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# Introdução to Geoinformatics: Geometries. Vector Model Lines: fundamental spatial data model Lines start and end at nodes line #1 goes from node #2 to.

## Presentation on theme: "Introdução to Geoinformatics: Geometries. Vector Model Lines: fundamental spatial data model Lines start and end at nodes line #1 goes from node #2 to."— Presentation transcript:

Introdução to Geoinformatics: Geometries

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

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

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

Vector geometries

Polygons Arcs and nodes

Vector geometries Points Island

Vector geometries fonte: Universidade de Melbourne

Vector geometries: the OGC model fonte: John Elgy

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

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

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

Vector and raster geometries Raster Vector fonte: Mohamed Yagoub

Raster geometry célula Extent Resolution source: Mohamed Yagoub

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

Cell space

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

Rasters or vectors? source: Mohamed Yagoub

Raster geometry fonte: Mohamed Yagoub

The mixed cell problem fonte: Mohamed Yagoub

Cells or vectors?

Cells or vector?

Cells or vectors? (RADAM x SRTM)

Cells or vectors? (RADAM x LANDSAT)

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)

isolines TIN 2,5 D geometries

Grey-coloured reliefShaded relief

2,5Dgeometries Regular grid

2,5 D geometries TIN (triangular irregular networks)

Conversion btw geometries

Point in Polygon = O(n) Geometrical operations

Line in Polygon = O(nm) Geometrical operations

Topological relationships

Disjoint Point/Point Line/Line Polygon/Polygon

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

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

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

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

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

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

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

4-intersections          disjoint contains inside equal            meet covers coveredBy overlap

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

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))

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

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

9-Intersection Model

49 DE-9IM: dimensionally extended 9 intersection model

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

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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