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Bahram Sadeghi Bigham - One of the best experts on this subject based on the ideXlab platform.

  • Polar Diagram of points with moving pole
    Journal of Information and Communication Technology, 2020
    Co-Authors: Bahram Sadeghi Bigham, Fateme Rabani
    Abstract:

    Polar Diagram is a generalization of Voronoi Diagram in which the angle is used as the metric. This Problem has many applications in visibility, image Processing, telecommunication, antenna, and Path Planning Problems. In recent years two kinds of Polar Diagram have been proposed and appropriate algorithm have been Presented for some types of sites. Also, some algorithms has presented for kinetic data and dynamic states. In this Paper, it is assumed that the Pole is moving and an algorithm is presented that updates near Pole Polar Diagram of sites with moving pole efficiently and in a sub linear time. In this approach, the Preprocessing time is 〖O(n^4 log〗_2⁡〖n)〗 and updating time for Diagram with each successive movement is 〖 O(log〗_2⁡〖n +k)〗 that k is the number of sites in region T which its site’s regions may be changed

  • an optimal solution for dynamic Polar Diagram
    Canadian Conference on Computational Geometry, 2010
    Co-Authors: Ebrahim Ehsanfar, Bahram Sadeghi Bigham, Najmeh Madadi
    Abstract:

    The Polar Diagram [1] of a set of points (i.e. sites) is a partition of the plane. It is a locus approach for problems processing angles. Also, Dynamic Polar Diagram problem is a problem in which some points can be added to or removed from the point set of the Polar Diagram. Sadeghi et al. [4] introduced this problem and solved it using an algorithm which is optimal in the case that some points are deleted from the set. But this algorithm is not optimal when some new points are inserted into the Diagram. In this paper, we present an algorithm to solve the Dynamic Polar Diagram in optimal time in which we insert some new points into the Diagram one by one. Our approach applies only on the regions that would be changed and solves the problem for each insertion in O(k + logn) time, in which 1 k n is the number of the sites which their regions would be changed.

  • dynamic Polar Diagram
    Information Processing Letters, 2008
    Co-Authors: Bahram Sadeghi Bigham, Ali Mohades, Lidia Ortega
    Abstract:

    The Polar Diagram [C.I. Grima, A. Marquez, L. Ortega, A new 2D tessellation for angle problems: The Polar Diagram, Computational Geometry 34 (2006) 58-74] of a set of points on the plane and the contracted dual of Polar Diagram (CDPD) [B. Sadeghi Bigham, A. Mohades, The dual of Polar Diagrams and its extraction, in: International Conference of Computational Methods in Sciences and Engineering ICCMSE, vol. 7, Greece, 2006, pp. 451-454] have been introduced recently. In this paper, we introduce the Dynamic Polar Diagram and present an algorithm to find it using CDPD and a hash structure for point location problem. In the dynamic Polar Diagram, the points can be added to or removed from the point set. For this problem, a brute-force method runs in O(nlogn) time and also there is a sketch of an algorithm in [C.I. Grima, A. Marquez, L. Ortega, A new 2D tessellation for angle problems: The Polar Diagram, Computational Geometry 34 (2006) 58-74] that takes O(n) time in all cases (best, average and worst). In our approach, we first determine an area out of which the Polar Diagram does not change due to insertion or deletion of a site. Then we present a new algorithm to solve the problem in O(k"p) time where k"p is the number of the sites whose Polar regions are affected by the new addition or deletion of p.

Lidia Ortega - One of the best experts on this subject based on the ideXlab platform.

  • dynamic Polar Diagram
    Information Processing Letters, 2008
    Co-Authors: Bahram Sadeghi Bigham, Ali Mohades, Lidia Ortega
    Abstract:

    The Polar Diagram [C.I. Grima, A. Marquez, L. Ortega, A new 2D tessellation for angle problems: The Polar Diagram, Computational Geometry 34 (2006) 58-74] of a set of points on the plane and the contracted dual of Polar Diagram (CDPD) [B. Sadeghi Bigham, A. Mohades, The dual of Polar Diagrams and its extraction, in: International Conference of Computational Methods in Sciences and Engineering ICCMSE, vol. 7, Greece, 2006, pp. 451-454] have been introduced recently. In this paper, we introduce the Dynamic Polar Diagram and present an algorithm to find it using CDPD and a hash structure for point location problem. In the dynamic Polar Diagram, the points can be added to or removed from the point set. For this problem, a brute-force method runs in O(nlogn) time and also there is a sketch of an algorithm in [C.I. Grima, A. Marquez, L. Ortega, A new 2D tessellation for angle problems: The Polar Diagram, Computational Geometry 34 (2006) 58-74] that takes O(n) time in all cases (best, average and worst). In our approach, we first determine an area out of which the Polar Diagram does not change due to insertion or deletion of a site. Then we present a new algorithm to solve the problem in O(k"p) time where k"p is the number of the sites whose Polar regions are affected by the new addition or deletion of p.

  • a new 2d tessellation for angle problems the Polar Diagram
    Computational Geometry: Theory and Applications, 2006
    Co-Authors: Clara I Grima, Alberto Marquez, Lidia Ortega
    Abstract:

    The new approach we propose in this paper is a plane partition with similar features to those of the Voronoi Diagram, but the Euclidean minimum distance criterion is replaced for the minimal angle criterion. The result is a new tessellation of the plane in regions called Polar Diagram, in which every site is owner of a Polar region as the locus of points with smallest Polar angle respect to this site. We prove that Polar Diagrams, used as preprocessing, can be applied to many problems in Computational Geometry in order to speed up their processing times. Some of these applications are the convex hull, visibility problems, and path planning problems.

Ali Mohades - One of the best experts on this subject based on the ideXlab platform.

  • dynamic Polar Diagram
    Information Processing Letters, 2008
    Co-Authors: Bahram Sadeghi Bigham, Ali Mohades, Lidia Ortega
    Abstract:

    The Polar Diagram [C.I. Grima, A. Marquez, L. Ortega, A new 2D tessellation for angle problems: The Polar Diagram, Computational Geometry 34 (2006) 58-74] of a set of points on the plane and the contracted dual of Polar Diagram (CDPD) [B. Sadeghi Bigham, A. Mohades, The dual of Polar Diagrams and its extraction, in: International Conference of Computational Methods in Sciences and Engineering ICCMSE, vol. 7, Greece, 2006, pp. 451-454] have been introduced recently. In this paper, we introduce the Dynamic Polar Diagram and present an algorithm to find it using CDPD and a hash structure for point location problem. In the dynamic Polar Diagram, the points can be added to or removed from the point set. For this problem, a brute-force method runs in O(nlogn) time and also there is a sketch of an algorithm in [C.I. Grima, A. Marquez, L. Ortega, A new 2D tessellation for angle problems: The Polar Diagram, Computational Geometry 34 (2006) 58-74] that takes O(n) time in all cases (best, average and worst). In our approach, we first determine an area out of which the Polar Diagram does not change due to insertion or deletion of a site. Then we present a new algorithm to solve the problem in O(k"p) time where k"p is the number of the sites whose Polar regions are affected by the new addition or deletion of p.

Maryam Tahmasbi - One of the best experts on this subject based on the ideXlab platform.

  • near pole Polar Diagram of objects and duality
    Social Science Research Network, 2012
    Co-Authors: Bahram Sadeghi Bighama, Marzieh Eskandari, Maryam Tahmasbi
    Abstract:

    The Polar Diagram of a set of points in a plane and its extracted dual EDPD were recently introduced for static and dynamic cases. In this paper, the near-pole Polar Diagram NPPD for a set of points is presented.This new Diagram can be considered as a generalization of the Polar Diagram and has applications in several communication systems and robotics problems. After reviewing the NPPD of points, we solve the problem for a set of line segments and simple polygons in optimal time (n log n), where n is the number of line segments or polygon vertices. We introduce duality for the NPPD of points and identify some applications

D A Shapiro - One of the best experts on this subject based on the ideXlab platform.

  • light scattering by dielectric bodies in the born approximation
    Physical Review A, 2017
    Co-Authors: A S Bereza, A V Nemykin, S V Perminov, L L Frumin, D A Shapiro
    Abstract:

    Light scattering is one of the most important elementary processes in near-field optics. We build up the Born series for scattering by dielectric bodies with sharp boundaries. The Green's function for a two-dimensional homogeneous dielectric cylinder is obtained. As an example, the formulas are derived for a scattered field of two parallel cylinders. The Polar Diagram is shown to agree with the numerical calculation by the known methods of discrete dipoles and boundary elements.