Now, all those effects have names. The summation over time I have been talking about its generally referred to as motion blur. Motion blur is generally not associated with video cameras, it's most known from photography. You can take photos with a very long shutter time (up to many seconds). By using a long shutter time you get an exaggerated situation of what I described before, and as a result everything that moves looks like a smeared out mess. I am sure you have seen pictures like that taken from a highway with cars at night. All the headlights are turned into long white lines. These lines are the summation over time of the positions of the headlights.
So what is the link with 3dfx's T-Buffer?
T-Buffer technology tries to solve the problem I described above. Instead of having a single isolated perfect snapshot in time, we are trying to recreate the summation over time created automatically by a Video Camera. If we can simulate this summation over time we should see an increased quality of the animations generated by the 3D card. Now, how can we generate such a summation over time in single frame?
The easiest way to do this is by simply combining several rendered images into one single frame. Now, at this point, we have to decide what we want: more true frames per second (being true perfect snapshots shown) or a combination of several images (sub frames) in one single frame. To help us decide we have to known that the human eye and brain combination is capable of identifying at least 30 individual frames per second. This means that if you are shown 30 frames/sec you can identify them as being separate images (there are special tests done to come to this conclusion. For example, you are shown dot patterns at a rate of 30fps and at the end you have to say whether a certain pattern was present in the series or not. if you move above 30fps you see several of those patterns as one making it impossible to identify whether a pattern was present or not, while at frame rates of 30fps and below you can identify the individual image contents and thus give the correct answer). What happens is that if you increase the frame rate the brain starts to see multiple frames as one single frame. So, what happens is that our eyes and brain add something similar to motion blur (real world sample: move your hand quickly left to right in front of your face notice how the hand looks "smeared" and "blurry"). The problem is that different people get this effect at different frame rates. While, for some people, this brain-induced "motion blur"-effect kicks in at 30fps it might kick in at 70fps for others. So, instead of relying on the brain to combine images and create motion blur, we could use the computer to combine images and thus create "fake" motion blur. What T-Buffer technology actually does is it takes several images rendered and combines them into one single frame. By doing this, the brain gets confused, and it suddenly sees a motion blurred image. The brain links this effect with speed and the feeling of realism is increased dramatically. So, it's very possible that an animation at 30fps using motion blur looks much more realistic than a perfect, still frame animation at 60fps simply due to the effect that the brain isn't fooled so easily to add motion blur at 60fps.