Length fidelity

Length fidelity is a property of geometrical images . Such a mapping is called true-to-length if the distance between two points and always coincides with the distance between the associated image points and . ${\displaystyle P}$ ${\displaystyle Q}$ ${\displaystyle P'}$ ${\displaystyle Q'}$

Examples of true-to-length images are mirror images , point reflections , shifts and rotations . In contrast, centric extensions are generally not true to length.

The term has a special meaning for the map network design (also map projection) within the cartography . It states that the distance in selected directions is retained when projecting onto an auxiliary body (except for a fixed scale factor that is valid for all mapped areas of the sphere ). A generally true-to-length mapping of a sphere on a plane is impossible. ${\displaystyle m}$

literature

• Hans Schupp: Elementary Geometry. UTB, Stuttgart 1977. ISBN 3-506-99189-2