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why call clip space homogeneous?

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I know clip space is project window that is in project plane (z = 1) I know homogeneous is the same repensentation of n-1 dimension in n dimension. but why does it call "homogeneous" clip space?

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This thread is better suited for Math and Physics.

The clip space is still in n dimensions, the perspective divide (ie projection) is done after clipping. No information is lost until the actual projection.
'Homogenous' is a mathematical concept that can mean a lot of different things. I guess, in this case, it just means that the space has a constant 'density'. The space has the form of a cube, instead of the cone that represent the normal perspective space.
So the clip function is the same regardless of FOV, because the projection transform skews the frustum into the homogenous cube.

Something like that. =)

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your question might mean.. why is clipping done in homog. space?

Usually u do clipping before perspective
division. This makes w usually != 1 its homogeneos inluding persp. distortion. But only in w.

The reason why its done there is simpe... the clipping planes are axis aligned in pre divis. homog. space. so a -1<x<1 check does clipping against left/right
plane. faster and easier.... got it?

btw.. homogeneus 4 space has a little bit more than the containing 3-space.
(vectors and points at infinity)

regards, gsus

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