Polar Diagram of Points with Moving Pole

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.

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