The Scope and Conceptual Content of Analytical Cartography

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.     

Delaunay Triangulations and Stereographic Projections

After describing Delaunay triangulations of vertices on a sphere and in a plane, we prove that every Delaunay triangulation of vertices on a sphere corresponds to the Delaunay triangulation in the plane of any stereographic projection of the spherical triangle vertices. We then exploit this correspondence to build robust algorithms for Delaunay triangulations in the plane or on the sphere. We also describe a collection of "fisheye" conformal transformations of the sphere that are the composition of one stereographic projection with the inverse of another stereographic projection.     

Political Ecology: An Integrative Approach to Geography and Environment-Development Studies (2003), edited by Karl S. Zimmerer and Thomas J. Bassett

Map reading is effective to the extent that the user has a basic understanding of the nature of geographical information, is familiar with the logic of various cartographic techniques, and grasps the map deciphering problems that may result through the matching of cartographic method to geographical data in specific mapping situations. The qualitative/quantitative dichotomy that was formerly so frequently resorted to when dealing with geographical information has been replaced by a more sensitive four-level measurement scheme or scaling system which is not only useful in sorting out the relations between environmental information and its cartographic portrayal, but which also provides an important key to understanding the special interpretative considerations that these relations create for the map reader. From a measurement perspective, the information yielded by a particular map symbol depends on the nature of the data that go into its construction, the nature of the data that survive the symbolic transformation, and the ability of the map user to decode the symbol effectively. The utility of measurement concepts in map reading is further demonstrated in the clarifying effect they can have in determining map information content and in the area of map generalization.     

Report on Cartographic and GIS Activity in the U.S. Fish and Wildlife Service

The U.S. Fish and Wildlife Service (FWS) is a federal agency whose mission is, working with others, to conserve fish and wildlife and their habitats for the continuing benefit of the American people. Under the management of fish and wildlife professionals, the National Wildlife Refuge System has become the world's premier network of wildlife habitats. The FWS is making use of modern cartographic methods and implementing Geographic Information Systems to more effectively manage the lands and resources entrusted to them.