Slicing an ear using prune-and-search

It is well known that a diagonal of a simple polygon P can be found in linear time with a simple and practically efficient algorithm. An ear of P is a triangle such that one of its edges is a diagonal of P and the remaining two edges are edges of P. An ear of P can easily be found by first triangulating P and subsequently searching the triangulation. However, although a polygon can be triangulated in linear time, such a procedure is conceptually difficult and not practically efficient. In this note we show that an ear of P can be found in linear time with a simple, practically efficient algorithm that does not require pre-triangulating P.