GIS Functions and Operators
GIS Functions and Operators The functions associated with raster cartographic modeling can be divided into five types: Those that work on single cell locations (local functions or operators) Those that work on cell locations within a neighborhood (focal functions) Those that work on cell locations within zones (zonal f ti ) functions) Those that work on all cells within the raster (global functions) Those that perform a specific application (for example, hydrologic analysis functions) Map Algebra Map algebra is a language specifically designed for geographic cell cell--based systems and provides the basis for cartographic modeling. Based on concepts originally presented by Joe Berry and C. C Dana Tomlin. Tomlin Map algebra provides a language to conveying logic constructs while maintaining the power of the mathematical th ti l base b underlying d l i the th cellcell ll-based b d structure. Mapp Algebra g operators p and functions apply pp y mathematical computations on a raster “map” vs. matrix algebra. Local Functions Local functions apply their calculations to a single cell location before calculating the next location, until all cells have been processed. To pperform the calculation,, the local function onlyy needs to know the values at the location for a single raster or for multiple rasters, as well as, in some cases, a comparison value. Operations or functions can be applied on single or multiple grids: output t t = (inlayer1 (i l 1 + inlayer2) i l 2) / 2 output = sin(inlayer1) output = min(inlayer1, inlayer2, inlayer3) Operators and Functions There are three types of operations: Arithmetic operators: *, /, -, + Boolean operators: p And, Or, Xor, Not Relational operators: ==, >, <, <>, >=, <= Output ([ Inlayer1] [ Inlayer 2]) / 2 Operators and Functions Mathematical functions are applied to the values in a single i l input i raster. There Th are four f groups off mathematical functions Logarithmic Arithmetic Trigonometric Powers Other local functions compute p statistics,, combine,, or other operations from a list of multiple inlayers. Output = min(Inlayer1, min( min(Inl Inl Inlayer1, 1 Inlayer2, Inl 2 Inlayer3) Inlayer3 Inl 3) 3) Focal Functions Focal (or neighborhood) functions compute an output grid in which the output value at each cell location is a function of the input cells in the specified neighborhood “around” each output (or target) location. Neighborhoods can be different sizes and geometries. Different arithmetic and statistical functions can be applied to summarize a neighborhood values. Example: Output = focalsum (Input, rectangle 3,3) rectangle, 3 3) Zonal Functions Zonal functions compute an output raster dataset where the output value for each location depends on the value of the cell att the th location l ti andd the th association i ti that th t location l ti has h within ithi a cartographic zone. Output = zonalsum(inlayer, zonalsum(inlayer, zonelayer) zonelayer) Output = zonalgeometry(zonelayer zonalgeometry(zonelayer, zonelayer, all) Global Functions Global, or perper-raster, functions compute an output raster d dataset i which in hi h the h output value l at eachh cell ll location l i is i potentially a function of all the cells combined from the various input p raster datasets. There are two main groups g p of global functions: Euclidean distance and weighted distance. O t t from Output f the th Euclidean E lid distance function, each cell contains the shortest distance to any input point. Application Functions There are a wide series of cellcell-based modeling functions developed p to solve specific p applications. pp There is some overlap in the categorization of an application function and the local, focal, zonal, and global functions (such as the fact that even though g slope p is usuallyy used in the application of analyzing surfaces, it is also a focal function). Application functions include the following: Density analysis Surface generation Surface analysis Hydrologic analysis Geometric transformation Generalization Resolution altering
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