On Point-inclusion Test in Convex Polygons and Polyhedrons

Abstract

A new algorithm for point-inclusion test in convex polygons is introduced. The proposed algorithm answers the point-inclusion test in convex polygons in $mathcal{O}(log n)$ time without any preprocessing and with $mathcal{O}(n)$ space. The proposed algorithm is extended to do the point-inclusion test in convex polyhedrons in three dimensional space. This algorithm can solve the point-inclusion test in convex $3D$ polyhedrons in $mathcal{O}(log n)$ time with $mathcal{O}(n)$ preprocessing time and $mathcal{O}(n)$ space.