x axis and 2 sides parallel to the y axis. See also: Minimum bounding rectangle. A golygon is a rectilinear polygon whose side lengths in sequence are consecutive integers. A rectilinear polygon which is not a rectangle is never convex, but it can be orthogonally convex. See Orthogonally convex rectilinear polygon . A monotone rectilinear polygon is a monotone polygon which is also rectilinear. A T-square is a fractal generated from a sequence of rectilinear polygons with interesting properties. Generalizations Orthogonal polyhedra - the natural generalization of orthogonal polygons to 3D. Rectilinearity Algorithmic problems involving rectilinear polygons Most of them may be stated for general polygons as well, but expectation of more efficient algorithms warrants a separate consideration Orthogonal range searching Orthogonal convex hull construction Boolean operations on polygons for orthogonal polygons (e.g., intersection and union) Motion planning/path planning/routing among rectilinear obstacles Visibility problems (Illumination problems) Rectilinear art gallery problems Maximal empty rectangle Rectangular decomposition Of particular interest to rectilinear polygons are problems of decomposing a given rectilinear polygon to simple units - usually rectangles or squares. There are several types of decomposition problems: In covering problems, the goal is to find a smallest set of units (squares or rectangles) whose union is equal to the polygon. The units may overlap. See Polygon covering. In packing problems, the goal is to find a largest set of non-overlapping units whose union is contained in the polygon. The union may be smaller than the polygon. In partitioning problems, the goal is to find a smallest set of non-overlapping units whose union is exactly equal to the polygon. See Polygon partition. References , chapter 8: "The Geometry of Rectangles" Types of polygons