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4. Computational geometry
Computational geometry provides fundamentals for metric representation of objects and relations in geographic space. Analytical cartography is an alternative term for many aspects of computational geometry applied to the geospatial domain. Computational so- lutions to geometric problems were required in the very earliest days of computer-assisted cartography and GIS. Computational geometry is challenging, in part because pure Eu- clidean geometry cannot be implemented in straightforward fashion in a finite-precisio digital environment, as discussed in an early paper by Douglas (1974) and discussed in de- tail by Franklin (1984). Line simplificatio (Douglas and Peucker, 1973) and many other aspects of map generalization (Buttenfiel and McMaster, 1991) fall under the general topic of computational geometry in GI Science, although they also relate to the cross- cutting issue of scale (below). Another set of computational geometry problems relate to the efficien computation of proximity, handled under the conceptual framework var- iously labelled as Voronoi diagrams, or Thiessen or proximal polygons. Preparata and Shamos (1991) provided a definit ve review of these problems, and Gold has done much work to integrate these methods into Geographic Information Science (see Gold, 1994, for example).
5. Efficien indexing, retrieval, and search in geographic databases
Efficien indexing of multidimensional data is an important problem in database research in computer science. Since geographic information is inherently at least two dimensional, these indexing issues have long been important in GIS. The so-called Morton ’matrix’ approach for ordering map areas on a sequential magnetic tape was a key early innovation in GIS (? ). Morton’s index was equivalent to interleaving the bits in x- and y-coordinates expressed as integers. The idea was re-discovered in the context of image processing and retrieval in the 1970s under the label quadtrees, which recursively divide an image into quadrants and subquadrants (see Samet, 1989, for a review). Samet (1989) reviews a number of related indexing schemes such as B-trees, R-trees, k-d trees, etc.
6. Spatial statistics
Spatial statistics is an important research area with strong links to Geographic Information Science. One of the properties that make spatial information special is the frequent pres- ence of spatial autocorrelation or spatial dependence. Spatial statistics (Cressie, 1993)
8 Foundations of Geographic Information Science
provides formal statistical methods for dealing with spatial autocorrelation, such as mea- suring it, or controlling for its effects when conducting statistical analyses based on data for spatial units. Spatial statistics can be used to characterize some aspects of data qual- ity, but otherwise this topic appears to stand in some isolation from other components of geographic information science.
7. Other geocomputation topics
A number of additional computational topics are important to GI Science but do not fi under the headings that immediately precede this one. One of these topics is map alge- bra, a comprehensive conceptual framework for raster-based spatial analysis developed in several articles and summarized in a 1990 book (Tomlin, 1990). This is not just a matter of implementing standard GIS operations based on a different representation of spatial information. Rather, map algebra leads to a different way of conceptualising geocom- putational problems based on proximity and local operators that could easily re-cast in a parallel computation environment. Closely related to map algebra are the many spatial operations that can be based on cellular automata (von Neumann, 1966; Couclelis, 1997).
3.3 Cognition
8. Cognitive Models of Geographic Phenomena
This research area involves the study of human perception, learning, memory, reasoning, and communication of and about geographic phenomena. An explicit agenda to examine human cognition of geographic environments was originally introduced into the GI Sci- ence agenda as a way to gain insight into the nature of spatial relations, to gain insights into geographic ontology, and to understand and improve human-computer interaction for GIS (Mark and Frank, 1991). There is a large body of work on spatial cognition in psy- chology and cognitive science, and some of this has dealt with the geographic domain— some benchmark examples include Stevens and Coupe (1978), Talmy (1983) and Her- skovits (1986). Studies of human spatial cognition are foundational to several other areas of GI Science. Attention to formalizing common-sense concepts for geographic space was highlighted by Egenhofer and Mark (1995) under the term ‘Na¨ıve geography’.
9. Human interaction with geographic information and technology
Human-computer interaction (HCI) for geographic information systems, and the design of user interfaces for GIS, is perhaps the most obvious example of the relevance of cognition to GIS (Mark and Gould, 1991; Medyckyj-Scott and Hearnshaw, 1993; Nyerges et al., 1995). The importance of this topic as a part of the GI Science research agenda depends on whether the issues of GIS usability can be separated into general issues of human- computer interaction on the one hand and issues of geographic concepts on the other. If not, then the GI Science research community must address problems in the overlap.
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same time, there was also an increase in research on economic and legal aspects of geo- graphic information, its production and sharing, including studies of how the use of GIS and associated technologies by individuals and institutions changes efficien y, effective- ness, equity, and power in society. A particularly active area of research and practice is “Public-Participation GIS” (PPGIS). The main aspects of the post-Modern critique have been presented by Pickles in his edited book (Pickles, 1995) and a more recent review article (Pickles, 1999). A good overview of the economic and legal aspects of geographic information is found in Masser and Onsrud (1993).
3.5 Crosscutting Research Themes
14. Time
Time and temporality, motion and change, are essential to many GIS applications, yet GIS software has been notoriously weak in providing tools for handling temporal dimensions of geographic information. Long ago, Blaut (1961) proposed that the Kant/Newton sepa- ration of reality into space, time, and theme, which Berry (1964) proposed as an organiz- ing framework for geography and GIS, made it difficul to deal with process and change. GIS seems ontologically committed to separating space and time, which then impedes certain scientifi uses of GIS. If space and time can truly be studied separately and the results later assembled, then time would not be part of the agenda for GI Science. Recent interest in time in geographic space and GIS (Langran, 1992; Peuquet, 1994; Egenhofer and Golledge, 1998) suggests that time is an integral part of GI Science research and one which cuts across most other GI Science topics.
15. Scale
Scale has multiple meanings relevant to GI Science. In cartography, scale refers to size on the map divided by size in the world—small-scale maps show large regions. Map scale interacts with geometry of the world to require map generalization (Buttenfiel and Mc- Master, 1991). In the physical sciences such as meteorology or geomorphology, the term scale is used to indicate the size, extent, or characteristic length for physical processes. Micro-, meso-, and global-scale atmospheric processes are familiar terms. In biology and geomorphology, interactions between size, shape, and function have been variously ex- plored under the heading of allometry—sometimes shape must change systematically in order to maintain function as size changes (for a review, see Church and Mark, 1980). Thirdly, the term scale is used to summarize resolution, the smallest entities that can be detected or represented, both for display and analysis (see Quattrochi, 1997). More re- cently, cognitive aspects of scale have been highlighted (Montello, 1993; Montello and Golledge, 1999). The issues surrounding the term scale are important to the GI Science curriculum and to the research agenda, and cut across most of the other topics described in this paper.
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4 COMPARISON OF TOPICS
Of course, the list of components of geographic information science proposed in this paper was prepared in full knowledge of the lists proposed by Goodchild (1992) and by the UCGIS. Still, it is instructive to compare the lists.
Topics on all three lists
Four topics appear on all three lists:
- data acquisition
- representation (data modelling)
- spatial analysis
- societal issues surrounding GI
The last three of these also correspond well with core issues in the bullets proposed in NSF’s NCGIA solicitation.
Topics on two lists
Three topics from Goodchild’s (1992) list also were identifie as key topics in this paper, but were not on the UCGIS list:
- computational geometry
- indexing for spatial databases
- spatial statistics
In fact, Goodchild combined the fi st two of these topics under his “ Data structures, algorithms and processes.” Three additional topics were on the UCGIS list and in this paper but not singled out by Goodchild:
- ontology
- cognition
- data quality
Another research topic, scale, is a research topic on the UCGIS list but identifie as a crosscutting research theme here. Lastly, one topic, visualization and display, was on Goodchild’s (1992) list, and re- cently was identifie as an emerging research theme by UCGIS, but is not on the list of GI Science fundamentals described in this paper; perhaps it should join scale and time as cross-cutting themes.
Topics on only one list
All of Goodchild’s topics from 1992 appear on one or both of the other lists. However, three of UCGIS’s original research challenges, and one of their emerging themes, appear on neither of the other lists:
