This article is about right-angled polygons. For "rectilineal figure" as defined in Euclid's Elements, see Simple polygon.
Some examples of rectilinear polygons
A rectilinear polygon is a polygon all of whose sides meet at right angles. Thus the interior angle at each vertex is either 90° or 270°. Rectilinear polygons are a special case of isothetic polygons.
In many cases another definition is preferable: a rectilinear polygon is a polygon with sides parallel to the axes of Cartesian coordinates. The distinction becomes crucial when spoken about sets of polygons: the latter definition would imply that sides of all polygons in the set are aligned with the same coordinate axes. Within the framework of the second definition it is natural to speak of horizontal edges and vertical edges of a rectilinear polygon.
Rectilinear polygons are also known as orthogonal polygons. Other terms in use are iso-oriented, axis-aligned, and axis-oriented polygons. These adjectives are less confusing when the polygons of this type are rectangles, and the term axis-aligned rectangle is preferred, although orthogonal rectangle and rectilinear rectangle are in use as well.
The importance of the class of rectilinear polygons comes from the following.
They are convenient for the representation of shapes in integrated circuit mask layouts due to their simplicity for design and manufacturing. Many manufactured objects result in orthogonal polygons.
Problems in computational geometry stated in terms of polygons often allow for more efficient algorithms when restricted to orthogonal polygons. An example is provided by the art gallery theorem for orthogonal polygons, which leads to more efficient guard coverage than is possible for arbitrary polygons.
and 26 Related for: Rectilinear polygon information
rectilinearpolygon is a polygon all of whose sides meet at right angles. Thus the interior angle at each vertex is either 90° or 270°. Rectilinear polygons...
Euclidean plane Rectilinear lens, a photographic lens Rectilinear locomotion, a form of animal locomotion Rectilinearpolygon, a polygon whose edges meet...
problems, depending on the type of polygon being covered. An example polygon covering problem is: given a rectilinearpolygon, find a smallest set of squares...
of size (137,95) in a big rectangle of size (1600,1230). Given a rectilinearpolygon (whose sides meet at right angles) R in the plane, a set S of points...
equilateral. A non-convex regular polygon is called a regular star polygon. Rectilinear: the polygon's sides meet at right angles, i.e. all its interior angles...
special sub-family of polygon partition problems arises when the large polygon is a rectilinearpolygon (also called: orthogonal polygon). In this case, the...
sides of a rectangle is a rhombus and vice versa. A rectangle is a rectilinearpolygon: its sides meet at right angles. A rectangle in the plane can be...
Guillotine partition is the process of partitioning a rectilinearpolygon, possibly containing some holes, into rectangles, using only guillotine-cuts...
or more generally a serial isogon of 90°, is any polygon with all right angles (a rectilinearpolygon) whose sides are consecutive integer lengths. Golygons...
point at infinity). The most well-known example of isothetic polygons are rectilinearpolygons, and the former term is commonly used as a synonym for the...
Orthoconvex treemaps can be used. There, all regions are orthoconvex rectilinearpolygons with aspect ratio at most 64; and the leaves are either rectangles...
some other dissection puzzles, including the problem of dissecting rectilinearpolygons into each other by axis-parallel cuts and translations. In two dimensions...
geodesic between any two of its points. The orthogonal convex hull or rectilinear convex hull is the intersection of all orthogonally convex and connected...
not be under surveillance. Covering a rectilinearpolygon with star polygons Star-shaped polygon, a class of polygon for which the art gallery problem can...
as possible. When the figure is a rectilinearpolygon and it should be partitioned into rectangles, and the polygon is hole-free, then the problem is...
that the original sheet might not be rectangular - it can be any rectilinearpolygon. In particular, it might contain holes (representing defects in the...
nonconvex. They are the 3D analogs of 2D orthogonal polygons, also known as rectilinearpolygons. Orthogonal polyhedra are used in computational geometry...
intersection with K. The orthogonal convex hull is also known as the rectilinear convex hull, or, in two dimensions, the x-y convex hull. The figure shows...
7234 crossings. Further values are collected by the Rectilinear Crossing Number project. Rectilinear Crossing numbers for Kn are 0, 0, 0, 0, 1, 3, 9, 19...
simple polygons in two articles "On solving rectilinearpolygons". Lexell discussed two separate groups of problems: the first had the polygon defined...
straight, though they showed some tendencies to making the digit more rectilinear. The eastern Arabs developed the digit from a form that looked something...
in a general-position point set and its largest subset forming a convex polygon, namely that the smallest number of points for which any general position...
environment could be used to accelerate polygon ordering. The technique made use of depth coherence, which states that a polygon on the far side of the plane cannot...
construction for a parallelogram of the same area as any "rectilinear figure" (simple polygon) by splitting it into triangles. Greek geometers often compared...
proof; rectilinearpolygons; guards that can patrol a line segment rather than a single point; special classes of polygons including star-shaped polygons, spiral...
Global Information