I am reading book "3D Math primer for graphics and game developement", and i am stuck at this topic as it does not explain it well.

To understand how the standard physical 3D space is extended into 4D, let’s first examine

homogenous coordinates in 2D, which are of the form (x, y, w). Imagine the standard 2D plane

existing in 3D at the plane w= 1. So the physical 2D point (x, y) is represented in homogenous

space (x,y, 1). For all points that are not in the plane w= 1, we can compute the corresponding 2D

point by projecting the point onto the plane w= 1 and dividing by w. So the homogenous coordinate (x,y,w) is mapped to the physical 2D point (x/w,y/w).

1. Where this w = 1 come from?

2. If some point is outside of this plane w = 1 then it have different w value?

3. Is w absolute distance to plane?

4. If i divide points with w which is 1 then i get same points, so what is the point?

5. Any other book you could recommend that explains this w thingy better?

Thank you for your time.