Oblique mirroring

Draw straight lines parallel to the vector through the points, mirror points over the intersection points with the axis

The oblique mirroring is very similar to the axis mirroring . The difference to axis mirroring is that with oblique mirroring, a point is not necessarily mirrored at right angles, but in a specified direction on the axis (e.g. by an angle or a vector ). This generally causes geometric figures to appear distorted after being mirrored.

The fixed points of the oblique mirroring lie on the mirror axis, exactly as with the axis mirroring, which is thus one - and indeed the only - fixed point straight line . Furthermore, all straight lines parallel to the given direction vector are fixed straight lines .

Oblique reflections are true to the straight line and true to area, but (at an angle ≠ 90 °) neither true to angle nor true to length, i.e. true to area affine images , but i. A. no congruence maps . The images of circles, rectangles and squares under an oblique reflection are generally not circles, rectangles and squares again, but ellipses and parallelograms.

As a special case (angle 90 °), the usual axis reflections also belong to the oblique reflections.

There are also oblique reflections in three-dimensional space and in higher-dimensional spaces.