A rectilinear polygon is a polygon all of whose edges 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 preferrable: 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. However, "orthogonal" is a misnomer because "rectilinear" means "of straight lines," and in the latter term the adjective "orthogonal" raises the question, "orthogonal to what?" Other terms in use are iso-oriented, axis-aligned, or 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.
See also orthogonal polyhedra (under polyhedron, "Other important families of polyhedra"), the natural generalization of orthogonal polygons to 3D.
Most of them may be stated for general polygons as well, but expectation of more efficient algorithms warrants a separate consideration