Digital Elevation Models
DEMs; Digital Terrain Model (DTM); Digital Surface Model
A Digital Elevation Model (DEM) represents the 3D shape of a terrain in a digital format. A terrain is mathematically modeled as a function z = f(x, y) which maps each point (x, y) in a planar domain D into an elevation value f(x, y). In this view, the terrain is the graph of function f over D.
In practice, a terrain is known at a finite set of points within D, which may (i) lie at the vertices of a regular grid, (ii) be scattered, or (iii) belong to contour lines (also known as isolines), i.e., the intersections of the terrain surface with a sequence of horizontal planes.
In case (i), the DEM consists of the grid structure plus elevation values at its vertices. This is called a Regular Square Grid(RSG). Within each grid cell, terrain elevation either is defined as constant, or it is modeled by a function, which can be linear (this involves cell decomposition in two triangles), or quadratic (usually,...
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