Point2D

Point2D refers to a location in a two-dimensional plane defined by an ordered pair of coordinates, typically written as (x, y). In most contexts, a point denotes a position rather than a direction or magnitude, which distinguishes it from a vector.

Coordinate systems and representation: Point2D is usually expressed in Cartesian coordinates, where x measures horizontal position and y measures vertical position. Depending on the application, the origin and axis directions can vary; for example, computer graphics often use screen coordinates with the origin at the top-left and y increasing downward. A point is commonly stored as two numbers, which may be integers or floating-point values. Some implementations treat points as mutable, others as immutable.

Basic operations: The distance between two points is computed by the Euclidean formula distance = sqrt((x2 − x1)² + (y2 − y1)²). The midpoint of two points is ((x1 + x2)/2, (y1 + y2)/2). Points can be translated by adding a vector (dx, dy) to obtain a new location. Additional operations include rotation around a chosen center, scaling relative to an origin, and applying affine transformations.

Applications: Point2D is a foundational concept in geometry, computer graphics, GIS, CAD, and UI design. It is used in algorithms for convex hulls, triangulation, collision detection, rendering, and spatial computations. In software libraries, Point2D often serves as a basic data structure that underpins higher-level constructs like shapes, polygons, and geometric predicates.

See also: point, vector, coordinate geometry, distance, transformation.