Making 3-D Graphics Move
So 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 screen.
However, since digital 3-D 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 3-D 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 Computer
All the factors we’ve discussed so far add complexity to the process of putting a 3-D 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 3-D 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 3-D 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 3-D 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 3-D games and graphics. That's where graphics co-processor boards come in.
How Graphics Boards Help
Since 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 3-D 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 3-D 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 3-D 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 rates.
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 3-D 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?
Lots More Information!
3-D Software and Hardware
3-D News, Users