Why do 3D games use 4-dimensional vectors instead of 3-dimensional?

Question

In 3D-games, i have heard that variables like velocity and position is not stored in trheedimensioal vectors, but in fourdimensional. Why? Any example?

Answer 1

For 3D graphics we need a 4-th dimension to generate perspective projection and to accomplish that we have to employ a so called method of affine transformations. To get more information on perspective projections see http://en.wikipedia.org/wiki/Transformation_matrix
Notr that the same method is also used for computing rotation and rescaling.

Another good application for a forth dimension in a 3-D vector I can see is time. I’m talking about relativity however it is not Einstein’s theory is being referred here. The 3-D games now days are multiplayer network based games. The system has to keep track on one event relative to the other since each player will have different ping time or the time it takes a for a signal from your computer to reach the server. The server will stamp time for your position and aim when you ‘squeezed’ the trigger. This data will be compared to the time stamps for position of the player you shot at. This insures fairness to player of varied ping time.

I hope it helps

Answer 2

Velocity and position are 3-D vectors, but games rely on much more than that. Think of when you needed to do something in a game, like open a secret door. Sure you knew its position and how to get to that spot (which all deal with 3-D vectors), but there is also an element of time. Time is often the 4-D that many physics issues refer to and is the same with gaming. Without the time aspect, firing a gun at someone wouldn't allow your opponent to dodge.

Answer 3

Do a research on linear functions (transpose).

In order to transpose a f(x) function into a 3D vector, a fourth variable is required to keep the function intact.

I did those theorem 2 years ago, so that's the little knowledge i can remember.

:-)

Answer 4

Does the 4th dimension exist ? I don't know.

Answer 5

http://www.devmaster.net/wiki/Transformation_matrices

Answer 6

because thats the way it is!