We study the problem of counting the number of lattice points inside a regular polygon with $n$ sides when its center is at the origin and present an exact algorithm with $\mathcal{O}(k^{2}\log n)$ time and two approximate answers for this problem, where $k$ is the absolute value of side length of the minimum bounding box of the regular polygon. Numerical results show the efficiency of the approximations in calculating the answer to this problem.
Imanparast,M . (2022). Approximating the Number of Lattice Points inside a Regular Polygon. Journal of Algorithms and Computation, 54(1), 89-98. doi: 10.22059/jac.2022.88337
MLA
Imanparast,M . "Approximating the Number of Lattice Points inside a Regular Polygon", Journal of Algorithms and Computation, 54, 1, 2022, 89-98. doi: 10.22059/jac.2022.88337
HARVARD
Imanparast M. (2022). 'Approximating the Number of Lattice Points inside a Regular Polygon', Journal of Algorithms and Computation, 54(1), pp. 89-98. doi: 10.22059/jac.2022.88337
CHICAGO
M Imanparast, "Approximating the Number of Lattice Points inside a Regular Polygon," Journal of Algorithms and Computation, 54 1 (2022): 89-98, doi: 10.22059/jac.2022.88337
VANCOUVER
Imanparast M. Approximating the Number of Lattice Points inside a Regular Polygon. J. Algo. Comp.. 2022;54(1):89-98. doi: 10.22059/jac.2022.88337
