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##### FC-22 - Geometric Primitives and Algorithms

Geometric primitives are the representations used and computations performed in a GIS that concern the spatial aspects of the data, data objects described by coordinates. In vector geometry, we distinguish in zero-, one-, two-, and three-dimensional objects, better known as points, linear features, areal or planar features, and volumetric features. A GIS stores and performs computations on all of these. Often, planar features form a collective known as a (spatial) subdivision. Computations on geometric objects show up in data simplification, neighborhood analysis, spatial clustering, spatial interpolation, automated text placement, segmentation of trajectories, map matching, and many other tasks. They should be contrasted with computations on attributes or networks.

There are various kinds of vector data models for subdivisions. The classical ones are known as spaghetti and pizza models, but nowadays it is recognized that topological data models are the representation of choice. We overview these models briefly.

Computations range from simple to highly complex: deciding whether a point lies in a rectangle needs four comparisons, whereas performing map overlay on two subdivisions requires advanced knowledge of algorithm design. We introduce map overlay, Voronoi diagrams, and Delaunay triangulations and mention algorithmic approaches to compute them.

##### FC-14 - Directional Operations

In the same manner as distance, direction plays an equally important role in GIS. This article first summarizes different ways of measuring direction, either quantitatively or qualitatively. Formulas and examples are provided. In the following discussion, fundamental differences between distance and direction in describing spatial relations is examined; properties of angles are emphasized in the context of GIS; and the classification of both cardinal and projective direction is illustrated. With a focus on quantitative operations, various directional operations are categorized and elaborated based on factors such as the underlying data model (vector or raster) and whether direction effect is explicitly or implicitly embedded in the data.

##### FC-32 - Semantic Information Elicitation

The past few decades have been characterized by an exponential growth of digital information resources. A considerable amount of this information is semi-structured, such as XML files and metadata records and unstructured, such as scientific reports, news articles, and historical archives. These resources include a wealth of latent knowledge in a form mainly intended for human use. Semantic information elicitation refers to a set of related processes: semantic information extraction, linking, and annotation that aim to make this knowledge explicit to help computer systems make sense of the content and support ontology construction, information organization, and knowledge discovery.

In the context of GIScience research, semantic information extraction aims at processing unstructured and semi-structured resources and identifying specific types of information: places, events, topics, geospatial concepts, and relations. These may be further linked to ontologies and knowledge bases to enrich the original unstructured content with well-defined meaning, provide access to information not explicit in the original sources, and support semantic annotation and search. Semantic analysis and visualization techniques are further employed to explore aspects latent in these sources such as the historical evolution of cities, the progression of phenomena and events and people’s perception of places and landscapes.

##### FC-31 - Academic Developments of GIS&T in English-speaking Countries: a Partial History

The constellation of science and technology that is now considered a unit (Geographic Information Science and Technology – GIS&T) has emerged from many source disciplines through many divergent and convergent pasts in different times and places. This narrative limits itself to the perspective of the English-speaking community, leaving other regions for a separate chapter As in the case of many technical developments in the second half of the twentieth century, academic institutions played a key (though far from exclusive) role in innovation and risk-taking. In a number of locations, academic innovators tried out new technology for handling geographic information, beginning as early as the 1960s. Three institutions (University of Washington, Laboratory for Computer Graphics – Harvard University, and Experimental Cartography Unit – Royal College of Art (UK)) deserve particular treatment as examples of the early innovation process. Their innovations may look crude by current standards, but they laid some groundwork for later developments. Academic institutions played a key role in innovation over the past decades, but the positioning of that role has shifted as first government, then commercial sectors have taken the lead in certain aspects of GIS&T. Current pressures on the academic sector may act to reduce this role.

##### FC-20 - The power of maps
• Describe how maps such as topographic maps are produced within certain relations of power and knowledge
• Discuss how the choices used in the design of a road map will influence the experience visitors may have of the area
• Explain how legal issues impact the design and content of such special purpose maps as subdivision plans, nautical charts, and cadastral maps
• Exemplify maps that illustrate the provocative, propagandistic, political, and persuasive nature of maps and geospatial data
• Demonstrate how different methods of data classification for a single dataset can produce maps that will be interpreted very differently by the user
• Deconstruct the silences (feature omissions) on a map of a personally well known area
• Construct two maps about a conflict or war producing one supportive of each side’s viewpoint
##### FC-15 - Shape

Shape is important in GI Science because the shape of a geographical entity can have far-reaching effects on significant characteristics of that entity. In geography we are mainly concerned with two-dimensional shapes such as the outlines of islands, lakes, and administrative areas, but three-dimensional shapes may become important, for example in the treatment of landforms. Since the attribute of shape has infinitely many degrees of freedom, there can be no single numerical measure such that closely similar shapes are assigned close numerical values. Therefore different shape descriptors have been proposed for different purposes. Although it is generally desirable for a shape descriptor to be scale invariant and rotation invariant, not all proposed descriptors satisfy both these requirements. Some methods by which a shape is described using a single number are described, followed by a discussion of moment-based approaches. It is often useful to represent a complex shape by means of a surrogate shape of simpler form which facilitates storage, manipulation, and comparison between shapes; some examples of commonly used shape surrogates are presented. Another important task is to compare different shapes to determine how similar they are. The article concludes with a discussion of a number of such measures of similarity.

##### FC-13 - Spatial Queries

Spatial query is a crucial GIS capability that distinguishes GIS from other graphic information systems. It refers to the search for spatial features based on their spatial relations with other features. This article introduces a spatial query's essential components, including target feature(s), reference feature(s), and the spatial relation between them.  The spatial relation is the core component in a spatial query. The document introduces the three types of spatial relations in GIS: proximity relations, topological relations, and direction relations, along with query examples to show the translation of spatial problems to spatial queries based on each type of relations. It then discusses the characteristics of the reasoning process for each type of spatial relations. Except for topological relations, the other two types of spatial relations can be measured either quantitatively as metric values or qualitatively as verbal expressions. Finally, the general approaches to carrying out spatial queries are summarized. Depending on the availability of built-in query functions and the unique nature of a query, a user can conduct the query by using built-in functions in a GIS program, writing and executing SQL statements in a spatial database, or using customized query tools.

##### FC-42 - Distance Operations

Distance is a central concept in geography, and consequently, there are various types of operations that leverage the concept of distance. This short article introduces common distance measures, the purpose of distance operations, different types of operations and considerations, as well as sample applications in the physical and social domains. Distance operations can be performed on both vector or raster data, but the operations and results may differ. While performing distance operations, it is important to remember how distance is conceptualized while performing the operation.

##### FC-40 - Neighborhoods

Neighborhoods mean different things in varied contexts like computational geometry, administration and planning, as well as urban geography and other fields. Among the multiple contexts, computational geometry takes the most abstract and data-oriented approach: polygon neighborhoods refer to polygons sharing a boundary or a point, and point neighborhoods are defined by connected Thiessen polygons or other more complicated algorithms. Neighborhoods in some regions can be a practical and clearly delineated administration or planning units. In urban geography and some related social sciences, the terms neighborhood and community have been used interchangeably on many occasions, and neighborhoods can be a fuzzy and general concept with no clear boundaries such that they cannot be easily or consensually defined. Neighborhood effects have a series of unique meanings and several delineation methods are commonly used to define social and environmental effects in health applications.

##### FC-08 - Time

Time is a fundamental concept in geography and many other disciplines. This article introduces time at three levels. At the philosophical level, the article reviews various notions on the nature of time from early mythology to modern science and reveals the dual nature of reality: external (absolute, physical) and internal (perceived, cognitive). At the analytical level, it introduces the measurement of time, the two frames of temporal reference: calendar time and clock time, and the standard time for use globally. The article continues to discuss time in GIS at the practical level. The GISystem was first created as a “static” computer-based system that stores the present status of a dynamic system. Now, GISystems can track and model the dynamics in geographical phenomena and human-environment interactions. Representations of time in dynamic GISystems adopt three perspectives: discrete time, continuous time and Minkowski’s spacetime, and three representations: ordinal, interval, and cyclical. The appropriate perspective and representation depend on the observed temporal patterns, which can be static, oscillating, chaotic, or stochastic. Recent progress in digital technology brings us opportunities and challenges to collect, manage and analyze spatio-temporal data to advance our understanding of dynamical phenomena.