Analytical Cartography

Origins and Developments

The roots of analytical cartography are found in World War II and the cold war. Before and during World War II, Germany had advanced significantly in geodetic control networks, analytical photogrammetry, and cartographic analysis. Analytical techniques such as map overlay were applied in military operations and systematic regional-scaled planning. In the United States, three top-secret projects reflected the sociotechnical ensembles of analytical cartography in the cold war: SAGE (Semi-Automatic Ground Environment), the development of a computer-based control system for early-warning radar; DISIC (the Dual Integrated Stellar Index Camera), the development and use of DISIC camera that automates the georectification process of imagery under the CORONA program; and MURAL, the development of the CORONA MURAL camera, designed to add the analytical construction of three-dimensional terrain maps to the automated CORONA program. CORONA was a spy satellite mission in the U.S. that operated between 1960 and 1972.

Analytical cartography was first introduced to American universities in the late 1960s by Tobler, through a course he initiated at the University of Michigan in Ann Arbor. Tobler's definition of analytical cartography was motivated by his view that geographers use maps as analytical tools to understand and [Page 9]theorize about the earth and the phenomena distributed on the earth's surface. The course was first named computer cartography, but Tobler soon realized that the substance is the theory and it should be independent of particular devices that become obsolete rather quickly. He also evaluated and rejected the names mathematical cartography, cartometry, and theoretical cartography. He chose the name analytical cartography, with the intention of formalizing the notion that geographers use cartographic methods frequently in their analytical investigations.

The first development of his analytical cartography syllabus was documented and published in American Cartography in 1976. It covered topics such as the relation to mathematical geography, geodesy, photogrammetry and remote sensing, computer graphics, geographical matrices, geographical matrix operators, sampling and resolution, quantization and coding, map generalization, pattern recognition, generalized spatial partitionings, generalized geographical operators, geographical coding and conversions, map projections, and GIS.

Conceptual and Analytical Theories

Analytical cartography is integrated with geographic information science, spatial analysis, and quantitative geography. Harold Moellering has summarized the representative conceptual theory in analytical cartography as follows.

• Geographic Map Transformations. Map projections are a special case of spatial coordinate transformations. Comparisons of spatial outlines can be achieved using spatial regression techniques. The mathematical development of cartograms is an additional outcome of this theory.
• Real and Virtual Maps. Joel Morrison and Moellering developed the concept of real and virtual maps. The expansion brought the concept of map transformation to a new level. The distinctions between real and virtual maps are based on two criteria: whether the map is directly viewable as a cartographic image and whether it is viewable as a permanent, tangible reality. The four types of real and virtual maps are real map (viewable and tangible); virtual map type I (viewable but not tangible); virtual map type II (not viewable but tangible); and virtual map type III (neither viewable nor tangible).
• Deep and Surface Structure in Cartography. Surface structure is the cartographically displayed data. Deep structure consists of the spatial data and relationships stored in a nongraphic form. Analytical cartography focuses on dealing with deep structure.
• Nyerges's Data Levels. The six-level definition of cartographic data structure incorporates the elements of data reality, information structure, canonical structure, data structure, storage structure, and machine encoding.
• Spatial Primitive Objects. The 0-, 1-, 2D spatial primitive and simple objects serve as fundamental digital building blocks to construct most spatial data objects from zero to three dimensions.
• The Sampling Theorem. The theorem shows mathematically that it is necessary to sample at least twice the highest spatial frequency in the field in order to represent the full details of the spatial field.

Besides conceptual theory, there is analytical theory in analytical cartography. A selection of analytical theory includes, to name a few, the view of spatial frequencies, spatial neighborhood operators, spatial adaptations of Fourier theory, spatial analytical uses of information theory, fractal spatial operators, critical features and Warntz networks, polygon analysis, overlay and transformations, map generalization, shape analysis, spatial data models and structures, analytical visualization, and spatial data standards.

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