Guarding a Terrain by Watchtowers

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Panahi Shahri, Masoume | 2014

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 46218 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Zarei, Alireza
Abstract:
Guarding terrains(or covering terrains) is a well known problem in the field of visibility and computational geometry. The aim of this problem is to select a minimal set of elements (such as points on terrain, line segment, points above terrain ,...),as guard set, such that every point of the terrain is visible from at least one member of the guard set.
This problem was introduced in 2-dimensions as art gallery problem. Various types of this problem have been defiend and studied in the literature. Guarding 3-dimensional terrains is an example of this problem. In 3-dimentional case, the guarded terrain can be modeled with triangulated irregullar network(TIN), as one of the surface models, for which the guarding problem will be solved.
In this thesis, guarding TINs with k vertex guards with minimum height (called watchtower) is studied. This problem was studid for k=1, k=2 and admissible results was proposed [2] [49].
Other than general TIN, which is a theoretical model, the concept of realistic TIN is considered in this thesis, which is more practical and is expected to be solved by relatively efficient algorithms
Keywords:
Computational Geometry ; Art Gallery Problem ; Triangulated Irregular Network Terrian (TIN) ; Polyhedral Terrains ; Minimum Guard Problem ; Realistic Model