COP center of projection on origin.
Using Similar Triangles – X,Y are projected to -d*X/Z, -d*Y/Z – which is the focal length.
Homogeneous coordinates enable linear multiplication,and are invariant under scale. We use them to not worry about the division of z until after the heavy math and in the end of it we can just divide by the homogeneous coordinate such as x/(z/f) which is in fact fx/z, we do this because z changes and we can’t divide linearly by a change.
Perspective Projection =f*x/z, f*y/z
Parellel Lines = f*a/c, f*b/c converge when c<>0
Orthoprojections =(x,y,z) = x, y
Weak projections scaled Orthoprojections = x/1/s,y/1/s =>(xs,xy)