Lecture09

Lecture09 - Cartographic Transformations Attribute Data...

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Analytical and Computer Cartography Lecture 9: Geometric Map Transformations Cartographic Transformations z Attribute Data (e.g. classification) z Locational properties (e.g. projection) z Graphics (e.g. symbolization) z Information content of maps (e.g. data structure conversion) Dimensional Transformations Geometric map transformations z Same dimension: e.g. point to point in a projection z Change structure: e.g. TIN to grid in a DEM z Change scale: e.g. Area to point as a city is generalized
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Planar geometries z Cartesian z Spherical (ellipsoidal) z Radial Analysis z Input: geometric feature (Point(s), line(s), Area(s), Surface(s), Volumes(s) z Output: Reduce feature to single dimension: e.g. centroid, length, perimeter, area in square unit lengths z Output: A scalar, numerical value reflecting quantity “Collapse” z E.g. shape, sinuosity, network metric z Can compute using algorithms Geometric features z Assume infinite thinness z Assume exact location z Assume unambiguous ontology (definition) e.g. wetlands Planar Map Transformations on Points - Length of a line z Repetitive application of point-to-point distance calculation z For n points, algorithm/formula uses n-1 segments (x 1 , y 1 ) (x n , y n )
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Length of a Line 0 1 2 3 4 5 6 7 8 0123456 Length of a generic line 8 5 1 5 -- (x i -x i-1 ) 2 + (y i -y i-1 ) 2 8 5 1 5 -- (x i -x i-1 ) 2 + (y i -y i-1 ) 2 4 4 1 1 -- (y i -y i-1 ) 2 5 4 3 2 1 i 2.828 4 -2 -2 5 2 2.236 1 2 -1 7 4 1.000 0 1 0 5 5 2.236 4 1 2 4 5 -- -- -- -- 3 3 Sqrt[(x i -x i-1 ) 2 + (y i -y i-1 ) 2] (x i -x i-1 ) 2 y i -y i-1 x i -x i-1 y i x i Sum = 8.3 units Planar Map Transformations on Points - Centroids z Multiple point or line or area to be transformed to single point z
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This note was uploaded on 12/28/2011 for the course GEOG 128 taught by Professor Staff during the Fall '08 term at UCSB.

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Lecture09 - Cartographic Transformations Attribute Data...

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