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...
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de Berg M, van Kreveld M, Overmars M, Schwarzkopf O. Computational geometry – Algorithms and applications. 2nd ed. Berlin: Springer; 2000.
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.
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).
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De Floriani, L., Magillo, P. (2018). Triangulated Irregular Network. In: Liu, L., Özsu, M.T. (eds) Encyclopedia of Database Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8265-9_437
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