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Maintaining the Visibility Graph of a Dynamic Simple Polygon

  • Tameem Choudhury
  • R. InkuluEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11394)

Abstract

We devise a fully-dynamic algorithm for maintaining the visibility graph of a given simple polygon P amid vertex insertions and deletions to the simple polygon. Our algorithm takes \(O(k(\lg {n'})^2)\) worst-case time to update the visibility graph when a vertex is inserted to the current simple polygon \(P'\), or when a vertex is deleted from \(P'\). Here, k is the number of combinatorial changes needed to the visibility graph due to the insertion (resp. deletion) of a vertex v to \(P'\), and \(n'\) is the number of vertices of \(P'\). This algorithm preprocesses the initial simple polygon P to build few data structures, including the visibility graph of P. Further, as part of efficiently updating the visibility graph, a fully-dynamic algorithm is designed to compute the vertices of the current simple polygon that are visible from a query point.

Keywords

Computational geometry Visibility Dynamic algorithms 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringIIT GuwahatiGuwahatiIndia

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