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- Type of Document: Ph.D. Dissertation
- Language: Farsi
- Document No: 44667 (19)
- University: Sharif University of Technology
- Department: Computer Engineering
- Advisor(s): Ghodsi, Mohammad
- Abstract:
- The study of visibility is at least 100 years old, when in 1913 Brunn proved a theorem about the kernel of a set. By now, visibility has become one of the most studied notions in computational geometry. The reasons are two-fold: 1) such problems arise naturally in areas where computational geometry tools and algorithms _nd applications including: computer graphics, robotics, motion planning, geographic information systems, computer games, computer-aided architecture, and pattern recognition; and where 2) their solutions are required, or serve as building blocks in the development of solutions to other problems, such as shortest paths or motion planning problems. Many natural problem instances arise and have been extensively studied in two and higher dimensions. In this thesis, we revisited some of the problems. Our target was to achieve much better results for these problems, comparing to the old results. Some other problems we studied were not studied before. The main problems we focused on are as follows: the problem of detecting weak visibility between two objects, the problem of computing the visibility polygon of a query point, the problem of computing the partial visibility polygon of a point and problems related to α-visibility
- Keywords:
- Visibility Polygon ; Visibility Problems ; Visibility Detection ; Partial Visibility ; Alpha-Visibility
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