Crossarea

Crossarea is a term used in several domains to denote a measure derived from the interaction of two regions, objects, or signals. It is not a standardized mathematical term, and its precise meaning depends on the context.

In geometry and geographic information systems, crossarea commonly denotes the area of overlap between two planar regions A and B, expressed as crossarea(A, B) = area(A ∩ B). This interpretation helps quantify how much two shapes or layers share space, such as the common land area between two zoning maps or the overlap between two land-cover categories.

In three-dimensional contexts, crossarea can refer to the cross-sectional area of a body with respect to a specified direction. Here, it means the area of the intersection of the object with a plane perpendicular to the chosen direction, effectively the cross-section through the object. While the standard term in this context is cross-sectional area, some authors may use crossarea informally to describe the same concept.

In data analysis and raster processing, crossarea may describe the amount of shared presence in two binary maps, computed by counting the grid cells where both maps indicate presence. This usage aligns with measuring overlap in discretized spaces.

Computationally, crossarea often reduces to calculating the area of polygon intersections when dealing with vector shapes, utilizing polygon clipping or general intersection algorithms. For raster data, it corresponds to cell-wise overlap counts multiplied by cell area.

Related concepts include area, intersection, cross-section, and overlap measures. Crossarea remains ambiguous without context, so explicit definition is typically provided in applications or publications.