mapalgebra&terrain

mapalgebra&terrain - Formalization is Map Algebra...

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Formalization is Map Algebra Based on work of Dana Tomlin, but independently invented in multiple places Input maps (transform op) output map Outputs can become inputs for further work Concatenation of transformation operations can become complex and, unfortunately, meaningless
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A crude view of what is called “map algebra”. Watch out for associativity 5 + 3 * 2 = {11, 16}
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Map algebra and cartographic modeling- both concepts originally introduced by Dana Tomlin.
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Tomlin’s idea was to development a standardized language for geographical analysis that was similar in purpose and form to mathematical expressions. output = f(input1, input2, input3)
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Each mathematical expression consists of: geographic data (terms), a set of data processing conventions (transformations), processing control (the order of operation and specific syntax that implements these transformations). NewCover = (thiscover * thatcover) / anothercover control data (GIS layers or scalar values) transformation Functions/operators
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Tomlin’s intent was to develop a “language” of analysis built around three classes of operators: Local, focal, zonal The set of known words in this language is comprised of function names, coverage names and control statements
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Traveltime = focalProximity of endpoints spreading in Mobility When placed in the proper sequence (syntactically and semantically correct) these words form mathematical sentences (equations) that are meaningful (semantically valid) to the software and to other GIS experts.
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Some software will permit gradual, rather than crisp, zones of influence– related to “inverse distance” for example… Travel time from 6 starting points across a landscape All location with 1 days travel of 6 starting points across a landscape Traveltime = focalProximity of endpoints spreading in Mobility
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mapalgebra&terrain - Formalization is Map Algebra...

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