UCGIS EMERGING THEME PROPOSAL ANALYTICAL CARTOGRAPHY by Harold Moellering Ohio State University geohal+@osu.edu The transition of the acronym of GIS in recent years from Geographic Information Systems to Geographic Information Science demonstrates a realization that the community must work towards developing a deeper and more fully developed body of conceptual, mathematical and analytical spatial theory. The field of Analytical Cartography as founded by Prof Waldo Tobler, and expanded by a number of subsequent researchers in the field, has as its main goal to strive to develop and blend this deeper mathematical theory that comes from the broader fields of cartography, discrete mathematics, geography, computer science, and image analysis. As such, the field of Analytical Cartography examines a wide variety of spatial theory with a common thread, following the leadership of Prof. Tobler, of expanding and extending that mathematical and analytical theory for the spatial sciences. Much of this theoretical work not only cuts across many of the themes in the UCGIS research structure, but also contains a logical consistency of its own that justifies Analytical Cartography being listed as an "Emerging Research Theme" in its own right. The following is a very brief listing and discussion of selected important subcomponents of the field of Analytical Cartography. * Geographic Transformations - This work began with Tobler's original work in coordinate transformation in geographic space, and expanded to include a number of other transformations in the geometric and topological domains that includes discrete and continuous spatial surfaces, spatial objects, in a variety of dimensions. * Real and Virtual Maps - This concept ties together the wide diversity of spatial data products as diverse as spatial data bases, terrain models, CRT and immersive displays, CD-ROM databases, web downloading, as well as hard copy maps and charts. Transformations between various forms of Real/Virtual maps provides the key to understanding spatial data processing systems and can be used to help design such systems. *Deep and Surface Spatial Structure - This is the key to understanding the major transformations that the spatial data sciences have made from the graphic domain to the analytical domain. It greatly helps one to see where many research opportunities lie. *Nyerges Data Levels - This concept helps one to more clearly understand levels of spatial data when designing such databases, and makes two data model levels explicit where conventional data models only use one. *The Sampling Theorem - This concept is fundamental to all of the spatial sciences when one considers resolution, data accuracy, cellular systems and the like. Tobler's forthcoming extension of the resels concept to N dimensions will provide insight into processes and procedures at higher dimensions. *Spatial Primitive Objects - This views spatial objects from the perspective of spatial dimensionality, having geometric and topological properties. Such primitive spatial objects become the building blocks of higher level spatial objects stored and manipulated in spatial databases. *Spatial Frequencies - This is a view that spatial surfaces and other spatial phenomena can be conceived of as containing spatial frequencies and mathematically analyzed from that perspective. This began with the use of Fourier theory and related transformations on surfaces and various spatial features. *Spatial Neighborhood Operators - Insights into the working of such data domain operators is helpful to all who process raster,grid cell, and voxel data. *Spatial Adaptations of Fourier Theory - Fourier theory can be extended to things like shape analysis and irregular hierarchical systems. *Fractal Spatial Operators - The notion of fractional dimensions of lines and surfaces provides added insight to the spatial sciences. Fractal concepts have been extended to several domains to support analytical work in other parts of the field. *Critical Features and Warntz Networks - The notion of mathematically critical points and lines coupled with the concept of a Warntz Network provides a powerful insight into the structure of a terrain surface. It is essentially the skeleton of that surface. *Polygon Analysis - Innovations in polygon analysis is a significant part of the field with Thiessen polygons, Delaunay triangles and their uses. Developments by Tobler on pycnophylactic transformations from discrete zonal structures to other zonal or continuous structures is a very interesting development in the field. *Analytical Map Generalization - Various analytical approaches in the field can supplement conventional digital approaches in the area. *Spatial Data Models and Structures - The development and analysis of TIN models as well as global tessellation models fall into this theme of research. *Analytical Visualization - This area utilizes analytical approaches to extend and develop better visualization processes for static, interactive and dynamic spatial displays. This is only a brief sampling of the many research topics in analytical cartography. Together they add a perspective to spatial analysis that would be very helpful to researchers in the Geographic Information Science. This has multiple applications in the field. -***(C) Copyright 2000, Harold Moellering, All N. American Rights Reserved*** Harold Moellering, Department of Geography, Ohio State University 43210 USA >>>>>>>>>> E-mail:geohal+@osu.edu -- FAX:+1(614) 292-6213 <<<<<<<<< **Numerical Cartography Lab Home Page at: http://ncl.sbs.ohio-state.edu/ **ICA Standards Commission Home Page at: http://ncl.sbs.ohio-state.edu/ica *************** Virtual Maps ===> Virtual Reality ***************