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Introdução to Geoinformatics: Geometries

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Vector Model Lines: fundamental spatial data model Lines start and end at nodes line #1 goes from node #2 to node #1 Vertices determine shape of line Nodes and vertices are stored as coordinate pairs node vertex

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Vector Model Polygon #2 is bounded by lines 1 & 2 Line 2 has polygon 1 on left and polygon 2 on right Polygons : fundamental spatial data model

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Vector Model less complex data model polygons do not share bounding lines Shapefile polygon spatial data model

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Vector geometries

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Polygons Arcs and nodes

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Vector geometries Points Island

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Vector geometries fonte: Universidade de Melbourne

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Vector geometries: the OGC model fonte: John Elgy

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Para que serve um polígono? Setores censitários em São José dos Campos

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Vectors and table Duality between entre location and atributes Lots geoid ownercadastral ID 22Guimarães Caetés 768 address 22 250186 23BevilácquaSão João 456 110427 24 RibeiroCaetés 790 271055 23

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Duality Location - Attributes Praia Brava Praia de Boiçucanga Exemplo de Unidade Territorial Básica - UTB

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Vector and raster geometries Raster Vector fonte: Mohamed Yagoub

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Raster geometry célula Extent Resolution source: Mohamed Yagoub

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Raster geometries (cell spaces) Regular space partitions Many attributes per cell

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Cell space

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2500 m2.500 m e 500 m Cellular Data Base Resolution

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Rasters or vectors? source: Mohamed Yagoub

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Raster geometry fonte: Mohamed Yagoub

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The mixed cell problem fonte: Mohamed Yagoub

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Cells or vectors?

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Cells or vector?

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Cells or vectors? (RADAM x SRTM)

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Cells or vectors? (RADAM x LANDSAT)

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Raster or vectors? “Boundaries drawn in thematic maps (such as soil, vegetation, and geology) are rarely accurate. Drawing them as thin lines often does not adequately represent their character. We should not worry so much about the exact locations and elegant graphical representations.” (P. A. Burrough)

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isolines TIN 2,5 D geometries

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Grey-coloured reliefShaded relief

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2,5Dgeometries Regular grid

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2,5 D geometries TIN (triangular irregular networks)

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Conversion btw geometries

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Point in Polygon = O(n) Geometrical operations

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Line in Polygon = O(nm) Geometrical operations

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Topological relationships

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Disjoint Point/Point Line/Line Polygon/Polygon

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Topological relationships Touches Point/Line Point/Polygon Line/Line Line/Polygon Polygon/Polygon

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Topological relationships Crosses Point/Line Point/Polygon Line/Line Line/Polygon

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Topological relationships Overlap Point/Point Line/Line Polygon/Polygon

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Topological relationships Within/contains Point/Point Point/Line Point/Polygon Line/Line Line/Polygon Polygon/Polygon

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Topological relationships Equals Point/Point Line/Line Polygon/Polygon

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Interior: A ◦ Exterior: A - Boundary: ∂A Topological relations

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Topological Concepts Interior, boundary, exterior Let A be an object in a “Universe” U. A U Green is A interior Red is boundary of A Blue –(Green + Red) is A exterior

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4-intersections disjoint contains inside equal meet covers coveredBy overlap

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OpenGIS: 9-intersection dimension-extended topological operations Relation disjointmeetoverlapequal 9-intersection model

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44 Example Consider two polygons A - POLYGON ((10 10, 15 0, 25 0, 30 10, 25 20, 15 20, 10 10)) B - POLYGON ((20 10, 30 0, 40 10, 30 20, 20 10))

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45 I(B)B(B) E(B) I(A) B(A) E(A) 9-Intersection Matrix of example geometries

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Specifying topological operations in 9- Intersection Model Question : Can this model specify topological operation between a polygon and a curve?

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9-Intersection Model

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49 DE-9IM: dimensionally extended 9 intersection model

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50 I(B)B(B) E(B) I(A) B(A) E(A) 9-Intersection Matrix of example geometries

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51 DE-9IM for the example geometries I(B)B(B)E(B) I(A)212 B(A)101 E(A)212

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