Centerdependent

Centerdependent is a term used to describe a property, behavior, or measurement that relies on a central reference point or center. A centerdependent quantity changes when the designated center is moved or redefined, unlike center-invariant quantities that remain unchanged under translation of the center. The concept is used across disciplines to distinguish effects that arise from a specific focal point from those that persist regardless of where the center is chosen.

In practice, centerdependent characteristics appear in areas such as geometry, image processing, statistics, and physics. For example, a centerdependent filter in image processing may produce outputs that vary with distance from or direction toward the image center. In statistics, a centerdependent weighting scheme assigns weights based on proximity to a central point such as the mean or centroid, altering conclusions if the center changes. In physics or computational modeling, potentials or field quantities may be described as centerdependent if their form or strength depends on the chosen center of coordinates.

To determine whether a quantity is centerdependent, one can analyze how it changes under a redefinition of the center. If translating or shifting the center results in different values or predictions, the quantity is centerdependent. Conversely, if the outcome remains the same under different center choices, it is center-invariant.

See also: center-invariant, center of mass, coordinate system, symmetry.