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FC-17 - Proximity and Distance Decay

Distance decay is an essential concept in geography. At its core, distance decay describes how the relationship between two entities generally gets weaker as the separation between them increases. Inspired by long-standing ideas in physics, the concept of distance decay is used by geographers to analyze two kinds of relationships. First, the term expresses how measured interactions (such as trade volume or migration flow) generally decrease as the separation between entities increases, as is analyzed by spatial interaction models. Second, the term is used to describe how the implicit similarity between observations changes with separation, as measured by variograms. For either type of relationship, we discuss how "separation" must be clearly articulated according to the mechanism of the relationship under study. In doing this, we suggest that separation need not refer to positions in space or time, but can involve social or behavioral perceptions of separation, too. To close, we present how the "death of distance" is transforming distance decay in uneven ways.

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-19 - Networks

A network is a widely used term with different definitions and methodologies depending on the applications. In GIS, a network refers to an arrangement of elements (i.e., nodes, links) and information on their connections and interactions. There are two types of networks: physical and logical. While a physical network has tangible objects (e.g., road segments), a logical network represents logical connections among nodes and links. A network can be represented with a mathematical notion called graph theory. Different network components are utilized to describe characteristics of a network including loops, walks, paths, circuits, and parallel edges. Network data are commonly organized in a vector format with network topology, specifically connectivity among nodes and links, whereas raster data can be also utilized for a least-cost problem over continuous space. Network data is utilized in a wide range of network analyses, including the classic shortest path problem.