# $P^2$ vs projection plane

I want to explain what I understood of definition of the two things.

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?

In computer graphics the projection plane is most commonly defined as a plane perpendicular to the camera at a specific distance from the camera (the distance is often labeled $$g$$). It is the plane that an image will be projected onto and is usually shown between the near and far planes of a projection matrix. In the attached image (from the fged website) it is the blue plane.
• The first image is an example projection, the green plane is the near plane, the gray plane is the far plane and the camera would be positioned at $o$ which is the origin. Oct 11 at 14:01