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Observer-Dependent TIN Simplification Based on Visibility Graph

Behrooznia, Nastaran | 2023

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 55892 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Zarei, Alireza
  7. Abstract:
  8. Geographical environments can be modeled through the medium of TINs, in which some discrete points are sampled as vertices, and the union of polygonal faces, particularly triangles, constitutes its surface. As regards the two-dimensional space, the TIN boundary is an x-monotone path and we focus on this case. If the number of vertices is too large to be stored or some sampled points should be removed due to a lack of vital information, the necessity of TIN simplification arises. On top of this situation, if a point observer locates on or above the TIN, the points visible to the observer have more priorities to be considered in the simplified TIN. For example, human eyes can see the closer or larger parts of the environment in more detail than the rest. The importance of the vertices can also be determined according to the visibility graph of the TIN, such that the visibility graph of the output should closely resemble that of the original TIN. In this research, we aim to define an appropriate error function based on the intervisibility among vertices and devise efficient simplification algorithms accordingly. First, we assume no point observer in the problem, then we take one into account by generalizing these achievements. The observer can either continuously move or remain stable at discrete times; we tackle both cases in the thesis
  9. Keywords:
  10. Computational Geometry ; Triangulated Irregular Network Terrian (TIN) ; Simplification ; Visibility Graph ; Point Observer ; Continuous Movement

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