Spatial Mathematics: Theory and Practice through Mapping is a book on the mathematics that underlies geographic information systems and spatial analysis. It was written by Sandra Arlinghaus and Joseph Kerski, and published in 2013 by the CRC Press.
Spatial Mathematics: Theory and Practice through Mapping is a book on the mathematics that underlies geographic information systems and spatial analysis. It was written by Sandra Arlinghaus and Joseph Kerski, and published in 2013 by the CRC Press.
The book has 10 chapters, divided into two sections on geodesy and on techniques for visualization of spatial data; each chapter has separate sections on theory and practice. [1] For practical aspects of geographic information systems it uses ArcGIS as its example system. [2]
In the first part of the book, Chapters 1 and 2 covers the geoid, the geographic coordinate system of latitudes and longitudes, and the measurement of distance and location. Chapter 3 concerns data structures for geographic information systems, data formatting based on raster graphics and vector graphics, methods for buffer analysis, [3] and its uses in turning point and line data into area data. Later in the book, but fitting thematically into this part, [1] [4] chapter 9 covers map projections. [3]
Moving from geodesy to visualization, [1] chapters 4 and 5 concern the use of color and scale on maps. Chapter 6 concerns the types of data to be visualized, and the types of visualizations that can be made for them. Chapter 7 concerns spatial hierarchies and central place theory, while chapter 8 covers the analysis of spatial distributions in terms of their covariance. Finally, chapter 10 covers network and non-Euclidean data. [1] [3]
Additional material on the theoretical concepts behind the topics of the book is provided on a web site, accessed through QR codes included in the book. [1]
Reviewer reactions to the book were mixed. Several reviewers noted that, for a book with "mathematics" in its title, the book was surprisingly non-mathematical, with both Azadeh Mousavi and Paul Harris calling the title "misleading". [1] [4] Harris complains that "the maths is treated quite lightly and superficially". [4] Alfred Stein notes the almost total absence of mathematical equations, [2] and Daniel Griffith similarly notes the lack of proof of its mathematical claims. [5]
Mousavi also writes that, although the book covers a broad selection of topics, it "suffers from lack of necessary depth" and that it is confusingly structured. [1] Sang-Il Lee points to a lack of depth as the book's principal weakness. [3] Stein notes that its reliance on a specific version of ArcGIS makes it difficult to reproduce its examples, especially for international users with different versions or for users of versions updated after its publication. [2] Another weakness highlighted by Griffith is "its limited connection to the existing literature, with its citations far too often being only those works by its authors". [5] Harris sees a missed opportunity in the omission of spatial statistics, movement data, and spatio-temporal data, the design of spatial data structures, and advanced techniques for visualizing geospatial data. [4]
Nevertheless, Mousavi recommends this book as an "introductory text on spatial information science" aimed at practitioners, and commends its use of QR codes and word clouds. [1] Stein praises the book's attempt to bridge mathematics and geography, and its potential use as a first step towards that bridge for practitioners. [2] Harris suggests it "in an introductory and applied context", and in combination with a more conventional textbook on geographic information systems. Lee argues that the overview of fundamental concepts and cross-disciplinary connections forged by the book make it "worth reading by anyone interested in the geospatial sciences". [3] And Griffith concludes that the book is successful in motivating its readers to "explore formal mathematical subject matter that interfaces with geography". [5]
A geographic information system (GIS) is a type of database containing geographic data, combined with software tools for managing, analyzing, and visualizing those data. In a broader sense, one may consider such a system to also include human users and support staff, procedures and workflows, body of knowledge of relevant concepts and methods, and institutional organizations.
A digital elevation model (DEM) is a 3D computer graphics representation of elevation data to represent terrain, commonly of a planet, moon, or asteroid. A "global DEM" refers to a discrete global grid. DEMs are used often in geographic information systems, and are the most common basis for digitally produced relief maps.
Geomatics is defined in the ISO/TC 211 series of standards as the "discipline concerned with the collection, distribution, storage, analysis, processing, presentation of geographic data or geographic information". Under another definition, it consists of products, services and tools involved in the collection, integration and management of geographic (geospatial) data. It is also known as geomatic(s) engineering. Surveying engineering was the widely used name for geomatic(s) engineering in the past.
Geoinformatics is the science and the technology which develops and uses information science infrastructure to address the problems of geography, cartography, geosciences and related branches of science and engineering.
A GIS software program is a computer program to support the use of a geographic information system, providing the ability to create, store, manage, query, analyze, and visualize geographic data, that is, data representing phenomena for which location is important. The GIS software industry encompasses a broad range of commercial and open-source products that provide some or all of these capabilities within various information technology architectures.
Geographic information science or geographical information science is the scientific discipline that studies geographic information, including how it represents phenomena in the real world, how it represents the way humans understand the world, and how it can be captured, organized, and analyzed. It can be contrasted with geographic information systems (GIS), which are the actual repositories of such data, the software tools for carrying out relevant tasks, and the profession of GIS users. That said, one of the major goals of GIScience is to find practical ways to improve GIS data, software, and professional practice.
Health geography is the application of geographical information, perspectives, and methods to the study of health, disease, and health care. Medical geography, a sub-discipline of or sister field of health geography, focuses on understanding spatial patterns of health and disease as related to the natural and social environment. Conventionally, there are two primary areas of research within medical geography: the first deals with the spatial distribution and determinants of morbidity and mortality, while the second deals with health planning, help-seeking behavior, and the provision of health services.
Spatial analysis or spatial statistics includes any of the formal techniques which studies entities using their topological, geometric, or geographic properties. Spatial analysis includes a variety of techniques, many still in their early development, using different analytic approaches and applied in fields as diverse as astronomy, with its studies of the placement of galaxies in the cosmos, to chip fabrication engineering, with its use of "place and route" algorithms to build complex wiring structures. In a more restricted sense, spatial analysis is the technique applied to structures at the human scale, most notably in the analysis of geographic data or transcriptomics data.
Time geography or time-space geography is an evolving transdisciplinary perspective on spatial and temporal processes and events such as social interaction, ecological interaction, social and environmental change, and biographies of individuals. Time geography "is not a subject area per se", but rather an integrative ontological framework and visual language in which space and time are basic dimensions of analysis of dynamic processes. Time geography was originally developed by human geographers, but today it is applied in multiple fields related to transportation, regional planning, geography, anthropology, time-use research, ecology, environmental science, and public health. According to Swedish geographer Bo Lenntorp: "It is a basic approach, and every researcher can connect it to theoretical considerations in her or his own way."
In the context of spatial analysis, geographic information systems, and geographic information science, a field is a property that fills space, and varies over space, such as temperature or density. This use of the term has been adopted from physics and mathematics, due to their similarity to physical fields such as the electromagnetic field or gravitational field. Synonymous terms include spatially dependent variable (geostatistics), statistical surface, and intensive property and crossbreeding between these disciplines is common. The simplest formal model for a field is the function, which yields a single value given a point in space
Digital Earth is the name given to a concept by former US vice president Al Gore in 1998, describing a virtual representation of the Earth that is georeferenced and connected to the world's digital knowledge archives.
A Spatial Data Infrastructure (SDI) is a data infrastructure implementing a framework of geographic data, metadata, users and tools that are interactively connected in order to use spatial data in an efficient and flexible way. Another definition is "the technology, policies, standards, human resources, and related activities necessary to acquire, process, distribute, use, maintain, and preserve spatial data".
Hexagon Geospatial's GeoMedia Professional is a geographic information system (GIS) management solution for map generation and the analysis of geographic information with smart tools that capture and edit spatial data. GeoMedia is used for: creating geographic data; managing geospatial databases; joining business data, location intelligence and geographic data together; creating hard and soft-copy maps; conduct analysis in 'real-time'; base platform for multiple applications, geographic data validation, publishing geospatial information and analyzing mapped information.
A 3D city model is digital model of urban areas that represent terrain surfaces, sites, buildings, vegetation, infrastructure and landscape elements in three-dimensional scale as well as related objects belonging to urban areas. Their components are described and represented by corresponding two- and three-dimensional spatial data and geo-referenced data. 3D city models support presentation, exploration, analysis, and management tasks in a large number of different application domains. In particular, 3D city models allow "for visually integrating heterogeneous geoinformation within a single framework and, therefore, create and manage complex urban information spaces."
Geography is a field of science devoted to the study of the lands, features, inhabitants, and phenomena of Earth. The recorded use of the word γεωγραφία was as a title of a book by Greek scholar Eratosthenes. Geography is an all-encompassing discipline that seeks an understanding of Earth and its human and natural complexities—not merely where objects are, but also how they have changed and come to be. While geography is specific to Earth, many concepts can be applied more broadly to other celestial bodies in the field of planetary science. One such concept, the first law of geography, proposed by Waldo Tobler, is "everything is related to everything else, but near things are more related than distant things." Geography has been called "the world discipline" and "the bridge between the human and the physical sciences".
A boundary problem in analysis is a phenomenon in which geographical patterns are differentiated by the shape and arrangement of boundaries that are drawn for administrative or measurement purposes. The boundary problem occurs because of the loss of neighbors in analyses that depend on the values of the neighbors. While geographic phenomena are measured and analyzed within a specific unit, identical spatial data can appear either dispersed or clustered depending on the boundary placed around the data. In analysis with point data, dispersion is evaluated as dependent of the boundary. In analysis with areal data, statistics should be interpreted based upon the boundary.
Geospatial topology is the study and application of qualitative spatial relationships between geographic features, or between representations of such features in geographic information, such as in geographic information systems (GIS). For example, the fact that two regions overlap or that one contains the other are examples of topological relationships. It is thus the application of the mathematics of topology to GIS, and is distinct from, but complimentary to the many aspects of geographic information that are based on quantitative spatial measurements through coordinate geometry. Topology appears in many aspects of geographic information science and GIS practice, including the discovery of inherent relationships through spatial query, vector overlay and map algebra; the enforcement of expected relationships as validation rules stored in geospatial data; and the use of stored topological relationships in applications such as network analysis. Spatial topology is the generalization of geospatial topology for non-geographic domains, e.g., CAD software.
CyberGIS, or cyber geographic information science and systems, is an interdisciplinary field combining cyberinfrastructure, e-science, and geographic information science and systems (GIS). CyberGIS has a particular focus on computational and data-intensive geospatial problem-solving within various research and education domains. The need for GIS has extended beyond traditional forms of geographic analysis and study, which includes adapting to new sources and kinds of data, high-performance computing resources, and online platforms based on existing and emerging information networks. The name cyberGIS first appeared in Geographic Information Science literature in 2010. CyberGIS is characterized as digital geospatial ecosystems. These systems are developed and have evolved through heterogeneous computing environments, as well as human communication and information environments. CyberGIS can be considered a new generation of geographic information systems (GIS). These systems are based on advanced computing and information infrastructure, which analyze and model geospatial data, providing computationally intensive spatial analysis, modeling, and collaborative geospatial problem-solving at previously unprecedented scales.
Sandra Lach Arlinghaus is an American educator who is adjunct professor in the School of Natural Resources and Environment at the University of Michigan. Her research concerns mathematical geography.
Geographic data and information is defined in the ISO/TC 211 series of standards as data and information having an implicit or explicit association with a location relative to Earth.