Maps communicate information about the world by using symbols to represent specific ideas or concepts. The relationship between a map symbol and the information that symbol represents must be clear and easily interpreted. The symbol design process requires first an understanding of the underlying nature of the data to be mapped (e.g., its spatial dimensions and level of measurement), then the selection of symbols that suggest those data attributes. Cartographers developed the visual variable system, a graphic vocabulary, to express these relationships on maps. Map readers respond to the visual variable system in predictable ways, enabling mapmakers to design map symbols for most types of information with a high degree of reliability.
A geographic information system in operation is highly complex, as the scope of the GIS&T Body of Knowledge demonstrates. Modern society relies on many complex systems, but most are self-contained mechanisms with limited and well defined interfaces. A GIS is a complex open system that extends across the realms of hardware, software, data, science, and human processes. A conceptual model of a GIS can be an effective tool to design, implement, operate, maintain, manage, and assessment tool.
Terrain representation is the manner by which elevation data are visualized. Data are typically stored as 2.5D grid representations, including digital elevation models (DEMs) in raster format and triangulated irregular networks (TINs). These models facilitate terrain representations such as contours, shaded relief, spot heights, and hypsometric tints, as well as automate calculations of surface derivatives such as slope, aspect, and curvature. 3D effects have viewing directions perpendicular (plan), parallel (profile), or panoramic (oblique view) to the elevation’s vertical datum plane. Recent research has focused on automating, stylizing, and enhancing terrain representations. From the user’s perspective, representations of elevation are measurable or provide a 3D visual effect, with much overlap between the two. The ones a user can measure or derive include contours, hypsometric tinting, slope, aspect, and curvature. Other representations focus on 3D effect and may include aesthetic considerations, such as hachures, relief shading, physiographic maps, block diagrams, rock drawings, and scree patterns. Relief shading creates the 3D effect using the surface normal and illumination vectors with the Lambertian assumption. Non-plan profile or panoramic views are often enhanced by vertical exaggeration. Cartographers combine techniques to mimic or create mapping styles, such as the Swiss-style.
The classic transportation problem concerns minimizing the cost of transporting a single product from sources to destinations. It is a network-flow problem that arises in industrial logistics and is considered as a special case of linear programming. The total number of units produced at each source, the total number of units required at each destination and the cost to transport one unit from each source to each destination are the basic inputs. The objective is to minimize the total cost of transporting the units produced at sources to meet the demands at destinations. The problem solution includes three basic steps: 1) finding an initial basic feasible solution, 2) checking if the current solution is optimal (with the lowest costs), and 3) improving the current solution through iteration. Modeling and solving the classic transportation problem rely strongly on network models, least-cost path algorithms, and location-allocation analysis in the field of geographic information science (GIScience). Thus, it represents a key component in the network analytics and modeling area of GIS&T.