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