Twoextents

Twoextents is a term used in some domains to describe a pair of extents that jointly characterize the coverage of an entity across two independent dimensions. It is encountered in fields such as geographic information systems, computer graphics, and temporal databases, where objects or events must be described by both where they occur and when they occur.

Definition: The concept refers to a pair of extents, typically denoted E_space and E_time. E_space is the spatial extent, a region that bounds all observed locations of the object (for example, the bounding box of its coordinates). E_time is the temporal extent, the interval between the earliest and latest observation or occurrence.

Formalization: Given a set of observations {(p_i, t_i)} with p_i in R^2 and t_i in R, the spatial extent E_space can be defined as the minimal bounding rectangle of {p_i}, and the temporal extent E_time as [min_i t_i, max_i t_i]. The twoextents are the ordered pair (E_space, E_time). Variants may use different spatial representations (bounding polygon) or include directional constraints.

Applications: In GIS, twoextents help summarize an object's range over time or a moving object’s footprint and duration. In graphics, they can support dual-culling strategies using both screen-space and world-space bounds. In temporal databases, twoextents can describe the coverage of a record across space and time.

See also: Extent, Bounding box, Temporal extent, Spatio-temporal data.