Projection plane:
The general processing steps for modeling and converting a world coordinate description of a scene to
device coordinates, we need projection plane.
Projective plane: We know that $P^2$ is all $\mathbb R^2$ points and point at infinity.In projection plane any point exists in $(∞,∞)$ if we want to represents it then we need projective plane.
For instance, a point in Cartesian $(1, 2)$ becomes $(1, 2, 1)$ in Homogeneous. If a point, $(1, 2)$, moves toward infinity, it becomes $(∞,∞)$ in Cartesian coordinates. And it becomes $(1, 2, 0)$ in Homogeneous coordinates, because of $(1/0, 2/0) ≈ (∞,∞).$ Notice that we can express the point at infinity without using $"∞".$
My question is what's difference between Projection plane and Projective plane?
Best Answer
I would say that "projection plane" describes its role. Namely, it implies that you are projecting from some higher-dimensional space (e.g. 3d) to that plane.
Conversely "projective plane" describes its structure. What kinds of points it contains, what axioms it satisfies. The fact that using homogeneous coordinates makes sense.
Your can do a projection from a 3d space onto a projection plane that also happens to be a projective plane. Doing so will allow you to preserve direction information for things "at infinity". You can even consider the map between 3d homogeneous coordinate vectors and their planar interpretation to be such a projection from a 3d space to the projective plane at $z=1$ using the origin as center of projection.
But the two concepts don't need to go together. You can do projection onto a plane while staying purely with an affine description of that plane. You can talk about the properties of the projective plane without any projection involved in the process. So from that perspective I'd consider the two concepts to be fairly independent.