For many of us, games on a computer or advanced game system are the most common ways we see 3-D graphics. These games, or movies made with computer-generated images, have to go through three major steps to create and present a realistic 3-D scene:

• 1.      Creating a virtual 3-D world.
• 2.      Determining what part of the world will be shown on the screen.
• 3.      Determining how every pixel on the screen will look so that the whole image appears as realistic as possible.

3D computer graphics are graphics that use a three-dimensional representation of geometric data that is stored in the computer for the purposes of performing calculations and rendering 2D images. Such images may be for later display or for real-time viewing. Despite these differences, 3D computer graphics rely on many of the same algorithms as 2D computer vector graphics in the wire frame model and 2D computer raster graphics in the final rendered display. In computer graphics software, the distinction between 2D and 3D is occasionally blurred; 2D applications may use 3D techniques to achieve effects such as lighting, and primarily 3D may use 2D rendering techniques. 3D computer graphics are often referred to as 3D models. Apart from the rendered graphic, the model is contained within the graphical data file. However, there are differences. A 3D model is the mathematical representation of any three-dimensional object (either inanimate or living). A model is not technically a graphic until it is visually displayed. Due to 3D printing, 3D models are not confined to virtual space. A model can be displayed visually as a two-dimensional image through a process called 3D rendering, or used in non-graphical computer simulations and calculations.

What Makes a Picture 3-D?

A picture that has or appears to have height, width and depth is three-dimensional (or 3-D). 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. The 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 3-D graphics are used: 2-D graphics are good at communicating something simple, very quickly. 3-D 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 3-D 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, 3-D 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 3-D 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 3-D image requires adding a lot of information, then the step from a 3-D 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 3-D graphics on PCs, Macintoshes, and, increasingly, game consoles like the Dreamcast and the Playstation II.

Creating a Virtual 3-D World

A virtual 3-D 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 3-D 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 3-D 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 3-D 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 3-D 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 3-D 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.