2DProjektion

2DProjektion is a general term for the process of mapping points from a higher‑dimensional space to a two‑dimensional plane. It is used in mathematics, computer graphics, engineering, and cartography to produce a two‑dimensional representation of a three‑dimensional scene or of higher‑dimensional data.

There are two principal classes of 2D projections. Orthographic (parallel) projection uses rays that are parallel to a fixed direction. Points are projected by dropping one or more coordinates, resulting in representations where size is roughly preserved for objects near the projection direction but there is no perspective foreshortening. This type is common in engineering drawings and many CAD systems because it preserves shape relations and scales.

Perspective (central) projection uses rays emanating from a single viewpoint. Objects farther from the viewpoint appear smaller, and lines that meet in a point converge to vanishing points on the projection plane. Perspective projection mimics human vision and is widely used in computer graphics, photography, and art. It introduces foreshortening and distortion that depend on the viewpoint and the projection plane.

Mathematically, a projection can be described by a projection operator or a projection matrix, often using homogeneous coordinates and a perspective divide to map 3D points onto a 2D plane. Projections may also be studied as special cases of projective geometry.

Applications of 2D projections include rendering three‑dimensional scenes on screens, producing technical drawings, and projecting geographic data in cartography. All projections involve some distortion of metric or angular properties, with the choice of projection reflecting the desired trade‑offs.