Rectilinear polygon

A rectilinear polygon is a polygon all of whose edge intersections are 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.

A rectilinear polygon has edges of two types: horizontal and vertical.

A rectilinear polygon has corners of two types: corners in which the smaller angle (90°) is interior to the polygon are called convex and corners in which the larger angle (270°) is interior are called concave.

A knob is an edge whose two endpoints are convex corners. An antiknob is an edge whose two endpoints are concave corners.

A rectilinear polygon that is also simple is also called hole-free because it has no holes - only a single continuous boundary. It has several interesting properties:

A rectilinear polygon can be covered by a finite number of squares or rectangles with edges parallel to the edges of the polygon (see Polygon covering). It is possible to distinguish several types of squares/rectangles contained in a certain rectilinear polygon P:

A maximal square in a polygon P is a square in P which is not contained in any other square in P. Similarly, a maximal rectangle is a rectangle not contained in any other rectangle in P.

...
Wikipedia