How a Change in Visibility Graph Affects its Underlying Polygon

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Esmradi, Ayda | 2018

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 51441 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Zarei, Alireza
Abstract:
The geometric deformation of the polygon naturally changes its Visibility Graph. Also, any change in the Visibility Graph, which includes adding or removing the edge, requires a change in the position of the polygon vertices. Of course, some changes in the graph may cause no polygon corresponding to such a graph.In this thesis, we want to study the necessary and sufficient conditions to change the Visibility Graph of a polygon, so that the new Visibility Graph corresponds to the graph obtained by adding the edge to the initial graph. We consider this problem in the case of spiral, funnel, and quasi-triangular input polygons
Keywords:
Computational Geometry ; Visibility Graph ; Spiral Polygon ; Quasi Triangle Polygon ; Funnel Polygon

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