Points end with a 1, and directions end with a 0. This suggests that the first 3 columns of a 4x4 affine matrix are somehow "directions" and the last column is a "point". Why might this be?

madssnake

The first three columns affect the rotations/scaling, which could be referred to as directional changes, but the last column will translate and move an image, moving its focal point. When the last column has a zero, the translation doesn't occur for any vectors (vectors = "directions"...?)

(Seed for discussion)

Points end with a 1, and directions end with a 0. This suggests that the first 3 columns of a 4x4 affine matrix are somehow "directions" and the last column is a "point". Why might this be?

The first three columns affect the rotations/scaling, which could be referred to as directional changes, but the last column will translate and move an image, moving its focal point. When the last column has a zero, the translation doesn't occur for any vectors (vectors = "directions"...?)