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arXiv · 1803.10184

A New Optimal Algorithm for Computing the Visibility Area of a simple Polygon from a Viewpoint

Hamid Hoorfar·Alireza Bagheri
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Abstract

Given a simple polygon $ \mathcal {P} $ of $ n $ vertices in the Plane. We study the problem of computing the visibility area from a given viewpoint $ q $ inside $ \mathcal {P} $ where only sub-linear variables are allowed for working space. Without any memory-constrained, this problem was previously solved in $ O(n) $-time and $ O(n) $-variables space. In a newer research, the visibility area of a point be computed in $ O(n) $-time, using $ O(\sqrt{n}) $ variables for working space. In this paper, we present an optimal-time algorithm, using $ O(c/\log n) $ variables space for computing visibility area, where $ c<n $ is the number of critical vertices. We keep the algorithm in the linear-time and reduce space as much as possible.

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Hamid Hoorfar, Alireza Bagheri. 2018-03-27. A New Optimal Algorithm for Computing the Visibility Area of a simple Polygon from a Viewpoint. https://arxiv.org/abs/1803.10184

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