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. doi: 10.22059/jac.2020.77122
MLA
Mahdi Imanparast; Mehdi 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
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
VANCOUVER
Imanparast, M., Kazemi Torbaghan, M. On Point-inclusion Test in Convex Polygons and Polyhedrons. Journal of Algorithms and Computation, 2020; 52(1): 197-207. doi: 10.22059/jac.2020.77122
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