Projective line at infinity (${\ell }_{\infty }=\{[x:y:0]\}$)

After choosing the affine chart $z\ne 0$ in the projective plane, its complement $z=0$ is the projective line at infinity. Affine parallel lines meet at the same projective point on this line, corresponding to their common direction. The choice of this line is part of the affine chart, not an intrinsic distinction preserved by every projective transformation.