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On Characterizing TIN Visibility Graph

Ostovari, Mojtaba | 2017

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 50388 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Zarei, Alireza
  7. Abstract:
  8. A triangulated irregular network (TIN) is a data structure that is usually used for representing and storing a geographic surface. TIN is a set of points and some segments between them that are distributed in space such that projection of segments on the plane is a triangulation for projection of points. Visibility graph of points is a graph in which there is a vertex correspond to each point of TIN and there is an edge between two vertexes if corresponding points can see each other. TIN’s visibility graph has many applications; for example, finding some points in a geographic surface that they can see all of the surface together, they are good places for radars.in first section of this thesis, we review definitions and applications of visibility graph of TIN and different geometry shapes. in second section, we survey on some researches related to recognizing of visibility graphs and in third and fourth section, we show that recognition of visibility graph of TIN, visibility graph of polygons with holes and internal and external visibility graph of simple polygons are complete for the class of existential theory of reals
  9. Keywords:
  10. Computational Geometry ; Triangulated Irregular Network Terrian (TIN) ; Visibility Graph ; Existential Reals Theory

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  • سپاس‌گزاری
  • چکیده
  • فهرست تصاویر
  • مقدمه
    • تعریف انواع گراف‌های دید
    • TIN
    • گراف دید TIN
    • شناخت گراف دید TIN
  • مروری بر تحقیقات پیشین
    • شناخت گراف دید چند‌ضلعی
    • شناخت و بازسازی گراف دید چند ضلعی برجی
    • شناخت گراف دید زنجیره‌یکنوا
    • شناخت گراف دید نقطه‌ها
  • پیچیدگی محاسبه شناخت گراف دید TIN
    • آرایش خط
    • مسئله بسط یافتنی
    • رسم گراف
    • ساخت TIN
    • پیچیدگی محاسبه
  • ‌پیچیدگی محاسبه شناخت گراف دید چندضلعی‌ها
    • شناخت گراف دید چندضلعی با حفره
    • مسأله تشخیص گراف دید داخلی به همراه خارجی چندضلعی ساده
    • نتیجه‌گیری
  • مراجع
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