introdução to geoinformatics: geometries. vector model lines: fundamental spatial data model lines...

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

node

vertex

vertex

vertex

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

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 owner cadastral ID

22 Guimarães Caetés 768

address

22250186

23 Bevilácqua São João 456 110427

24 Ribeiro Caetés 790 271055

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Duality Location - Attributes

Praia Praia BravaBrava

Praia de Praia de BoiçucangaBoiçucanga

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 m 2.500 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

2,5 D geometries

Grey-coloured relief

Shaded relief

2,5D geometries

Regular grid

2,5 D geometries

TIN (triangular irregular networks)

Conversion btw geometries

Point in Polygon = O(n)

Geometrical operations

Line in Polygon = O(n•m)

Geometrical operations

Topological relationships

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) isA exterior

)( oA

)( A

)( A

4-intersections

disjoint contains inside equal

meet covers coveredBy overlap

OpenGIS: 9-intersection dimension-extended topological operations

Relation

disjoint meet overlap equal

9-intersection

model

111

100

100

111

110

100

111

111

111

100

010

001

)()()(

)()()(

)()()(

BABABA

BABABA

BABABA

o

o

oooo

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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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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 polygonand a curve?

9-Intersection Model

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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

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DE-9IM for the example geometries

I(B) B(B) E(B)

I(A) 2 1 2

B(A) 1 0 1

E(A) 2 1 2