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Visibility extension via mirror-edges to cover invisible segments

Vaezi, A ; Sharif University of Technology | 2019

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  1. Type of Document: Article
  2. DOI: 10.1016/j.tcs.2019.02.011
  3. Publisher: Elsevier B.V , 2019
  4. Abstract:
  5. Given a simple polygon P with n vertices, the visibility polygon (VP) of a point q, or a segment pq‾ inside P can be computed in linear time. We propose a linear time algorithm to extend the VP of a viewer (point or segment), by converting some edges of P into mirrors, such that a given non-visible segment uw‾ can also be seen from the viewer. Various definitions for the visibility of a segment, such as weak, strong, or complete visibility are considered. Our algorithm finds every edge that, when converted to a mirror, makes uw‾ visible to our viewer. We find out exactly which interval of uw‾ becomes visible, by every edge middling as a mirror, all in linear time. In other words, in this article, we present an algorithm that, in linear time, for every edge e of P reveals precisely which part of uw‾ is mirror-visible through e. © 2019 The Authors
  6. Keywords:
  7. Mirror ; Viewer ; Visibility polygon ; Clustering algorithms ; Geometry ; Visibility ; Linear time ; Linear-time algorithms ; Simple polygon ; Viewer ; Mirrors
  8. Source: Theoretical Computer Science ; Volume 789 , 2019 , Pages 22-33 ; 03043975 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S0304397519301173