2D transformation and viewing: The camera projects the 2D world co-ordinate $(x_w, y_w)$ on its projection plane which co-ordinates $(x_v, y_v)$.
3D transformation and viewing: The camera projects the 3D world co-ordinate $(x_w, y_w, z_w)$ on its projection plane which co-ordinates $(x_v, y_v, z_v)$.Then $(x_v, y_v, z_v)$ can be transforms to $(x_v, y_v)$ of display device coordinates.
My questions are:
$A.$ In 2D transformation and viewing projection plane is 2D means it has 2 dimensions height and width. But I am confused projection plane which is a plane (2D) has equation is of the form $ax+by+cz+d=0.$ But here $z$ coordinate is missing, so how will it be plane?
In contrast 3D has projection plane means it has 3 dimensions height, width and depth. But we know that 2D plane $ax+by+cz+d=0.$ But how we're saying 3D? I am struggling to differentiate projection plane and dimensions. What I have misunderstood in the concepts of both cases?
$B.$ In 2D transformation and viewing how world co-ordinate $(x_w, y_w)$ is 2D? Because we know real world is 3D.
$C. $ In perspective projection how we will represents vanishing point coordinates in projection plane? For example I catch one image of railway tracks where two parallel lines intersects. During projection what could be it's world co-ordinate and projection plane coordinates respectively? It's normal form of projection from $(x_w, y_w, z_w)$ to $(x_p, y_p,z_{vp})$ in projection plane?