Trading Time for Space: an O(1) Average time Algorithm for Point-in-Polygon Location Problem. Theoretical Fiction or Practical Usage?

Abstract

Algorithms for Point in polygon problem solution are very often used especially in computer graphics applications The naive implementation has O(N) processing time complexity or O(lg N) complexity if a convex polygon is considered . A new algorithm of O(l) processing complexity was developed . The important feature of the algorithm is that preprocessing complexity is O (N) and memory requirements depend on geometrical properties of the given polygon Usage of the algorithm is expected in applications where many points are tested whether resides in the given polygon or not. The presented approach can be considered as alternative to the parallel processing usage. Experimental results are included, too.