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Efcient Algorithms for Visibility Testing of Objects and Counting

Alipour, Sharareh | 2015

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 48842 (19)
  4. University: Sharif University of Technology
  5. Department: Computer Engineering
  6. Advisor(s): Ghodsi, Mohammad
  7. Abstract:
  8. Planar visibility computing is defned as determining the region of the plane that is visible from a specifc observer. This concept has many applications in computer graphics, robotic and computer games. In certain visibility problems, counting the number of visible objects in an appropriate time is required. For obtaining a solution fast, current algorithms give an approximated count. In this thesis, we consider visibility testing problem and visibility counting problem.For a given set S = fs1; s2; :::; sng of non-intersecting segments and a query point p in the plane, the visibility testing problem checks the inter-visibility of p and a segment si 2 S and the visibility counting problem counts the number of visible segments from p. We have introduced two approximation algorithms. In the frst algorithm, we have a trade-off between space and query time and also a trade-off between approximation factor and query time. In the second algorithm, we have used random sampling method. The expected query time of this algorithm is better than the frst algorithm in certain cases. Next, we have proposed a randomized algorithm that gives the exact solution for the visibility counting problem with the same time and space complexity of [35]. Then, we have considered the problems in 3D and have given algorithms to solve them. We have implemented these algorithms on real data sets.The results show that the time complexity and approximation factor of the proposed algorithms are effective and applicable in practice. At last, we have introduced a probabilistic model for these problems and proposed some solutions for them. In certain cases, we have proved that the probabilistic visibility testing problem is #P − complete. Also, we have presented some approximation algorithms to solve the probabilistic visibility counting problem
  9. Keywords:
  10. Computational Geometry ; Randomized Algorithm ; Approximate Algorithm ; Visibility Algorithm

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