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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., and Schwarzkopf O. Computational Geometry – Algorithms and Applications. 2nd ed. Springer-Verlag, Berlin, 2000.
De Floriani L., Magillo P., and Puppo E. Applications of computational geometry to Geographic Information Systems. Chapter 7 in Handbook of Computational Geometry, J.R. Sack, J. Urrutia (eds.). Elsevier Science, 1999, pp. 333–388.
van Kreveld M. Digital elevation models and TIN algorithms. In Algorithmic Foundations of Geographic Information Systems, M. van Kreveld, J. Nievergelt, T. Roos, P. Widmayer (eds.). Springer-Verlag, Berlin, 1997, pp. 37–78.LNCS 1340 (tutorials),
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Floriani, L.D., Magillo, P. (2009). Triangulated Irregular Network. In: LIU, L., ÖZSU, M.T. (eds) Encyclopedia of Database Systems. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-39940-9_437
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DOI: https://doi.org/10.1007/978-0-387-39940-9_437
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