1. Introdução to Geoinformatics: vector geometries

2. Vector geometries

3. Vector geometries
Arcs and nodes
Polygons

4. Vector geometries
fonte: Universidade de Melbourne

5. Vector Model: Lines vertex node 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

6. Vector Model: Polygons
Polygon #2 is bounded by lines 1 & 2
Line 2 has polygon 1 on left and polygon 2 on right

7. Types of topology
source: ESRI

8. Planar enforcement All the space on a map must be filled
Any point must fall in one polygon alone
Polygons must not overlap

9. Vector geometries
Island
Points

10. Topology: polygon-polyline
source: ESRI

11. Topology: polygon-polyline
Shapefile polygon spatial data model
less complex data model
polygons do not share bounding lines

12. Topology: the OGC model
source: John Elgy

13. What’s the use of a polygon?
Census tracts in São José dos Campos

14. Topology: arc-node-polygon
source: ESRI

15. Topology: arc-node-polygon
source: GIS Basics (Campbell and Chin, 2012)

16. Vectors and table Duality between entre location and atributes Lots
geoid
owner
address
cadastral ID 22
Guimarães
Caetés 768
250186 23 22 23
Bevilácqua
São João 456
110427 24
271055
Ribeiro
Caetés 790

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

18. Geometrical operations
Point in Polygon = O(n)

19. Geometrical operations
Line in Polygon = O(n•m)

20. Topological relationships

21. Topological relationships
Disjoint
Point/Point
Line/Line
Polygon/Polygon

22. Topological relationships
Touches
Point/Line
Point/Polygon
Line/Line
Line/Polygon
Polygon/Polygon

23. Topological relationships
Crosses
Point/Line
Point/Polygon
Line/Line
Line/Polygon

24. Topological relationships
Overlap
Point/Point
Line/Line
Polygon/Polygon

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

26. Topological relationships
Equals
Point/Point
Line/Line
Polygon/Polygon

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

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

29. 4-intersections disjoint contains inside equal
 
 
 
 
 
 
disjoint contains inside equal
 
 
 
 
 
 
 
meet covers coveredBy overlap

30. OpenGIS: 9-intersection dimension-extended topological operations
Relation
disjoint
meet
overlap
equal
9-intersection
model

31. 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))

32. 9-Intersection Matrix of example geometries
I(B)
B(B)
E(B)
I(A)
B(A)
E(A)

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

34. 9-Intersection Model

35. Examples of functions defined by SFSQL

36. DE-9IM: dimensionally extended 9 intersection model

37. 9-Intersection Matrix of example geometries
I(B)
B(B)
E(B)
I(A)
B(A)
E(A)

38. DE-9IM for the example geometries
I(B)
B(B)
E(B)
I(A) 2 1
B(A)
E(A)