perdirection

Perdirection is a term used in certain fields of vector analysis and data processing to denote the decomposition or evaluation of a quantity with respect to specified directions, rather than in aggregate. The word is formed from the prefix per- meaning through or by, combined with direction, to emphasize a per-directional viewpoint. It is not a widely standardized term across disciplines, but it appears in niche discussions and algorithm descriptions that focus on directional components of a field.

In formal terms, perdirection can be defined for a directional quantity by representing it as a set of components corresponding to a chosen set of directions. For a scalar field defined over a plane, perdirection may yield a function that maps each direction to a directional value obtained by projecting or integrating the field along that direction. For vector fields, perdirection often means assigning a component or contribution to each direction, resulting in a directional vector or a directional spectrum.

Applications of perdirection concepts appear in meteorology, fluid dynamics, robotics, and computer graphics, where understanding how a quantity behaves with respect to different directions is important. For example, a wind field might be described in eight perdirection components corresponding to the cardinal and intercardinal directions, highlighting directional tendencies that are not obvious from a single magnitude and orientation.

Computational approaches to perdirection include binning measurements into directional sectors or using continuous angular decompositions, such as Fourier analysis on the circle, to obtain a directional spectrum. Limitations include dependency on the chosen set of directions or reference frame, potential ambiguity without a canonical orientation, and the risk of oversimplification when projecting complex fields onto discrete directions.

See also: directional decomposition, vector components, directional statistics.