Oblique reflection

If two points are oblique reflections of each other, they will still stay so under affine transformations.

For an oblique reflection, one requires instead of perpendicularity that AB be parallel to a given reference line.

[1] Formally, let there be a plane P in the three-dimensional space, and a line L in space not parallel to P. To obtain the oblique reflection of a point A in space in respect to the plane P, one draws through A a line parallel to L, and lets the oblique reflection of A be the point B on that line on the other side of the plane such that the midpoint of AB is in P. If the reference line L is perpendicular to the plane, one obtains the usual reflection.

Let the direction of the reference line L be given by the vector (a, b, c), with c≠0 (that is, L is not parallel to P).

Back to three dimensions, one can then define oblique reflection in respect to a line, with a plane serving as a reference.