University of TehranJournal of Algorithms and Computation2476-277652120200601On Point-inclusion Test in Convex Polygons and Polyhedrons1972077712210.22059/jac.2020.77122ENMahdiImanparastDepartment of Computer Science, University of Bojnord, Bojnord, IranMehdiKazemi TorbaghanDepartment of Mathematics, University of BojnordJournal Article20200718A 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.https://jac.ut.ac.ir/article_77122_472a280448e87d499860383248c46f29.pdf