Weak Visibility of Line Segments in Different Environments

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Nouri Bygi, Mojtaba | 2015

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Type of Document: Ph.D. Dissertation
Language: Farsi
Document No: 47415 (19)
University: Sharif University of Technology
Department: Computer Engineering
Advisor(s): Ghodsi, Mohammad
Abstract:
Visibility is an important topic in computational geometry, computer graphics, and motion planning. Two points inside a polygon are visible to each other if their connecting segment remains completely inside the polygon. Visibility polygon of a point in a simple polygon P is the set of points inside P that are visible from the point. The visibility problem has also been considered for line segments. A point v is said to be weakly visible to a line segment pq if there exists a point w 2 pq, such that w and v are visible to each other. The problem of computing the weak visibility polygon (or WVP) of pq inside a polygon P is to compute all points of P that are weakly visible from pq. In this thesis we consider the problem of computing weak visibility of a line segment inside various environments. The main problems we focused on are as follows: computiong the weak visibility polygon of a line segment in simple polygons, computing the weak visibility polygon of a line segment in polygonal domains, computing the size of the weak visibility of a line segment in simple polygons, and maitaining the visibility of a moving line segment in polygonal domains
Keywords:
Visibility Polygon ; Computational Geometry ; Visibility Problems ; Weak Visibility ; Visibility Counting

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