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.
Imanparast, M., & Kazemi Torbaghan, M. (2020). On Point-inclusion Test in Convex Polygons and Polyhedrons. Journal of Algorithms and Computation, 52(1), 197-207. https://doi.org/10.22059/jac.2020.77122
MLA
Imanparast, M., & Kazemi Torbaghan, M. "On Point-inclusion Test in Convex Polygons and Polyhedrons", Journal of Algorithms and Computation, 52, 1, 2020, 197-207. doi: 10.22059/jac.2020.77122
HARVARD
Imanparast M., Kazemi Torbaghan M. (2020). 'On Point-inclusion Test in Convex Polygons and Polyhedrons', Journal of Algorithms and Computation, 52(1), pp. 197-207. doi: 10.22059/jac.2020.77122
CHICAGO
M. Imanparast & M. Kazemi Torbaghan, "On Point-inclusion Test in Convex Polygons and Polyhedrons," Journal of Algorithms and Computation, 52 1 (2020): 197-207, doi: 10.22059/jac.2020.77122
VANCOUVER
Imanparast M., Kazemi Torbaghan M. On Point-inclusion Test in Convex Polygons and Polyhedrons. J. Algo. Comp. 2020;52(1):197-207. doi: 10.22059/jac.2020.77122
