The multi-L-REP decomposition and its application to a point-in-polygon inclusion test

This paper presents a scheme for decomposing polygons called multi-L-REP. The scheme can be considered as a generalization of the L-REP decomposition, which associates the edges of a polygon with a set of layered triangles. In the multi-L-REP these layered triangles are grouped into regions of a plane division. The paper also shows some alternative algorithms for its construction, and one of its applications: the point-in polygon inclusion test. Finally, a special case of multi-L-REP that has several interesting properties and shows a very fast point-in-polygon inclusion test is presented.