CaGIS vol. 27, no. 3

The Nature of Analytical Cartography: An Introduction

Harold Moellering

Since its auspicious beginnings in the early 1960s by Prof. Waldo Tobler (1961), analytical cartography has grown and flourished scientifically, analytically, and intellectually. Analytical cartography has added a new dimension to cartography with its goal of developing a scientific base of analytical and mathematical theory as the fundamental underpinning of cartographic research. This focus on theory is in stark contrast with the traditional focus of cartography on artistry and technology in map design and production that has been practiced for more than four thousand years. Analytical cartography is also very different from the other major cartographic theme-map communication and representation-, which dates back to Robinson's (1952) seminal research that established the "Communication School" of cartography. An earlier issue of this journal dedicated to analytical cartography (Moellering 1991) contained five research articles reflecting a variety of philosophical, mathematical, technical and applied aspects of analytical cartography. These papers were carefully selected to show the breadth and depth of research going on at that time in analytical cartography. This issue systematically explores the nature of analytical cartography, defining the scope and conceptual content of the field with all of its richness, diversity, and research opportunities. Apart from theory we examine some of the applications of analytical theory in cartographic practice, highlighting major computational limitations to such work. The discussions have also identified linkages to related cognate fields of research, especially the emerging area of geographic information science. One such link between analytical cartography and these other fields is through the Mathematical Mode of Inquiry (MMOI) advocated by Casetti (1999) for human geography.

The Development of Analytical Cartography: A Personal Note

Waldo Tobler

In the late 1960s, I initiated a course with the title "Analytical Cartography" at the University of Michigan in Ann Arbor. At the behest of Dr. H. Moellering of Ohio State University (who was at one time a student in the course), a short personal historical perspective of the development of the course was presented at the recent Hawaii meeting of the Association of American Geographers. That review tried to put the subject and the development of the course in the context of the time. This is a written synopsis of the Hawaii presentation.

On the Origins of Analytical Cartography

Keith C. Clarke and John G. Cloud

This paper examines the development of analytical cartography and the contributions Waldo Tobler has made to it, starting well before his definition of the subject in 1976. Analytical cartography's roots in World War II and the Cold War are examined, and the influences and precedents for the academic course that Tobler described are discussed. The systems of knowledge production developed for analytical cartography in its social context are summarized and are found to show a powerful dependence on a working relationship between academia, industry, government, and the intelligence mapping community. Current research trends in analytical cartography, including the organization of research, its institutions, and its priorities, are discussed, and it is proposed that declassifying the "missing pool" of analytical cartographic research literature could be of great benefit in the future. The four-way academic/industrial/government/intelligence partnership is seen as an opportune direction forward for analytical cartography. The next generational shift in the center of the discipline may occur in networks that even Waldo Tobler did not anticipate.

KEYWORDS: Analytical cartography, Cold War, SAGE, CORONA, military intelligence

Scope and Conceptual Content of Analytical Cartography

Harold Moellering

Over the last three decades analytical cartography has grown from Tobler's concept of "solving cartographic problems" into a broader and deeper scientific specialization that includes the development and expansion of analytical/mathematical spatial theory and model building. In many instances Tobler himself has led the way to these new insights and developments. Fundamental concepts begin with Tobler's cartographic transformations; Nyerges' deep and surface structure and data levels; and Moellering's real and virtual maps; the sampling theorem; and concepts of spatial primitives and objects. This list can be expanded to include additional analytical concepts such as spatial frequencies, spatial surface neighborhood operators, information theory, fractals, Fourier theory, topological network theory, and analytical visualization, to name a few. This base of analytical theory can be employed to analyze and/or develop such things as spatial surfaces, terrain analysis, spatial data schemas, spatial data structures, spatial query languages, spatial overlay and partitioning, shape analysis, surface generalization, cartographic generalization, and analytical visualization. More analytical uses of theory, strategies of analysis, and implementations are being developed and continue to multiply as the field continues to grow and mature. A primary goal is to expand the mathematical/analytical theory of spatial data analysis, and theory building and analytical visualization as analytical cartography takes its place in the geographic information sciences. The research future for this area appears very bright indeed.

KEYWORDS: Analytical cartography, map transformations, spatial theory, real and virtual maps, deep and surface structure, sampling theorem, spatial frequencies, analytical operators, information theory, fractals, Fourier theory, spatial overlay, Warntz network theory, map generalization, analytical visualization, geographic information science

Applications of Analytical Cartography

Wm Randolph Franklin

Several applications of analytical cartography are presented. They include terrain visibility (including visibility indices, viewsheds, and inter-visibility), map overlay (including solving round-off errors with C++ class libraries and computing polygon areas from incomplete information), mobility, and interpolation and approximation of curves and of terrain (including curves and surfaces in CAD/CAM, smoothing terrains with over-determined systems of equations, and drainage patterns). General themes become apparent, such as simplicity, robustness, and the tradeoff between different data types. Finally several future applications are discussed, such as the lossy compression of correlated layers, and just good enough computation when high precision is not justified.

Complexity and Intractability: Limitations to Implementation in Analytical Cartography

Alan Saalfeld

The computational complexity of algorithms is an important consideration for all computer systems, including geographic information systems and mapping systems. Mathematical cartographers and GIS professionals need to understand and to take into account the limitations imposed on problem solving by the very nature of computation itself. We look at three active research sub-areas of analytical cartography to highlight the differences between traditional mathematical solutions and solutions with computationally tractable algorithms. The three sub-areas are map projections, map feature labeling, and map generalization.

KEYWORDS: Algorithms, computational complexity, tractability, projections, map labeling, generalization