# x,y,z, and w?

can someone explain to me what the 4th dimension is? where is the fourth dimension? is there some place where i could read up on this?

if you turn right after the 3rd and stop a while before the 5th you will find the 4th dimension just joking
w is not really a dimension but a scaling factor (used to get some matrix stuff easier done - means you can calculate translations by matrix multiplication instead of an addition)
for kartesian coordiantes its:

x’=x/w
y’=y/w
z’=z/w

when setting w=1 you have standard kartesian coordinates but the advantage of using matrix multiplication for all transformations

Originally posted by satan:
[b]if you turn right after the 3rd and stop a while before the 5th you will find the 4th dimension just joking
w is not really a dimension but a scaling factor (used to get some matrix stuff easier done - means you can calculate translations by matrix multiplication instead of an addition)
for kartesian coordiantes its:

x’=x/w
y’=y/w
z’=z/w

when setting w=1 you have standard kartesian coordinates but the advantage of using matrix multiplication for all transformations[/b]

this is not completly true, in fact w IS a fourth dimension (but no one - at least no human - is able to imagine a fourth spatial dimension)
by dividing x, y and z by w you actually project this 4d point into 3d space.
but don’t think too much about it, this fourth dimension is just needed do do things like translation and perspective projection with matrices (with just a 3x3 matrix this wouldn’t be possible)

i know, i just wanted to make the difference between the ‘dimensions in 3d space’ and the scaling factor
and to the imagination of more than 3 dimensions
my math teacher at university told us that he sometimes had stundents without any problems imagening more than 3 dimensions, but you are right that ordinary people like you and me have problems with that
but let’s stop here 'cause i have holidays and do not want to do to much math stuff

[This message has been edited by satan (edited 02-16-2002).]