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Proximity Analysis
Proximity analysis is a class of spatial analysis tools and algorithms that employ geographic distance as a central principle. Distance is fundamental to geographic inquiry and spatial analysis, due to principles such as the friction of distance, Tobler's first law of geography, and Spatial autocorrelation, which are incorporated into analytical tools. Proximity methods are thus used in a variety of applications, especially those that involve movement and interaction. Distance measures All proximity analysis tools are based on a measure of distance between two locations. This may seen as a simplistic geometric measurement, but the nature of geographic phenomena and geographic activity requires several candidate methods to measure and express distance and distance-related measures. * Euclidean distance, the straight-line geometric distance measured on a planar surface. In geographic information systems, this can be easily calculated from locations in a cartesian Projected coordin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Spatial Analysis
Spatial analysis is any of the formal Scientific technique, techniques which study entities using their topological, geometric, or geographic properties, primarily used in Urban design, Urban Design. 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 applied to genomics, as in Spatial transcriptomics, transcriptomics data, but is primarily for spatial data. Complex issues arise in spatial analysis, many of which are neither clearly defined nor completely resolved, but form the basis for current resear ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Information Spaces
Information space is the set of concepts, and relations among them, held by an information system; it describes the range of possible values or meanings an entity can have under the given rules and circumstances. Scholarly definitions Another definition, which is a bit more idealistic, is that an Information Space is the total result of the semantic activity of the humanity, "the world of names and titles", conjugated to the ontological world. Being a primary concept, the information space cannot be precisely defined and is set as a dialectical opposition to the material, physical, object space. Author Max H. Boisot, wrote a book on ''Information Space: A framework for learning in organizations, institutions and culture''. In his book, Boisot (1995, p. 5) Boisot, M. H. ''Information Space: A framework for learning in organizations, institutions and culture''. Routledge: London, 1995. describes information space as a conceptual framework or tool for studying how knowledg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Dijkstra Animation
Dijkstra ( ) is a Dutch family name of West Frisian origin. It most commonly refers to: * Edsger W. Dijkstra (1930–2002), Dutch computer scientist ** Named after him: Dijkstra's algorithm, Dijkstra Prize, Dijkstra–Scholten algorithm People * Bram Dijkstra (born 1938), American professor of English literature and cultural historian * Edsger W. Dijkstra (1930–2002), Dutch computer scientist, programmer, software engineer, mathematician, and science essayist * Erik Dijkstra (born 1977), Dutch journalist and television presenter * Jan Dijkstra (1910–1993), Dutch mayor * Jesse Six Dijkstra (born 1994), Dutch politician * (1896–1978), Dutch painter, illustrator and stained glass artist * Lenie Dijkstra (born 1967), Dutch racing cyclist * Lou Dijkstra (1909–1964), Dutch speed skater, father of Sjoukje Dijkstra * Margaret Dijkstra, pseudonym of Eva Gerlach (born 1948), Dutch poet * Marjolein Dijkstra (born 1967), Dutch physicist * Mart Dijkstra (born 1990), Dutch footballer * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Distance Matrix
In mathematics, computer science and especially graph theory, a distance matrix is a square matrix (two-dimensional array) containing the distances, taken pairwise, between the elements of a set. Depending upon the application involved, the ''distance'' being used to define this matrix may or may not be a metric (mathematics), metric. If there are elements, this matrix will have size . In graph-theoretic applications, the elements are more often referred to as points, nodes or vertices. Non-metric distance matrix In general, a distance matrix is a weighted adjacency matrix of some graph. In a Network (mathematics), network, a directed graph with weights assigned to the arcs, the distance between two nodes of the network can be defined as the minimum of the sums of the weights on the shortest paths joining the two nodes (where the number of steps in the path is bounded). This distance function, while well defined, is not a metric. There need be no restrictions on the weights oth ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Lloyd's Algorithm
In electrical engineering and computer science, Lloyd's algorithm, also known as Voronoi iteration or relaxation, is an algorithm named after Stuart P. Lloyd for finding evenly spaced sets of points in subsets of Euclidean spaces and partitions of these subsets into well-shaped and uniformly sized convex cells. Like the closely related ''k''-means clustering algorithm, it repeatedly finds the centroid of each set in the partition and then re-partitions the input according to which of these centroids is closest. In this setting, the mean operation is an integral over a region of space, and the nearest centroid operation results in Voronoi diagrams. Although the algorithm may be applied most directly to the Euclidean plane, similar algorithms may also be applied to higher-dimensional spaces or to spaces with other non-Euclidean metrics. Lloyd's algorithm can be used to construct close approximations to centroidal Voronoi tessellations of the input, which can be used for quantiza ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Optimal Facility Location
The study of facility location problems (FLP), also known as location analysis, is a branch of operations research and computational geometry concerned with the optimal placement of facilities to minimize transportation costs while considering factors like avoiding placing hazardous materials near housing, and competitors' facilities. The techniques also apply to cluster analysis. Minimum facility location A simple facility location problem is the Weber problem, in which a single facility is to be placed, with the only optimization criterion being the minimization of the weighted sum of distances from a given set of point sites. More complex problems considered in this discipline include the placement of multiple facilities, constraints on the locations of facilities, and more complex optimization criteria. In a basic formulation, the facility location problem consists of a set of potential facility sites ''L'' where a facility can be opened, and a set of demand points ''D'' tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Gravity Model
Gravity models are used in various social sciences to predict and describe certain behaviors that mimic gravitational interaction as described in Isaac Newton's laws of gravity. Generally, the social science models contain some elements of mass and distance, which lends them to the metaphor of physical gravity. A gravity model provides an estimate of the volume of flows of, for example, goods, services, or people between two or more locations. This could be the movement of people between cities or the volume of trade between countries. A gravity model cannot accurately predict flows, but is instead a measure against which actual observed values can be compared, highlighting where those flows are unexpectedly high or low. Social science gravity models: * Gravity model of trade * Trip distribution * Gravity model of migration * Two-step floating catchment area (2SFCA) method The two-step floating catchment area (2SFCA) method is a method for combining a number of related types of i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Inverse Square Law
In science, an inverse-square law is any scientific law stating that the observed "intensity" of a specified physical quantity is inversely proportional to the square of the distance from the source of that physical quantity. The fundamental cause for this can be understood as geometric dilution corresponding to point-source radiation into three-dimensional space. Radar energy expands during both the signal transmission and the reflected return, so the inverse square for both paths means that the radar will receive energy according to the inverse fourth power of the range. To prevent dilution of energy while propagating a signal, certain methods can be used such as a waveguide, which acts like a canal does for water, or how a gun barrel restricts hot gas expansion to one dimension in order to prevent loss of energy transfer to a bullet. Formula In mathematical notation the inverse square law can be expressed as an intensity (I) varying as a function of distance (d) from so ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Distance Decay
Distance decay is a geographical term which describes the effect of distance on cultural or spatial interactions. The distance decay effect states that the interaction between two locales declines as the distance between them increases. Once the distance is outside of the two locales' activity space, their interactions begin to decrease. It is thus an assertion that the mathematics of the inverse square law in physics can be applied to many geographic phenomena, and is one of the ways in which physics principles such as gravity are often applied metaphorically to geographic situations. Mathematical models Distance decay is graphically represented by a curving line that swoops concavely downward as distance along the x-axis increases. Distance decay can be mathematically represented as an inverse-square law by the expression : I = \text \times d^ or : I \propto 1/d^2, where is interaction and is distance. In practice, it is often parameterized to fit a specific situation, s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Voronoi Diagram
In mathematics, a Voronoi diagram is a partition of a plane into regions close to each of a given set of objects. It can be classified also as a tessellation. In the simplest case, these objects are just finitely many points in the plane (called seeds, sites, or generators). For each seed there is a corresponding region, called a Voronoi cell, consisting of all points of the plane closer to that seed than to any other. The Voronoi diagram of a set of points is dual to that set's Delaunay triangulation. The Voronoi diagram is named after mathematician Georgy Voronoy, and is also called a Voronoi tessellation, a Voronoi decomposition, a Voronoi partition, or a Dirichlet tessellation (after Peter Gustav Lejeune Dirichlet). Voronoi cells are also known as Thiessen polygons, after Alfred H. Thiessen. Voronoi diagrams have practical and theoretical applications in many fields, mainly in science and technology, but also in visual art. Simplest case In the simplest case, shown in the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Cost Distance Analysis
In spatial analysis and geographic information systems, cost distance analysis or cost path analysis is a method for determining one or more optimal routes of travel through unconstrained (two-dimensional) space.de Smith, Michael, Paul Longley, Michael Goodchild (2018Cost Distance ''Geospatial Analysis'', 6th Edition The optimal solution is that which minimizes the total cost of the route, based on a Field (geography), field of cost density (cost per linear unit) that varies over space due to local factors. It is thus based on the fundamental geographic principle of Friction of distance. It is an optimization problem with multiple deterministic algorithm solutions, implemented in most GIS software. The various problems, algorithms, and tools of cost distance analysis operate over an unconstrained two-dimensional space, meaning that a path could be of any shape. Similar cost optimization problems can also arise in a constrained space, especially a one-dimensional Network theory, li ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Buffer (GIS)
In geographic information systems (GIS) and spatial analysis, buffer analysis is the determination of a zone around a geographic feature containing locations that are within a specified distance of that feature, the buffer zone (or just buffer). A buffer is likely the most commonly used tool within the proximity analysis methods. History The buffer operation has been a core part of GIS functionality since the original integrated GIS software packages of the late 1970s and early 1980s, such as ARC/INFO, Odyssey, and MOSS. Although it has been one of the most widely used GIS operations in subsequent years, in a wide variety of applications, there has been little published research on the tool itself, except for the occasional development of a more efficient algorithm. Basic algorithm The fundamental method to create a buffer around a geographic feature stored in a vector data model, with a given radius ''r'' is as follows: * Single point: Create a circle around the point with r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
