Expanding Visibility Polygons by Mirrors

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Vaezi, Arash | 2012

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 44166 (19)
University: Sharif University of Technology
Department: Computer Engineering
Advisor(s): Ghodsi, Mohammad
Abstract:
We consider extending the visibility polygon of a given point q inside a simple polygon by converting one or some of the edges to mirrors. It is known that the visibility polygon of a point inside a polygon in the presence of a mirror can be computed in linear time. We propose a linear time algorithm that checks whether a given segment inside a simple polygon is visible by a given point q via a mirror-edge, and finds all such edges. And we prove that finding edges to add exactly k unit squares to the visibility polygon of a query point q in most cases is NP-complete and its minimization is NP-hard. These cases contain single and muliple, either with secular or difuse reflections. Moreover, considering the same cases findig edges to add at least k unit squares with minimum number of mirror-edges is NP-hard, too. The mutiple reflections case of the specular version of the at least k problem, has been left open
Keywords:
Mirror ; Visibility Polygon ; Specular Reflection ; Diffuse Reflection ; Single Reflection ; Multiple Reflection