Image files are derived from the DEM data and computational methods are used to interpolate among the data points in order to illustrate the shape of Earth's terrain. Maps and GIS methods, i.e. the use of database themes and layers, are applicable in many contexts other than describing Earth's surface. Layered maps of interiors of buildings showing various types of infrastructure, room configuration, furniture, emergency escape routes, labels according to function, etc., are used for facilities management and maintenance, and other purposes. In common use, maps display enough evidence to determine intersection and approximations for distance. With projections from non-planar surfaces to planar surfaces, e.g. from Earth's surface to a plane, not all of distance, shape and area can be preserved.
Some distortion is inevitable.
But while tolerance of such distortion is subjective, there is no such tolerance of errors in topology, i.e. intersection and betweenness. Illustrations that are topologically correct but that compromise correctness of distance and area, e.g. to facilitate reading or to save space, are used in special contexts. As is the case with use of computers in many other applications, their use in the generation of maps introduces enormous flexibility, and it simultaneously forces precise organization and quantification of tasks heretofore handled easily by intuition or visual perception. The flexibility is discussed in Lessons 13 and 14. The ability to display layers representing subsets of the GIS database obligates the programmer to address some companion issues.