Isothetic polygon

An isothetic polygon is a polygon whose alternate sides belong to two parametric families of straight lines which are pencils of lines with centers at two points (possibly the point at infinity).

The term is produced from Greek roots: iso- for "equal, same, similar" and thetos (position, placement), i.e., the term is supposed to mean "polygon with similarly placed sides".

Much emphasis was placed on the development of efficient algorithms for operations with orthogonal polygons, since the latter ones had an important application: representation of shapes in integrated circuit mask layouts due to their simplicity for design and manufacturing.

It was observed that the efficiency of many geometric algorithms for orthogonal polygons does not really depend on the fact that their sides meet at right angles, but rather on the fact that their sides are naturally split into two alternating sets (of vertical and horizontal segments).

In the context of digital geometry, isothetic polygons are practically axis-parallel and have integer coordinates of their vertices.