Secrets of 3D computer graphics

Creative Blurring

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 dist

inct 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 Computer

All 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, Work

Looking 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

Sx = height of our window into the world

Sy - width of our window into the world

Sz = a depth variable that determines which objects are visible in front of other, hidden objects

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.

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