rettlinset

Rettlinset is a term used in geometry and computer graphics to denote a class of rectilinear sets—subsets of the plane that are built from axis-aligned components such as rectangles and line segments. The term is not standardized; different authors and communities adopt different definitions depending on context, leading to several closely related interpretations.

In one common definition, a rettlinset in R^2 is a finite union of axis-aligned rectangles. In another usage, it refers to a set that contains every axis-aligned line segment between any pair of its points, making it orthogonally convex with respect to the coordinate axes. Under either interpretation, the boundary of a rettlinset is formed by horizontal and vertical edges.

Representations often decompose a rettlinset into rectangles or describe its boundary as a rectilinear polygon. This makes rettlinsets convenient for rasterization, grid-based geographic information systems, visual rendering on pixel grids, and certain VLSI layout problems where axis-aligned geometry is preferred.

Typical examples include a single rectangle, a plus-shaped figure formed by intersecting rectangles, and larger polyomino-like regions. Non-examples include polygons with diagonally oriented edges or curved boundaries, which do not fit the rectilinear constraint implied by the term.

See also: rectilinear polygon, orthogonal polygon, polyomino, axis-aligned geometry.