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) consists of integrated computer hardware and software that store, manage, analyze, edit, output, and visualize geographic data. Much of this often happens within a spatial database; however, this is not essential to meet the definition of a GIS. In a broader sense, one may consider such a system also to include human users and support staff, procedures and workflows, the body of knowledge of relevant concepts and methods, and institutional organizations.
A digital elevation model (DEM) or digital surface model (DSM) is a 3D computer graphics representation of elevation data to represent terrain or overlaying objects, commonly of a planet, moon, or asteroid. A "global DEM" refers to a discrete global grid. DEMs are used often in geographic information systems (GIS), and are the most common basis for digitally produced relief maps. A digital terrain model (DTM) represents specifically the ground surface while DEM and DSM may represent tree top canopy or building roofs.
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. Surveying engineering was the widely used name for geomatic(s) engineering in the past. Geomatics was placed by the UNESCO Encyclopedia of Life Support Systems under the branch of technical geography.
Geoinformatics is a scientific field primarily within the domains of Computer Science and technical geography. It focuses on the programming of applications, spatial data structures, and the analysis of objects and space-time phenomena related to the surface and underneath of Earth and other celestial bodies. The field develops software and web services to model and analyse spatial data, serving the needs of geosciences and related scientific and engineering disciplines. The term is often used interchangeably with Geomatics, although the two have distinct focuses; Geomatics emphasizes acquiring spatial knowledge and leveraging information systems, not their development. At least one publication has claimed the discipline is pure computer science outside the realm of geography.
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 geoinformation science is a scientific discipline at the crossroads of computational science, social science, and natural science 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 is a sub-field of geography, specifically part of technical geography. It has applications to both physical geography and human geography, although its techniques can be applied to many other fields of study as well as many different industries.
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 in relation 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.
Geovisualization or geovisualisation, also known as cartographic visualization, refers to a set of tools and techniques supporting the analysis of geospatial data through the use of interactive visualization.
Spatial analysis is any of the formal techniques which studies entities using their topological, geometric, or geographic properties. Spatial analysis includes a variety of techniques using different analytic approaches, especially spatial statistics. It may be applied in fields as diverse as astronomy, with its studies of the placement of galaxies in the cosmos, or 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 geospatial analysis, the technique applied to structures at the human scale, most notably in the analysis of geographic data. It may also be applied to genomics, as in transcriptomics data.
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 (vector or scalar) such as the electromagnetic field or gravitational field. Synonymous terms include spatially dependent variable (geostatistics), statistical surface ( thematic mapping), and intensive property (physics and chemistry) 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 (i.e., t = f(x, y, z) )
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.
Geography is the study of the lands, features, inhabitants, and phenomena of Earth. 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. Geography has been called "a bridge between natural science and social science disciplines."
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 complementary 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.
CARTO is a software as a service (SaaS) spatial analysis platform that provides GIS, web mapping, data visualization, spatial analytics, and spatial data science features. The company is positioned as a Location Intelligence platform due to its tools for geospatial data analysis and visualization that do not require advanced GIS or development experience. As a cloud-native platform, CARTO runs natively on cloud data warehouse platforms overcoming any previous limits on data scale for spatial workloads.
Sandra Lach Arlinghaus is an American Geographer who is adjunct professor in the School for Environment and Sustainability at the University of Michigan. Her research concerns mathematical geography much of which is archived in the persistent archive, Deep Blue, at The University of Michigan. She is the Founder of the Institute of Mathematical Geography (IMaGe) and of Solstice: An Electronic Journal of Geography and Mathematics; full archives of both are also archived in Deep Blue. She is noted as a 'mathematician' in the online Mathematical Genealogy Project of the North Dakota State University/American Mathematical Society that is housed online. She has served on various boards of directors, including : Project My Heart / Your Heart, Chene Street History Study, and Meridian Architectural Trust.
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. It is also called geospatial data and information, georeferenced data and information, as well as geodata and geoinformation.
Technical geography is the branch of geography that involves using, studying, and creating tools to obtain, analyze, interpret, understand, and communicate spatial information.
Web GIS, or Web Geographic Information Systems, are GIS that employ the World Wide Web to facilitate the storage, visualization, analysis, and distribution of spatial information over the Internet. The World Wide Web, or the Web, is an information system that uses the internet to host, share, and distribute documents, images, and other data. Web GIS involves using the World Wide Web to facilitate GIS tasks traditionally done on a desktop computer, as well as enabling the sharing of maps and spatial data. While Web GIS and Internet GIS are sometimes used interchangeably, they are different concepts. Web GIS is a subset of Internet GIS, which is itself a subset of distributed GIS, which itself is a subset of broader Geographic information system. The most common application of Web GIS is Web mapping, so much so that the two terms are often used interchangeably in much the same way as Digital mapping and GIS. However, Web GIS and web mapping are distinct concepts, with web mapping not necessarily requiring a Web GIS.
Natalia V. Andrienko is a Ukrainian computer scientist who has worked in Moldova, Russia, Germany, and England; her research involves information visualization and visual analytics for geographic information systems and spatial data. She is a professor at City, University of London in England, a lead scientist for the Fraunhofer Institute for Intelligent Analysis and Information Systems (IAIS) in Sankt Augustin, Germany, and a principal investigator for the Lamarr Institute for Machine Learning and Artificial Intelligence in Dortmund, Germany.