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Mukund
03-26-2012, 10:57 AM
Hello All!

I am reading this excellent collection of articles on projective spaces, transformations etc.

I came across this sentence:

Note that in projective space points (meaning location) and translations are represented by different types (unlike vector algebra) this is reasonable as they are different entities.

LINK (http://www.euclideanspace.com/maths/geometry/space/nonEuclid/projective/index.htm)

I'm not able to understand what exactly that meant.
PS: In projective space, using homogenous coordinates, we get
(x, y, z, w) = point if w != 0
and (x, y, z, w) = vector if w = 0, for a 4D projective space.
Am i right?

So, what exactly does the author try to explain here?

Thanks in advance!

mbentrup
03-28-2012, 07:45 AM
(x,y,z,w) with w = 0 is also a point (provided one of x,y,z != 0). These are the "infinite far" points of the projective space, so you could say that they represent directions, but a translation is defined by a direction plus a length or distance.

A translation in a projective space would be represented by a translation matrix.

Mukund
04-01-2012, 03:23 AM
Thanks for the reply mbentrup!