%0 Journal Article
%T On Point-inclusion Test in Convex Polygons and Polyhedrons
%J Journal of Algorithms and Computation
%I University of Tehran
%Z 2476-2776
%A Imanparast, Mahdi
%A Kazemi Torbaghan, Mehdi
%D 2020
%\ 06/01/2020
%V 52
%N 1
%P 197-207
%! On Point-inclusion Test in Convex Polygons and Polyhedrons
%K Point-in-polygon
%K Point-inclusion test
%K Convex polygons
%K Convex polyhedrons
%K Preprocessing time
%R 10.22059/jac.2020.77122
%X 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.
%U https://jac.ut.ac.ir/article_77122_472a280448e87d499860383248c46f29.pdf