light.*](images/68-01.jpg)
#### Perspective Correctness
Another problem is that Gouraud shading isn't perspective-correct. With
Gouraud shading, lighting varies linearly across the face of a polygon,
in equal increments per pixel—but unless the polygon is parallel to the
screen, the same sort of perspective correction is needed to step
lighting across the polygon properly as is required for texture mapping.
Lack of perspective correction is not as visibly wrong for lighting as
it is for texture mapping, because smooth lighting gradients can
tolerate considerably more warping than can the detailed bitmapped
images used in texture mapping, but it nonetheless shows up in several
ways.
First, the extent of the mismatch between Gouraud shading and
perspective lighting varies with the angle and orientation of the
polygon being lit. As a polygon turns to become more on-edge, for
example, the lighting warps more and therefore shifts relative to the
perspective-texture mapped texels it's shading, an effect I'll call
*viewing variance*. Lighting can similarly shift as a result of
clipping, for example if one or more polygon edges are completely
clipped; I'll refer to this as *clipping variance*.
These are fairly subtle effects; more pronounced is the *rotational
variance* that occurs when Gouraud shading any polygon with more than
three vertices. Consistent lighting for a polygon is fully defined by
three lighting values; taking four or more vertices and interpolating
between them, as Gouraud shading does, is basically a hack, and does not
reflect any consistent underlying model. If you view a Gouraud-shaded
quad head-on, then rotate it like a pinwheel, the lighting will shift as
the quad turns, as shown in Figure 68.2. The extent of the lighting
shift can be quite drastic, depending on how different the colors at the
vertices are.
It was rotational variance that finally brought the lighting issue to a
head for Quake. We'd look at the floors, which were Gouraud-shaded
quads; then we'd pivot, and the lighting would shimmy and shift,
especially where there were spotlights and shadows. Given the goal of
rendering the world as accurately and convincingly as possible, this was
unacceptable.
The obvious solution to rotational variance is to use only triangles,
but that brings with it a new set of problems. It takes twice as many
triangles as quads to describe the same scene, increasing the size of
the world database and requiring extra rasterization, at a performance
cost. Triangles still don't provide perspective lighting; their lighting
is rotationally invariant, but it's still wrong—just wrong in a more
consistant way. Gouraud-shaded triangles still result in odd lighting
patterns, and require lots of triangles to support shadowing and other
lighting detail. Finally, triangles don't solve clipping or viewing
variance.
![**Figure 68.2**  *How Gouraud shading varies with polygon screen
orientation.*](images/68-02.jpg)
Yet another problem is that while it may work well to add extra geometry
so that spotlights and shadows show up well, that's feasible only for
static lighting. Dynamic lighting—light cast by sources that move—has to
work with whatever geometry the world has to offer, because its needs
are constantly changing.
These issues led us to conclude that if we were going to use Gouraud
shading, we would have to build Quake levels from many small triangles,
with sufficiently finely detailed geometry so that complex lighting
could be supported and the inaccuracies of Gouraud shading wouldn't be
too noticeable. Unfortunately, that line of thinking brought us back to
the problem of a much larger world database and a much heavier
rasterization load (all the worse because Gouraud shading requires an
additional interpolant, slowing the inner rasterization loop), so that
not only would the world still be less than totally solid, because of
the limitations of Gouraud shading, but the engine would also be too
slow to support the complex worlds we had hoped for in Quake.
### The Quest for Alternative Lighting
None of which is to say that Gouraud shading isn't useful in general.
Descent uses it to excellent effect, and in fact Quake uses Gouraud
shading for moving entities, because these consist of small triangles
and are always in motion, which helps hide the relatively small lighting
errors. However, Gouraud shading didn't seem capable of meeting our
design goals for rendering quality and speed for drawing the world as a
whole, so it was time to look for alternatives.
There are many alternative lighting approaches, most of them
higher-quality than Gouraud, starting with Phong shading, in which the
surface normal is interpolated across the polygon's surface, and going
all the way up to ray-tracing lighting techniques in which full
illumination calculations are performed for all direct and reflected
paths from each light source for each pixel. What all these approaches
have in common is that they're slower than Gouraud shading, too slow for
our purposes in Quake. For weeks, we kicked around and rejected various
possibilities and continued working with Gouraud shading for lack of a
better alternative—until the day John came into work and said, "You
know, I have an idea...."
#### Decoupling Lighting from Rasterization
John's idea came to him while was looking at a wall that had been carved
into several pieces because of a spotlight, with an ugly lighting glitch
due to a t-junction. He thought to himself that if only there were some
way to treat it as one surface, it would look better and draw faster—and
then he realized that there was a way to do that.
The insight was to split lighting and rasterization into two separate
steps. In a normal Gouraud-based rasterizer, there's first an off-line
preprocessing step when the world database is built, during which
polygons are added to support additional lighting detail as needed, and
lighting values are calculated at the vertices of all polygons. At
runtime, the lighting values are modified if dynamic lighting is
required, and then the polygons are drawn with Gouraud shading.
Quake's approach, which I'll call surface-based lighting, preprocesses
differently, and adds an extra rendering step. During off-line
preprocessing, a grid, called a light map, is calculated for each
polygon in the world, with a lighting value every 16 texels horizontally
and vertically. This lighting is done by casting light from all the
nearby lights in the world to each of the grid points on the polygon,
and summing the results for each grid point. The Quake preprocessor
filters the values, so shadow edges don't have a stair-step appearance
(a technique suggested by Billy Zelsnack); additional preprocessing
could be done, for example Phong shading to make surfaces appear
smoothly curved. Then, at runtime, the polygon's texture is tiled into a
buffer, with each texel lit according to the weighted average
intensities of the four nearest light map points, as shown in Figure
68.3. If dynamic lighting is needed, the light map is modified
accordingly before the buffer, which I'll call a surface, is built. Then
the polygon is drawn with perspective texture mapping, with the surface
serving as the input texture, and with no lighting performed during the
texture mapping.
So what does surface-based lighting buy us? First and foremost, it
provides consistent, perspective-correct lighting, eliminating all
rotational, viewing, and clipping variance, because lighting is done in
surface space rather than in screen space. By lighting in surface space,
we bind the lighting to the texels in an invariant way, and then the
lighting gets a free ride through the perspective texture mapper and
ends up perfectly matched to the texels. Surface-based lighting also
supports good, although not perfect, detail for overlapping lights and
shadows. The 16-texel grid has a resolution of two feet in the Quake
frame of reference, and this relatively fine resolution, together with
the filtering performed when the light map is built, is sufficient to
support complex shadows with smoothly fading edges. Additionally,
surface-based lighting eliminates lighting glitches at t-junctions,
because lighting is unrelated to vertices. In short, surface-based
lighting meets all of Quake's visual quality goals, which leaves only
one question: How does it perform?
#### Size and Speed
As it turns out, the raw speed of surface-based lighting is pretty good.
Although an extra step is required to build the surface, moving lighting
and tiling into a separate loop from texture mapping allows each of the
two loops to be optimized very effectively, with almost all variables
kept in registers. The surface-building inner loop is particularly
efficient, because it consists of nothing more than interpolating
intensity, combining it with a texel and using the result to look up a
lit texel color, and storing the results with a dword write every four
texels. In assembly language, we got this code down to 2.25 cycles per
lit texel in Quake. Similarly, the texture-mapping inner loop, which
overlaps an FDIV for floating-point perspective correction with integer
pixel drawing in 16-pixel bursts, has been squeezed down to 7.5 cycles
per pixel on a Pentium, so the combined inner loop times for building
and drawing a surface is roughly in the neighborhood of 10 cycles per
pixel. It's certainly possible to write a Gouraud-shaded
perspective-correct texture mapper that's somewhat faster than 10
cycles, but 10 cycles/pixel is fast enough to do 40 frames/second at
640x400 on a Pentium/100, so the cycle counts of surface-based lighting
are acceptable. It's worth noting that it's possible to write a one-pass
texture mapper that does approximately perspective-correct lighting.
However, I have yet to hear of or devise such an inner loop that isn't
complicated and full of special cases, which makes it hard to optimize;
worse, this approach doesn't work well with the procedural and
post-processing techniques I'll discuss shortly.
![**Figure 68.3**  *Tiling the texture and lighting the texels from the
light map.*](images/68-03.jpg)
Moreover, surface-based lighting tends to spend more of its time in
inner loops, because polygons can have any number of sides and don't
need to be split into multiple smaller polygons for lighting purposes;
this reduces the amount of transformation and projection that are
required, and makes polygon spans longer. So the performance of
surface-based lighting stacks up very well indeed—except for caching.
I mentioned earlier that a 64x64 texture tile fits nicely in the
processor cache. A typical surface doesn't. Every texel in every surface
is unique, so even at 320x200 resolution, something on the rough order
of 64,000 texels must be read in order to draw a single scene. (The
number actually varies quite a bit, as discussed below, but 64,000 is in
the ballpark.) This means that on a Pentium, we're guaranteed to miss
the cache once every 32 texels, and the number can be considerably worse
than that if the texture access patterns are such that we don't use
every texel in a given cache line before that data gets thrown out of
the cache. Then, too, when a surface is built, the surface buffer won't
be in the cache, so the writes will be uncached writes that have to go
to main memory, then get read back from main memory at texture mapping
time, potentially slowing things further still. All this together makes
the combination of surface building and unlit texture mapping a
potential performance problem, but that never posed a problem during the
development of Quake, thanks to surface caching.
### Surface Caching
When he thought of surface-based lighting, John immediately realized
that surface building would be relatively expensive. (In fact, he
assumed it would be considerably more expensive than it actually turned
out to be with full assembly-language optimization.) Consequently, his
design included the concept of caching surfaces, so that if the same
surface were visible in the next frame, it could be reused without
having to be rebuilt.
With surface rebuilding needed only rarely, thanks to surface caching,
Quake's rasterization speed is generally the speed of the unlit,
perspective-correct texture-mapping inner loop, which suffers from more
cache misses than Gouraud-shaded, tiled texture mapping, but doesn't
have the overhead of Gouraud shading, and allows the use of larger
polygons. In the worst case, where everything in a frame is a new
surface, the speed of the surface-caching approach is somewhat slower
than Gouraud shading, but generally surface caching provides equal or
better performance, so once surface caching was implemented in Quake,
performance was no longer a problem—but size became a concern.
The amount of memory required for surface caching looked forbidding at
first. Surfaces are large relative to texture tiles, because every texel
of every surface is unique. Also, a surface can contain many texels
relative to the number of pixels actually drawn on the screen, because
due to perspective foreshortening, distant polygons have only a few
pixels relative to the surface size in texels. Surfaces associated with
partly hidden polygons must be fully built, even though only part of the
polygon is visible, and if polygons are drawn back to front with
overdraw, some polygons won't even be visible, but will still require
surface building and caching. What all this meant was that the surface
cache initially looked to be very large, on the order of several
megabytes, even at 320x200—too much for a game intended to run on an 8
MB machine.
#### Mipmapping To The Rescue
Two factors combined to solve this problem. First, polygons are drawn
through an edge list with no overdraw, as I discussed a few chapters
back, so no surface is ever built unless at least part of it is visible.
Second, surfaces are built at four mipmap levels, depending on distance,
with each mipmap level having one-quarter as many texels as the
preceding level, as shown in Figure 68.4.
For those whose heads haven't been basted in 3-D technology for the past
several years, *mipmapping* is 3-D graphics jargon for a process that
normalizes the number of texels in a surface to be approximately equal
to the number of pixels, reducing calculation time for distant surfaces
containing only a few pixels. The mipmap level for a given surface is
selected to result in a texel:pixel ratio approximately between 1:1 and
1:2, so texels map roughly to pixels, and more distant surfaces are
correspondingly smaller. As a result, the number of surface texels
required to draw a scene at 320x200 is on the rough order of 64,000; the
number is actually somewhat higher, because of portions of surfaces that
are obscured and viewspace-tilted polygons, which have high
texel-to-pixel ratios along one axis, but not a whole lot higher. Thanks
to mipmapping and the edge list, 600K has proven to be plenty for the
surface cache at 320x200, even in the most complex scenes, and at
640x480, a little more than 1 MB suffices.
![**Figure 68.4**  *How mipmapping reduces surface caching requirements.*](images/68-04.jpg)
All mipmapped texture tiles are generated as a preprocessing step, and
loaded from disk at runtime. One interesting point is that a key to
making mipmapping look good turned out to be box-filtering down from one
level to the next by averaging four adjacent pixels, then using error
diffusion dithering to generate the mipmapped texels.
Also, mipmapping is done on a per-surface basis; the mipmap level for a
whole surface is selected based on the distance from the viewer of the
nearest vertex. This led us to limit surface size to a maximum of
256x256. Otherwise, surfaces such as floors would extend for thousands
of texels, all at the mipmap level of the nearest vertex, and would
require huge amounts of surface cache space while displaying a great
deal of aliasing in distant regions due to a high texel:pixel ratio.
#### Two Final Notes on Surface Caching
Dynamic lighting has a significant impact on the performance of surface
caching, because whenever the lighting on a surface changes, the surface
has to be rebuilt. In the worst case, where the lighting changes on
every visible surface, the surface cache provides no benefit, and
rendering runs at the combined speed of surface building and texture
mapping. This worst-case slowdown is tolerable but certainly noticeable,
so it's best to design games that use surface caching so only some of
the surfaces change lighting at any one time. If necessary, you could
alternate surface relighting so that half of the surfaces change on even
frames, and half on odd frames, but large-scale, constant relighting is
not surface caching's strongest suit.
Finally, Quake barely begins to tap surface caching's potential. All
sorts of procedural texturing and post-processing effects are possible.
If a wall is shot, a sprite of pockmarks could be attached to the wall's
data structure, and the sprite could be drawn into the surface each time
the surface is rebuilt. The same could be done for splatters, or
graffiti, with translucency easily supported. These effects would then
be cached and drawn as part of the surface, so the performance cost
would be much less than effects done by on-screen overdraw every frame.
Basically, the surface is a handy repository for all sorts of effects,
because multiple techniques can be composited, because it caches the
results for reuse without rebuilding, and because the texels constructed
in a surface are automatically drawn in perspective.