Secrets of 3D computer graphics
Secrets of 3D computer graphics
SECRETS OF 3D COMPUTER GRAPHICS
Report: second-year graduate
What Makes a Picture 3D
What Are 3D Graphics
How to Make It Look Like the Real Thing
Depth of Field
Making 3D Graphics Move
Fluid Motion for Us Is Hard Work for the
Transforms and Processors: Work, Work,
How Graphics Boards Help
probably reading this on the screen of a computer monitor -- a display that has
two real dimensions, height and width. But when you look at a movie like
"Toy Story II" or play a game like Tomb Raider, you see a window into a
three-dimensional world. One of the truly amazing things about this window is
that the world you see can be the world we live in, the world we will live in
tomorrow, or a world that lives only in the minds of a movie’s or game's
creators. And all of these worlds can appear on the same screen you use for
writing a report or keeping track of a stock portfolio.
does your computer trick your eyes into thinking that the flat screen extends
deep into a series of rooms? How do game programmers convince you that you're
seeing real characters move around in a real landscape? In this edition of How
Stuff Works, we will tell you about some of the visual tricks 3D graphic
designers use, and how hardware designers make the tricks happen so fast that
they seem like a movie that reacts to your every move.
What Makes a Picture 3D
picture that has or appears to have height, width and depth is three-dimensional
(or 3D). A picture that has height and width but no depth is two-dimensional
(or 2-D). Some pictures are 2-D on purpose. Think about the international
symbols that indicate which door leads to a restroom, for example.
symbols are designed so that you can recognize them at a glance. That’s why they
use only the most basic shapes. Additional information on the symbols might try
to tell you what sort of clothes the little man or woman is wearing, the color
of their hair, whether they get to the gym on a regular basis, and so on, but
all of that extra information would tend to make it take longer for you to get
the basic information out of the symbol: which restroom is which. That's one of
the basic differences between how 2-D and 3D graphics are used: 2-D graphics
are good at communicating something simple, very quickly. 3D graphics tell a
more complicated story, but have to carry much more information to do it.
Take a look at the triangles above.
Each of the triangles on the left has three lines and three angles -- all
that's needed to tell the story of a triangle. We see the image on the right as
a pyramid -- a 3D structure with four triangular sides. Note that it takes five
lines and six angles to tell the story of a pyramid -- nearly twice the
information required to tell the story of a triangle.
For hundreds of years, artists have
known some of the tricks that can make a flat, 2-D painting look like a window
into the real, 3D world. You can see some of these on a photograph that you
might scan and view on your computer monitor: Objects appear smaller when
they're farther away; when objects close to the camera are in focus, objects
farther away are fuzzy; colors tend to be less vibrant as they move farther
away. When we talk about 3D graphics on computers today, though, we're not
talking about still photographs -- we're talking about pictures that move.
If making a 2-D picture into a 3D
image requires adding a lot of information, then the step from a 3D still
picture to images that move realistically requires far more. Part of the
problem is that we’ve gotten spoiled. We expect a high degree of realism in
everything we see. In the mid-1970s, a game like "Pong" could impress
people with its on-screen graphics. Today, we compare game screens to DVD
movies, and want the games to be as smooth and detailed as what we see in the
movie theater. That poses a challenge for 3D graphics on PCs, Macintoshes, and,
increasingly, game consoles like the Dreamcast and the Playstation II.
What Are 3D Graphics
many of us, games on a computer or advanced game system are the most common
ways we see 3D graphics. These games, or movies made with computer-generated
images, have to go through three major steps to create and present a realistic 3D
a virtual 3D world.
what part of the world will be shown on the screen.
how every pixel on the screen will look so that the whole image appears as
realistic as possible.
Creating a Virtual 3D World
A virtual 3D world isn't the same
thing as one picture of that world. This is true of our real world also. Take a
very small part of the real world -- your hand and a desktop under it. Your
hand has qualities that determine how it can move and how it can look. The
finger joints bend toward the palm, not away from it. If you slap your hand on
the desktop, the desktop doesn't splash -- it's always solid and it's always
hard. Your hand can't go through the desktop. You can't prove that these things
are true by looking at any single picture. But no matter how many pictures you
take, you will always see that the finger joints bend only toward the palm, and
the desktop is always solid, not liquid, and hard, not soft. That's because in
the real world, this is the way hands are and the way they will always behave.
The objects in a virtual 3D world, though, don’t exist in nature, like your
hand. They are totally synthetic. The only properties they have are given to
them by software. Programmers must use special tools and define a virtual 3D
world with great care so that everything in it always behaves in a certain way.
What Part of the Virtual World Shows
on the Screen?
At any given moment, the screen shows
only a tiny part of the virtual 3D world created for a computer game. What is
shown on the screen is determined by a combination of the way the world is
defined, where you choose to go and which way you choose to look. No matter
where you go -- forward or backward, up or down, left or right -- the virtual 3D
world around you determines what you will see from that position looking in
that direction. And what you see has to make sense from one scene to the next.
If you're looking at an object from the same distance, regardless of direction,
it should look the same height. Every object should look and move in such a way
as to convince you that it always has the same mass, that it's just as hard or
soft, as rigid or pliable, and so on.
Programmers who write computer games
put enormous effort into defining 3D worlds so that you can wander in them
without encountering anything that makes you think, “That couldn't happen in
this world!" The last thing you want to see is two solid objects that can
go right through each other. That’s a harsh reminder that everything you’re
seeing is make-believe.
The third step involves at least as
much computing as the other two steps and has to happen in real time for games
and videos. We'll take a longer look at it next.
How to Make It Look Like the Real
matter how large or rich the virtual 3D world, a computer can depict
(изображать на картине, рисовать) that world only by putting pixels on the 2-D
screen. This section will focus on just how what you see on the screen is made
to look realistic, and especially on how scenes are made to look as close as
possible to what you see in the real world. First we'll look at how a single stationary
object is made to look realistic. Then we'll answer the same question for an
entire scene. Finally, we'll consider what a computer has to do to show
full-motion scenes of realistic images moving at realistic speeds.
A number of image parts go into
making an object seem real. Among the most important of these are shapes,
surface textures, lighting, perspective, depth of field and anti-aliasing.
When we look out our windows, we see
scenes made up of all sorts of shapes, with straight lines and curves in many
sizes and combinations. Similarly, when we look at a 3D graphical image on our
computer monitor, we see images made up of a variety of shapes, although most
of them are made up of straight lines. We see squares, rectangles,
parallelograms, circles and rhomboids, but most of all we see triangles.
However, in order to build images that look as though they have the smooth
curves often found in nature, some of the shapes must be very small, and a
complex image -- say, a human body -- might require thousands of these shapes
to be put together into a structure called a wireframe (каркасный (проволочный)
метод изображения объекта).
At this stage the structure might be
recognizable as the symbol of whatever it will eventually picture, but the next
major step is important: The wireframe has to be given a surface.
illustration shows the wireframe of a hand made from relatively few polygons --
outline of the wireframe can be made to look more natural and rounded, but many
more polygons -- 3,444 -- are required.
When we meet a surface in the real
world, we can get information about it in two key ways. We can look at it,
sometimes from several angles, and we can touch it to see whether it's hard or
soft. In a 3D graphic image, however, we can only look at the surface to get
all the information possible. All that information breaks down into three
Color: What color is it? Is it the same
color all over?
Texture: Does it appear to be smooth, or does
it have lines, bumps, craters or some other irregularity on the surface?
Reflectance: How much light does it reflect? Are
reflections of other items in the surface sharp or fuzzy?
way to make an image look "real" is to have a wide variety of these
three features across the different parts of the image. Look around you now:
Your computer keyboard has a different color/texture/reflectance than your
desktop, which has a different color/texture/reflectance than your arm. For
realistic color, it’s important for the computer to be able to choose from
millions of different colors for the pixels making up an image. Variety in
texture comes both from mathematical models for surfaces ranging from frog skin
to Jell-o gelatin to stored “texture maps” that are applied to surfaces. We
also associate qualities that we can't see -- soft, hard, warm, cold -- with
particular combinations of color, texture and reflectance. If one of them is
wrong, the illusion of reality is shattered.
Adding a surface to the wireframe begins
to change the image from something obviously mathematical to a picture we might
recognize as a hand.
take a look at lighting and perspective in the next section.
Lighting and Perspective
you walk into a room, you turn on a light.
You probably don't spend a lot of time thinking about the way the light comes
from the bulb or tube and spreads around the room. But the people making 3D
graphics have to think about it, because all the surfaces surrounding the
wireframes have to be lit from somewhere. One technique, called ray-tracing,
plots the path that imaginary light rays take as they leave the bulb, bounce
off of mirrors, walls and other reflecting surfaces, and finally land on items
at different intensities from varying angles. It's complicated enough when you
think about the rays from a single light bulb, but most rooms have multiple
light sources -- several lamps, ceiling fixtures, windows, candles and so on.
Lighting plays a key role in two
effects that give the appearance of weight and solidity to objects: shading and
shadows. The first, shading, takes place when the light shining on an object is
stronger on one side than on the other. This shading is what makes a ball look
round, high cheekbones seem striking and the folds in a blanket appear deep and
soft. These differences in light intensity work with shape to reinforce the
illusion that an object has depth as well as height and width. The illusion of
weight comes from the second effect -- shadows.
in an image not only adds depth to the object through shading, it
"anchors" objects to the ground with shadows.
Solid bodies cast shadows when a
light shines on them. You can see this when you observe the shadow that a
sundial or a tree casts onto a sidewalk. And because we’re used to seeing real
objects and people cast shadows, seeing the shadows in a 3D image reinforces
the illusion that we’re looking through a window into the real world, rather
than at a screen of mathematically generated shapes.
Perspective is one of those words
that sounds technical but that actually describes a simple effect everyone has
seen. If you stand on the side of a long, straight road and look into the
distance, it appears as if the two sides of the road come together in a point
at the horizon. Also, if trees are standing next to the road, the trees farther
away will look smaller than the trees close to you. As a matter of fact, the
trees will look like they are converging on the point formed by the side of the
road. When all of the objects in a scene look like they will eventually
converge at a single point in the distance, that's perspective. There are
variations, but most 3D graphics use the "single point perspective"
In the illustration, the hands are
separate, but most scenes feature some items in front of, and partially
blocking the view of, other items. For these scenes the software not only must
calculate the relative sizes of the items but also must know which item is in
front and how much of the other items it hides. The most common technique for
calculating these factors is the Z-Buffer. The Z-buffer gets its name from the
common label for the axis, or imaginary line, going from the screen back
through the scene to the horizon. (There are two other common axes to consider:
the x-axis, which measures the scene from side to side, and the y-axis, which
measures the scene from top to bottom.)
The Z-buffer assigns to each polygon
a number based on how close an object containing the polygon is to the front of
the scene. Generally, lower numbers are assigned to items closer to the screen,
and higher numbers are assigned to items closer to the horizon. For example, a
16-bit Z-buffer would assign the number -32,768 to an object rendered as close
to the screen as possible and 32,767 to an object that is as far away as
In the real world, our eyes can’t see
objects behind others, so we don’t have the problem of figuring out what we
should be seeing. But the computer faces this problem constantly and solves it
in a straightforward way. As each object is created, its Z-value is compared to
that of other objects that occupy the same x- and y-values. The object with the
lowest z-value is fully rendered, while objects with higher z-values aren’t
rendered where they intersect. The result ensures that we don’t see background
items appearing through the middle of characters in the foreground. Since the
z-buffer is employed before objects are fully rendered, pieces of the scene
that are hidden behind characters or objects don’t have to be rendered at all.
This speeds up graphics performance. Next, we'll look at the depth of field
Depth of Field
optical effect successfully used to create 3D is depth of field. Using our
example of the trees beside the road, as that line of trees gets smaller,
another interesting thing happens. If you look at the trees close to you, the
trees farther away will appear to be out of focus. And this is especially true
when you're looking at a photograph or movie of the trees. Film directors and
computer animators use this depth of field effect for two purposes. The first
is to reinforce the illusion of depth in the scene you're watching. It's
certainly possible for the computer to make sure that every item in a scene, no
matter how near or far it's supposed to be, is perfectly in focus. Since we're
used to seeing the depth of field effect, though, having items in focus
regardless of distance would seem foreign and would disturb the illusion of
watching a scene in the real world.
The second reason directors use depth
of field is to focus your attention on the items or actors they feel are most
important. To direct your attention to the heroine of a movie, for example, a
director might use a "shallow depth of field," where only the actor
is in focus. A scene that's designed to impress you with the grandeur of
nature, on the other hand, might use a "deep depth of field" to get
as much as possible in focus and noticeable.
A technique that also relies on
fooling the eye is anti-aliasing. Digital graphics systems are very good at
creating lines that go straight up and down the screen, or straight across. But
when curves or diagonal lines show up (and they show up pretty often in the
real world), the computer might produce lines that resemble stair steps instead
of smooth flows. So to fool your eye into seeing a smooth curve or line, the
computer can add graduated shades of the color in the line to the pixels
surrounding the line. These "grayed-out" pixels will fool your eye
into thinking that the jagged stair steps are gone. This process of adding
additional colored pixels to fool the eye is called anti-aliasing, and it is
one of the techniques that separates computer-generated 3D graphics from those
generated by hand. Keeping up with the lines as they move through fields of
color, and adding the right amount of "anti-jaggy" color, is yet
another complex task that a computer must handle as it creates 3D animation on
your computer monitor.
jagged "stair steps" that occur when images are painted from pixels
in straight lines mark an object as obviously computer-generated.
gray pixels around the lines of an image -- "blurring" the lines --
minimizes the stair steps and makes an object appear more realistic.
We'll find out how to animate 3D
images in the coming sections.
all the tricks we've talked about so far are put together, scenes of tremendous
realism can be created. And in recent games and films, computer-generated
objects are combined with photographic backgrounds to further heighten the
illusion. You can see the amazing results when you compare photographs and
This is a photograph of a sidewalk
near the How Stuff Works office. In one of the following images, a ball was
placed on the sidewalk and photographed. In the other, an artist used a
computer graphics program to create a ball.
Can you tell which is the real ball?
Look for the answer at the end of the article.
Making 3D Graphics Move
far, we've been looking at the sorts of things that make any digital image seem
more realistic, whether the image is a single "still" picture or part
of an animated sequence. But during an animated sequence, programmers and
designers will use even more tricks to give the appearance of "live
action" rather than of computer-generated images.
How many frames per second?
When you go to see a movie at the
local theater, a sequence of images called frames runs in front of your eyes at
a rate of 24 frames per second. Since your retina will retain an image for a
bit longer than 1/24th of a second, most people's eyes will blend the frames
into a single, continuous image of movement and action.
If you think of this from the other
direction, it means that each frame of a motion picture is a photograph taken
at an exposure of 1/24 of a second. That's much longer than the exposures taken
for "stop action" photography, in which runners and other objects in
motion seem frozen in flight. As a result, if you look at a single frame from a
movie about racing, you see that some of the cars are "blurred"
because they moved during the time that the camera shutter was open. This
blurring of things that are moving fast is something that we're used to seeing,
and it's part of what makes an image look real to us when we see it on a
However, since digital 3D images are
not photographs at all, no blurring occurs when an object moves during a frame.
To make images look more realistic, blurring has to be explicitly added by
programmers. Some designers feel that "overcoming" this lack of
natural blurring requires more than 30 frames per second, and have pushed their
games to display 60 frames per second. While this allows each individual image
to be rendered in great detail, and movements to be shown in smaller
increments, it dramatically increases the number of frames that must be
rendered for a given sequence of action. As an example, think of a chase that
lasts six and one-half minutes. A motion picture would require 24 (frames per
second) x 60 (seconds) x 6.5 (minutes) or 9,360 frames for the chase. A digital
3D image at 60 frames per second would require 60 x 60 x 6.5, or 23,400 frames
for the same length of time.
The blurring that programmers add to
boost realism in a moving image is called "motion blur" or
"spatial anti-aliasing." If you've ever turned on the "mouse
trails" feature of Windows, you've used a very crude version of a portion
of this technique. Copies of the moving object are left behind in its wake,
with the copies growing ever less distinct and intense as the object moves
farther away. The length of the trail of the object, how quickly the copies
fade away and other details will vary depending on exactly how fast the object
is supposed to be moving, how close to the viewer it is, and the extent to
which it is the focus of attention. As you can see, there are a lot of
decisions to be made and many details to be programmed in making an object
appear to move realistically.
There are other parts of an image
where the precise rendering of a computer must be sacrificed for the sake of
realism. This applies both to still and moving images. Reflections are a good
example. You've seen the images of chrome-surfaced cars and spaceships
perfectly reflecting everything in the scene. While the chrome-covered images
are tremendous demonstrations of ray-tracing, most of us don't live in
chrome-plated worlds. Wooden furniture, marble floors and polished metal all
reflect images, though not as perfectly as a smooth mirror. The reflections in
these surfaces must be blurred -- with each surface receiving a different blur
-- so that the surfaces surrounding the central players in a digital drama
provide a realistic stage for the action.
Fluid Motion for Us Is Hard Work for
the factors we've discussed so far add complexity to the process of putting a 3D
image on the screen. It's harder to define and create the object in the first
place, and it's harder to render it by generating all the pixels needed to display
the image. The triangles and polygons of the wireframe, the texture of the
surface, and the rays of light coming from various light sources and reflecting
from multiple surfaces must all be calculated and assembled before the software
begins to tell the computer how to paint the pixels on the screen. You might
think that the hard work of computing would be over when the painting begins,
but it's at the painting, or rendering, level that the numbers begin to add up.
Today, a screen resolution of 1024 x
768 defines the lowest point of "high-resolution." That means that
there are 786,432 picture elements, or pixels, to be painted on the screen. If
there are 32 bits of color available, multiplying by 32 shows that 25,165,824
bits have to be dealt with to make a single image. Moving at a rate of 60
frames per second demands that the computer handle 1,509,949,440 bits of
information every second just to put the image onto the screen. And this is
completely separate from the work the computer has to do to decide about the
content, colors, shapes, lighting and everything else about the image so that
the pixels put on the screen actually show the right image. When you think
about all the processing that has to happen just to get the image painted, it's
easy to understand why graphics display boards are moving more and more of the
graphics processing away from the computer's central processing unit (CPU). The
CPU needs all the help it can get.
Transforms and Processors: Work, Work,
at the number of information bits that go into the makeup of a screen only
gives a partial picture of how much processing is involved. To get some inkling
of the total processing load, we have to talk about a mathematical process
called a transform. Transforms are used whenever we change the way we look at
something. A picture of a car that moves toward us, for example, uses
transforms to make the car appear larger as it moves. Another example of a
transform is when the 3D world created by a computer program has to be
"flattened" into 2-D for display on a screen. Let's look at the math
involved with this transform -- one that's used in every frame of a 3D game --
to get an idea of what the computer is doing. We'll use some numbers that are
made up but that give an idea of the staggering amount of mathematics involved
in generating one screen. Don't worry about learning to do the math. That has
become the computer's problem. This is all intended to give you some
appreciation for the heavy-lifting your computer does when you run a game.
The first part of the process has
several important variables:
X = 758
-- the height of the "world" we're looking at.
Y = 1024
-- the width of the world we're looking at
Z = 2 --
the depth (front to back) of the world we're looking at
height of our window into the world
width of our window into the world
Sz = a
depth variable that determines which objects are visible in front of other,
D = .75
-- the distance between our eye and the window in this imaginary world.
First, we calculate the size of the
windows into the imaginary world.
Now that the window size has been
calculated, a perspective transform is used to move a step closer to projecting
the world onto a monitor screen. In this next step, we add some more variables.
So, a point (X, Y, Z, 1.0) in the three-dimensional
imaginary world would have transformed position of (X', Y', Z', W'), which we
get by the following equations:
At this point, another transform must
be applied before the image can be projected onto the monitor's screen, but you
begin to see the level of computation involved -- and this is all for a single
vector (line) in the image! Imagine the calculations in a complex scene with
many objects and characters, and imagine doing all this 60 times a second.
Aren't you glad someone invented computers?
In the example below, you see an
animated sequence showing a walk through the new How Stuff Works office. First,
notice that this sequence is much simpler than most scenes in a 3D game. There
are no opponents jumping out from behind desks, no missiles or spears sailing
through the air, no tooth-gnashing demons materializing in cubicles. From the
"what's-going-to-be-in-the-scene" point of view, this is simple
animation. Even this simple sequence, though, deals with many of the issues
we've seen so far. The walls and furniture have texture that covers wireframe
structures. Rays representing lighting provide the basis for shadows. Also, as
the point of view changes during the walk through the office, notice how some
objects become visible around corners and appear from behind walls -- you're
seeing the effects of the z-buffer calculations. As all of these elements come
into play before the image can actually be rendered onto the monitor, it's
pretty obvious that even a powerful modern CPU can use some help doing all the
processing required for 3D games and graphics. That's where graphics
co-processor boards come in.
How Graphics Boards Help
the early days of personal computers, most graphics boards have been
translators, taking the fully developed image created by the computer's CPU and translating it into the electrical
impulses required to drive the computer's monitor.
This approach works, but all of the processing for the image is done by the CPU
-- along with all the processing for the sound, player input (for games) and
the interrupts for the system. Because of everything the computer must do to
make modern 3D games and multi-media presentations happen, it's easy for even
the fastest modern processors to become overworked and unable to serve the
various requirements of the software in real time. It's here that the graphics
co-processor helps: it splits the work with the CPU so that the total
multi-media experience can move at an acceptable speed.
As we've seen, the first step in
building a 3D digital image is creating a wireframe world of triangles and
polygons. The wireframe world is then transformed from the three-dimensional
mathematical world into a set of patterns that will display on a 2-D screen.
The transformed image is then covered with surfaces, or rendered, lit from some
number of sources, and finally translated into the patterns that display on a
monitor's screen. The most common graphics co-processors in the current
generation of graphics display boards, however, take the task of rendering away
from the CPU after the wireframe has been created and transformed into a 2-D
set of polygons. The graphics co-processor found in boards like the VooDoo3 and
TNT2 Ultra takes over from the CPU at this stage. This is an important step,
but graphics processors on the cutting edge of technology are designed to
relieve the CPU at even earlier points in the process.
One approach to taking more
responsibility from the CPU is done by the GeForce 256 from Nvidia. In addition
to the rendering done by earlier-generation boards, the GeForce 256 adds
transforming the wireframe models from 3D mathematics space to 2-D display
space as well as the work needed to show lighting. Since both transforms and
ray-tracing involve serious floating point mathematics (mathematics that
involve fractions, called "floating point" because the decimal point can
move as needed to provide high precision), these tasks take a serious
processing burden from the CPU. And because the graphics processor doesn't have
to cope with many of the tasks expected of the CPU, it can be designed to do
those mathematical tasks very quickly.
The new Voodoo 5 from 3dfx takes over
another set of tasks from the CPU. 3dfx calls the technology the T-buffer. This
technology focuses on improving the rendering process rather than adding
additional tasks to the processor. The T-buffer is designed to improve
anti-aliasing by rendering up to four copies of the same image, each slightly
offset from the others, then combining them to slightly blur the edges of
objects and defeat the "jaggies" that can plague computer-generated
images. The same technique is used to generate motion-blur, blurred shadows and
depth-of-field focus blurring. All of these produce smoother-looking, more
realistic images that graphics designers want. The object of the Voodoo 5
design is to do full-screen anti-aliasing while still maintaining fast frame
Computer graphics still have a ways
to go before we see routine, constant generation and presentation of truly
realistic moving images. But graphics have advanced tremendously since the days
of 80 columns and 25 lines of monochrome text. The result is that millions of
people enjoy games and simulations with today's technology. And new 3D
processors will come much closer to making us feel we're really exploring other
worlds and experiencing things we'd never dare try in real life. Major advances
in PC graphics hardware seem to happen about every six months. Software
improves more slowly. It's still clear that, like the Internet, computer
graphics are going to become an increasingly attractive alternative to TV.
Back to the images of the ball. How
did you do? Image A has a computer-generated ball. Image B shows a photograph
of a real ball on the sidewalk. It's not easy to tell which is which, is it?