Triangulated Irregular Network
TIN; Triangulated terrains
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...