1. Introdução to Geoinformatics: Geometries

2. 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

3. 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

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

5. Vector geometries

6. Polygons Arcs and nodes

7. Vector geometries Points Island

8. Vector geometries fonte: Universidade de Melbourne

9. Vector geometries: the OGC model fonte: John Elgy

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

11. 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

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

13. Vector and raster geometries Raster Vector fonte: Mohamed Yagoub

14. Raster geometry célula Extent Resolution source: Mohamed Yagoub

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

16. Cell space

17. 2500 m2.500 m e 500 m Cellular Data Base Resolution

18. Rasters or vectors? source: Mohamed Yagoub

19. Raster geometry fonte: Mohamed Yagoub

20. The mixed cell problem fonte: Mohamed Yagoub

21. Cells or vectors?

22. Cells or vector?

23. Cells or vectors? (RADAM x SRTM)

24. Cells or vectors? (RADAM x LANDSAT)

25. 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)

26. isolines TIN 2,5 D geometries

27. Grey-coloured reliefShaded relief

28. 2,5Dgeometries Regular grid

29. 2,5 D geometries TIN (triangular irregular networks)

30. Conversion btw geometries

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

32. Line in Polygon = O(nm) Geometrical operations

33. Topological relationships

34. Disjoint Point/Point Line/Line Polygon/Polygon

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

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

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

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

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

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

41. 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

42. 4-intersections          disjoint contains inside equal            meet covers coveredBy overlap

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

44. 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. 45 I(B)B(B) E(B) I(A) B(A) E(A) 9-Intersection Matrix of example geometries

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

47. 9-Intersection Model

49. 49 DE-9IM: dimensionally extended 9 intersection model

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

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