Encyclopedia of Database Systems

2018 Edition
| Editors: Ling Liu, M. Tamer Özsu

Triangulated Irregular Network

  • Leila De Floriani
  • Paola Magillo
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_437

Synonyms

TIN; Triangulated terrains

Definition

A Triangulated Irregular Network (TIN) is a special case of a Digital Elevation Model (DEM).

A terrain can be mathematically modeled as a function z = f (x, y) mapping a point (x, y) in a domain D in the plane to its elevation value f (x, y). In practice, the value of function f is known at a finite set S of points within D. A DEM provides an estimated value for function f at any point (x, y) of the domain, based on the values at the points of S. A DEM consists of a subdivision of the domain into cells and of a piece-wise interpolating function defined on such cells.

A TIN is a DEM in which the domain subdivision is a triangle mesh, i.e., a set T of triangles such that: (i) the set of vertices of T is S, (ii) the interiors of any two triangles of T do not intersect, (iii) if the boundaries of two triangles intersect, then the intersection is either a common vertex, or a common edge.

Usually, a linear interpolating function is defined on...

This is a preview of subscription content, log in to check access.

Recommended Reading

  1. 1.
    de Berg M, van Kreveld M, Overmars M, Schwarzkopf O. Computational geometry – Algorithms and applications. 2nd ed. Berlin: Springer; 2000.zbMATHGoogle Scholar
  2. 2.
    De Floriani L, Magillo P, Puppo E. Applications of computational geometry to geographic information systems. Chapter 7. In: Sack JR, Urrutia J, editors. Handbook of computational geometry. New York: Elsevier Science; 1999. p. 333–88.zbMATHGoogle Scholar
  3. 3.
    van Kreveld M. Digital elevation models and TIN algorithms. In: van Kreveld M, Nievergelt J, Roos T, Widmayer P, editors. Algorithmic foundations of geographic information systems. Berlin: Springer; 1997. p. 37–78. LNCS 1340 (tutorials).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of GenovaGenoaItaly

Section editors and affiliations

  • Ralf Hartmut Güting
    • 1
  1. 1.Computer ScienceUniversity of HagenHagenGermany