A Transformational View of Cartography

Abstract

Cartographic transformations are applied to locative geographic data and to substantive geographic data. Conversion between locative aliases are between points, lines, and areas. Substantive transformations occur in map interpolation, filtering, and generalization, and in map reading. The theoretical importance of the inverses is in the study of error propagation effects. Leonard Bernstein, in a recent television lecture, made an exciting, and largely successful, attempt to describe musical concepts in terms of Noam Chomsky's ideas concerning transformational grammars, as originally devised for linguistics. 2, 4 A similar, though less ambitious, attempt is made here to look at a range of cartographic activities from a transformational point of view. The treatment is not particularly Chompskian, although some work on picture languages is available. 7, 11, 21, 23 The idea of transformations is hardly new to cartography. The well-known example is the procedure by which we associate locations on the two-dimensional surface of the earth with locations on the two-dimensional surface of a piece of paper. 16 The study of the subject of map projections once constituted the bulk of what was known as "mathematical cartography." An extension 'was suggested in 1958 by Julian Perkal: "Cartographic transformations, employed to represent the surface of the earth on maps, are of two simple types: map projections and generalization. Map projections are obtained by an objective mathematical operation. The subject of this paper is the second cartographic transformation-map generalization." Perkal then proceeded to derive mathematical rules for a particular method of generalizing lines on maps. As can be seen in his paper the method embodies a notion of spatial resolution. 20 Since that time considerable further work has been done on line generalization, and it is now known that the problem admits of more solutions than were recognized in Perkal's early paper. 9, 25, 28, 41 At the time that Perkal wrote, computer cartography had not reached the large scale implementation which it now enjoys. Automatic plotters were not commonplace and he did not have available the computer tapes, now in widespread use, of world coastlines and hydrography, of political boundaries, of city street patterns, or of world topography. These fundamental geographical data can now be processed automatically, either to solve geographical problems directly, or to provide geographic illustration in the form of pictures. Thus, a broader view is required of mathematical cartography and has elsewhere been labeled analytical cartography. 35 This is the changing paradigmatic world of cartography. Perkal recognized only two classes of cartographic transformation: map projections and map generalization. But the entire process of making, and using, a map can be viewed as a sequence of transformations. Original observations are manipulated and digested in various ways to obtain the data going into a map. In the design phase these are converted to a graphic representation,...

Mining Spatio-Temporal Data of Fatal Accident

“…Inselberg and Dimsdale [10] introduced parallel coordinates plot, PCP, to analyze the multivariate meanings of each cluster [18]. Besides that, cartographic map [11] is used in this study to analyze the spatial distribution of the spatio-temporal patterns and investigate the location of these patterns.…”

“…Next, to analyze the clustering performance, it was necessary to assess the clustering results using various cluster validation techniques. Furthermore, visualization techniques such as Principal Component Analysis (PCA) [9], parallel coordinates plot (PCP) [10], and cartographic map [11] are proposed in this research to interpret and present the optimal clustering result in an easy-understanding form.…”

The world of geography: Visualizing a knowledge domain with cartographic means

“…For a large number of clusters (i.e., at a local scale), labels will correspond to much more specific areas of investigation in the geographic knowledge domain, e.g., ''snowfall'' or ''redevelopment.'' Cartography is essentially a science dealing with the transformation of spatial information (9). Following this paradigm, a number of geometric and topological transformations are applied to the raw geometric configuration produced by neural network training and, finally, symbolization occurs in off-theshelf geographic information systems (GIS) software.…”

Information systems for regional development planning: a state-of-the-art survey

“…Various techniques have been developed in this area (see also Tobler, 1979;Steiner, 1980). The main purpose of these techniques is to represent unstructured spatial data in a systematic way, inter alia by characterizing objects by means of their location or position in a network.…”