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Efficient Visibility Computation and Simplification in Different Environments

Zarei, Alireza | 2008

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 39026 (19)
  4. University: Sharif University of Technology
  5. Department: Computer Engineering
  6. Advisor(s): Ghodsi, Mohammad
  7. Abstract:
  8. In this thesis, we considered several types of the visibility problem. These problems include computing the visibility polygon of a point observer inside a polygonal domain, maintaining visibility polygon of a moving point observer, visibility coherence in space, maintaining visibility polygon of a moving segment observer and visibility dependent simplification. Furthermore, we considered these problems in both offline and streaming settings. These problems arise in different practical areas, such as computer graphics, machine vision, robotics, motion planning, geographic information systems (GIS) and computational geometry. We obtained effective theoretical results as well as superior practical algorithms. Our results are divided into two categories: visibility computation-maintenance and visibility simplification. Our results on the former category include efficient algorithms for computing the visibility polygon of a query point observer in 2D scenes, maintaining the visibility polygon of moving point or segment observers in 2D scenes, and a data structure for sketching visibility coherence between objects in space. For the latter, we proposed observer-dependent simplification criteria and proposed simplification algorithms for simplifying boundary of the visibility polygon of a point or segment observer in 2D for both streaming and offline input models. Moreover, we obtained a general streaming algorithm that can be used for classical line simplification problems
  9. Keywords:
  10. Computational Geometry ; Streaming Algorithm ; Visibility Algorithm ; Line Simplification

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