LinksRechtsSpiegelung

LinksRechtsSpiegelung is a term used in geometry and computer graphics to describe the left–right mirror image operation. It refers to reflecting an object across a vertical axis, producing a mirror image with reversed left-right orientation. In two dimensions the canonical form is the reflection about the y-axis, mapping coordinates as (x, y) to (-x, y) with respect to the mirror line x = 0. More generally, any line can serve as the axis of reflection, producing the symmetric counterpart of every point across that line. In three dimensions, reflection across a plane reverses one spatial coordinate relative to that plane.

The operation preserves distances and angles, making it an isometry, but it reverses orientation. Consequently, the transformation has determinant -1 and is classified as an improper rotation or mirror reflection rather than a proper rotation. In practice, horizontal and vertical mirroring are common conventions: a horizontal flip (left–right reversal) corresponds to reflection across a vertical axis, while a vertical flip (up–down reversal) corresponds to reflection across a horizontal axis.

Applications of LinksRechtsSpiegelung span several fields. In image processing and graphic design, it is used to create symmetrical compositions, generate mirror images for logos, or correct orientation. In typography and font design, mirrored glyphs serve stylistic or functional purposes. In data augmentation for machine learning, mirrored images can expand training datasets. In science, mirror symmetry plays a role in visual perception studies and in discussions of parity in physics, though parity operations in physics involve inversion of all coordinates rather than a single axis.

See also Spiegellung, Parität, Spiegelbild.