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Map Algebra
Map algebra is an algebra for manipulating geographic data, primarily Field (geography) , fields. Developed by Dr. Dana Tomlin and others in the late 1970s, it is a set of primitive operations in a geographic information system (GIS) which allows one or more Raster graphics, raster Layers (digital image editing), layers ("maps") of similar dimensions to produce a new raster layer (map) using mathematical or other operations such as addition, subtraction etc. History Prior to the advent of GIS, the overlay principle had developed as a method of literally superimposing different thematic maps (typically an isarithmic map or a chorochromatic map) drawn on transparent film (e.g., cellulose acetate) to see the interactions and find locations with specific combinations of characteristics. The technique was largely developed by Landscape architecture , landscape architects and Urban planning , city planners, starting with Warren Manning and further refined and popularized by Jaqueline ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebra
Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary algebra deals with the manipulation of variables (commonly represented by Roman letters) as if they were numbers and is therefore essential in all applications of mathematics. Abstract algebra is the name given, mostly in education, to the study of algebraic structures such as groups, rings, and fields (the term is no more in common use outside educational context). Linear algebra, which deals with linear equations and linear mappings, is used for modern presentations of geometry, and has many practical applications (in weather forecasting, for example). There are many areas of mathematics that belong to algebra, some having "algebra" in their name, such as commutative algebra, and some not, such as Galois theory. The word ''algebra'' is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harvard Laboratory For Computer Graphics And Spatial Analysis
The Harvard Laboratory for Computer Graphics and Spatial Analysis (1965 to 1991) pioneered early cartographic and architectural computer applications that led to integrated geographic information systems (GIS). Some of the Laboratory's influential programs included SYMAP, SYMVU, GRID, CALFORM, and POLYVRT. The Laboratory's Odyssey project created a geographic information system that served as a milestone in the development of integrated mapping systems. The Laboratory influenced numerous computer graphic, mapping and architectural systems such as Intergraph, Computervision, and Esri. Founding In 1963, during a training session held at Northwestern University, Chicago architect Howard T. Fisher encountered computer maps on urban planning and civil engineering produced by Edgar Horwood's group at the University of Washington. Fisher conceived a computer mapping software program, SYMAP (Synergistic Mapping), to produce conformant, proximal, and contour maps on a line printer. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geomorphometry
Geomorphometry, or geomorphometrics ( grc, γῆ, gê, earth + grc, μορφή, morphḗ, form, shape + grc, μέτρον, métron, measure), is the science and practice of measuring the characteristics of terrain, the shape of the surface of the Earth, and the effects of this surface form on human and natural geography. It gathers various mathematical, statistical and image processing techniques that can be used to quantify morphological, hydrological, ecological and other aspects of a land surface. Common synonyms for geomorphometry are geomorphological analysis (after geomorphology), terrain morphometry, terrain analysis, and land surface analysis. Geomorphometrics is the discipline based on the computational measures of the geometry, topography and shape of the Earth's horizons, and their temporal change. This is a major component of geographic information systems (GIS) and other software tools for spatial analysis. In simple terms, geomorphometry aims at extracting (land) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Index (statistics)
In statistics and research design, an index is a composite statistic – a measure of changes in a representative group of individual data points, or in other words, a compound measure that aggregates multiple indicators. Indexes – also known as composite indicators – summarize and rank specific observations. Much data in the field of social sciences and sustainability are represented in various indices such as Gender Gap Index, Human Development Index or the Dow Jones Industrial Average. The ‘Report by the Commission on the Measurement of Economic Performance and Social Progress’, written by Joseph Stiglitz, Amartya Sen, and Jean-Paul Fitoussi in 2009 Stiglitz, J., Sen, A., & Fitoussi, J.-P. (2009). eport by the Commission on the Measurement of Economic Performance and Social Progress. suggests that these measures have experienced a dramatic growth in recent years due to three concurring factors: * improvements in the level of literacy (including statistical) * increa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science). The use of mathematical models to solve problems in business or military operations is a large part of the field of operations research. Mathematical models are also used in music, linguistics, and philosophy (for example, intensively in analytic philosophy). A model may help to explain a system and to study the effects of different components, and to make predictions about behavior. Elements of a mathematical model Mathematical models can take many forms, including dynamical systems, statisti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arithmetic Mean
In mathematics and statistics, the arithmetic mean ( ) or arithmetic average, or just the ''mean'' or the ''average'' (when the context is clear), is the sum of a collection of numbers divided by the count of numbers in the collection. The collection is often a set of results of an experiment or an observational study, or frequently a set of results from a survey. The term "arithmetic mean" is preferred in some contexts in mathematics and statistics, because it helps distinguish it from other means, such as the geometric mean and the harmonic mean. In addition to mathematics and statistics, the arithmetic mean is used frequently in many diverse fields such as economics, anthropology and history, and it is used in almost every academic field to some extent. For example, per capita income is the arithmetic average income of a nation's population. While the arithmetic mean is often used to report central tendencies, it is not a robust statistic, meaning that it is greatly influe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multivariate Interpolation
In numerical analysis, multivariate interpolation is interpolation on functions of more than one variable; when the variates are spatial coordinates, it is also known as spatial interpolation. The function to be interpolated is known at given points (x_i, y_i, z_i, \dots) and the interpolation problem consists of yielding values at arbitrary points (x,y,z,\dots). Multivariate interpolation is particularly important in geostatistics, where it is used to create a digital elevation model from a set of points on the Earth's surface (for example, spot heights in a topographic survey or depths in a hydrographic survey). Regular grid For function values known on a regular grid (having predetermined, not necessarily uniform, spacing), the following methods are available. Any dimension * Nearest-neighbor interpolation * n-linear interpolation (see bi- and trilinear interpolation and multilinear polynomial) * n-cubic interpolation (see bi- and tricubic interpolation) * Kriging * Inverse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Structure
In mathematics, an algebraic structure consists of a nonempty set ''A'' (called the underlying set, carrier set or domain), a collection of operations on ''A'' (typically binary operations such as addition and multiplication), and a finite set of identities, known as axioms, that these operations must satisfy. An algebraic structure may be based on other algebraic structures with operations and axioms involving several structures. For instance, a vector space involves a second structure called a field, and an operation called ''scalar multiplication'' between elements of the field (called '' scalars''), and elements of the vector space (called '' vectors''). Abstract algebra is the name that is commonly given to the study of algebraic structures. The general theory of algebraic structures has been formalized in universal algebra. Category theory is another formalization that includes also other mathematical structures and functions between structures of the same type (homomor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Voxel
In 3D computer graphics, a voxel represents a value on a regular grid in three-dimensional space. As with pixels in a 2D bitmap, voxels themselves do not typically have their position (i.e. coordinates) explicitly encoded with their values. Instead, rendering systems infer the position of a voxel based upon its position relative to other voxels (i.e., its position in the data structure that makes up a single volumetric image). In contrast to pixels and voxels, polygons are often explicitly represented by the coordinates of their vertices (as points). A direct consequence of this difference is that polygons can efficiently represent simple 3D structures with much empty or homogeneously filled space, while voxels excel at representing regularly sampled spaces that are non-homogeneously filled. Voxels are frequently used in the visualization and analysis of medical and scientific data (e.g. geographic information systems (GIS)). Some volumetric displays use voxels to describe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ArcInfo
ArcInfo (formerly ARC/INFO) is a full-featured geographic information system produced by Esri, and is the highest level of licensing (and therefore functionality) in the ArcGIS Desktop product line. It was originally a command-line based system. The command-line processing abilities are now available through the GUI of the ArcGIS Desktop product. History ARC/INFO ESRI launched the first version of ARC/INFO - which it claims as "the very first modern GIS" - in 1982 on minicomputers. The name refers to its architecture as a geographic information system composed of: # geographic input, processing, and output tools ("ARC") with # a complementary, but separate database ("INFO")INFO, a single-user, relational database product developed by Henco, Inc., now supported by Doric. Inc. Retrieved from http://www.doric.com/. The early releases of ARC/INFO comprised a set of FORTRAN programs linked together and accessed through a command-line interface built with the scripting language of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
TerrSet
TerrSet (formerly IDRISI) is an integrated geographic information system (GIS) and remote sensing software developed by Clark Labs at Clark University for the analysis and display of digital geospatial information. TerrSet is a PC grid-based system that offers tools for researchers and scientists engaged in analyzing earth system dynamics for effective and responsible decision making for environmental management, sustainable resource development and equitable resource allocation. Key features of TerrSet include: * GIS analytical tools for basic and advanced spatial analysis, including tools for surface and statistical analysis, decision support, land change and prediction, and image time series analysis; * an image processing system with multiple hard and soft classifiers, including machine learning classifiers such as neural networks and classification tree analysis, as well as image segmentation for classification; * Land Change Modeler, a land planning and decision support tool ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
