originrelative

Originrelative is a term used to describe coordinate representations where positions are expressed relative to a designated origin rather than a fixed global frame. The term blends "origin" and "relative" and is common in informal writing, tutorials, and software docs; it is not a formally standardized term in most fields.

Definition: In n-dimensional space, with an origin O, the originrelative coordinate of a point P is P_rel = P − O. If the origin varies with time, O = O(t), then P_rel(t) = P(t) − O(t). Converting back to global coordinates requires the origin’s position and, if orientation matters, its rotation.

Applications: Originrelative representations simplify local motion analysis. In robotics and animation, measurements and poses are often kept in a moving local frame. In computer graphics, local or object-relative coordinates are transformed to world coordinates as part of a scene graph. In geodesy, local coordinate systems reduce numerical error near the origin.

Relation to other concepts: It overlaps with local coordinates and body-fixed frames. It is distinct from world coordinates, where the origin is fixed. Transforms between originrelative and global coordinates require the origin’s pose and, if applicable, time dependence.

Limitations: Accurate use requires tracking the origin and consistent transformations; neglecting origin changes yields errors.

See also: local coordinates, world coordinates, reference frame, coordinate transformation.