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Introdução to Geoinformatics: Geometries

Introdução to Geoinformatics: Geometries. node. node. vertex. vertex. vertex. vertex. 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

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Introdução to Geoinformatics: Geometries

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  1. Introdução to Geoinformatics: Geometries

  2. node node vertex vertex vertex vertex 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

  3. Vector Model Polygons: fundamental spatial data model • Polygon #2 is bounded by lines 1 & 2 • Line 2 has polygon 1 on left and polygon 2 on right

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

  5. Vector geometries

  6. Vector geometries • Polygons • Arcsand 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 owner address cadastral ID 250186 Caetés 768 22 Guimarães 22 23 110427 23 Bevilácqua São João 456 271055 24 Ribeiro Caetés 790

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

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

  14. Raster geometry Extent célula Resolution source: Mohamed Yagoub

  15. Raster geometries (cell spaces) Regular spacepartitions Manyattributes per cell

  16. Cellspace

  17. 2500 m 2.500 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 Dgeometries

  27. Grey-coloured relief Shaded relief 2,5 Dgeometries

  28. 2,5D geometries Regular grid

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

  30. Conversion btw geometries

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

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

  33. Topological relationships

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

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

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

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

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

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

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

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

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

  43. OpenGIS: 9-intersection dimension-extended topological operations

  44. 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)) Example

  45. E(B) I(B) B(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

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

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

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