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!

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!