coordinatebased

Coordinatebased is an adjective describing objects, representations, or methods that rely on a coordinate system to specify positions or values. It contrasts with coordinatefree or intrinsic descriptions. In mathematics, a coordinatebased approach expresses geometric objects as equations in a chosen coordinate system.

In geometry and algebra, coordinatebased methods assign numerical coordinates to points and vectors, enabling computations with algebraic formulas. Analytic geometry, for example, represents lines and curves by equations in x, y (or higher dimensions). In computer graphics, objects and transforms are commonly described using coordinatebased matrices and vector coordinates, enabling rasterization and rendering.

In GIS, coordinatebased data uses a defined coordinate reference system such as a projected or geographic coordinate system; measurements like distance, area, and direction depend on the coordinate system. In chemistry and bioinformatics, coordinatebased models specify atomic or residue coordinates in 3D space for molecules or proteins, facilitating simulations and docking.

Limitations: coordinatebased representations can be sensitive to the choice of coordinate system and may introduce redundancy or singularities; some problems are more naturally expressed in a coordinatefree or intrinsic form.