1. 1 Provision of interoperable datasets to open GI to EU communities Magistrato alle Acque di Venezia Project founded by eContentplus Programme Thematic Working Group Elevation “Towards Seamless Terrains”

2. Towards Seamless Terrains 1 – Generalities 2 – Terrain modeling 3 – Various fragmentations 4 – Coordinate transformation 5 – Cross-border aggregation –Same models –Different models 6 – Final remarks Project founded by eContentplus Programme

3. 1 – Generalities Project founded by eContentplus Programme http://www.gug.bv.tum.de/seiten-e/technik/physik.htmhttp://www.gug.bv.tum.de/seiten-e/technik/physik.htm l

4. Other example http://www.kartografie.nl/geometrics/Reference%20surfaces/body.htm Project founded by eContentplus Programme

5. Example of cross-border inconsistency Fragment of the Dutch topo map showing the border of elgium and the Netherlands. The Mean Sea Level of Belgium differ - 2.34m from the MSL of The Netherlands. As a result, contour lines are abruptly ending at the border. http://www.kartografie.nl/geometrics/Reference%20surfaces/body.htm Project founded by eContentplus Programme

6. http://www.bkg.bund.de/nn_159884/EN/FederalOffice/Products/Reference__sys/NatRefHeight/EN__Height03__node.html__nnn=true

7. Use Case Diagram User Dataset Provider #1 Dataset Provider #1 Wants a unique seamless terrain Offers terrain #1 Offers terrain #2 Project founded by eContentplus Programme

8. 2 – Terrain Modeling TIN’s Orthogonal grids Level curves Project founded by eContentplus Programme

9. TIN Project founded by eContentplus Programme Terrain Triangles Vertices * 3-3 Terrain Triangles Segments 1-2 3-3 2-2 Vertices 2-n Other point’s elevation estimation by planar interpolation z = ax+by+c

10. a/ Direct representation TRIANGLE(#triangle, #vertex1, #vertex2, #vertex3) VERTEX(#vertex, x, y, z) b/ Segment-oriented representation TRIANGLE (#triangle, #segment1, #segment2, #segment3) SEGMENT(#segment, #vertex1, #vertex2) VERTEX(#vertex, x, y, z) c/ Including more topology SEGMENT (#segment, #vertex1, #vertex2, #triangle1, #triangle2) Project founded by eContentplus Programme

11. Orthogonal grid For instance, every 100 m Project founded by eContentplus Programme Other point’s elevation estimation by bilinear interpolation z = axy+bx+cy+d

12. Contour levels Project founded by eContentplus Programme

13. Contour levels Project founded by eContentplus Programme Terrain Level curves z Level curve piece * Vertices x, y * Other point’s elevation estimation based on neighbors, f.i. Gravity (Newton) interpolation

14. 3 – Various Fragmentation Thematic fragmentation Zonal fragmentation Hybrid fragmentation Project founded by eContentplus Programme

15. Layer Fragmentation Thematic Partitioning Electricity Database Building Database Parcel Database Project founded by eContentplus Programme

16. Zonal Fragmentation Geographic Partitioning Zone A Database Zone B Database Zone C Database Project founded by eContentplus Programme

17. 4 – Coordinate Transformation X, Y Z Z Ellipsoid 2 Ellipsoid 1 Project founded by eContentplus Programme

18. Two problems General formulas : –X = f (x, y) –Y = g (x, y) –Z = h (x, y, z) Point global identifiers –points already existing –points created in the integration process Project founded by eContentplus Programme

19. 5 – Cross-border integration Coordinate transformation, and then Same model –TIN –Grid –Contour levels Different models –General methodology Project founded by eContentplus Programme

20. TIN integration Construct a global TIN based on both TIN’s New triangles (green) are created having vertices in both TIN’s Project founded by eContentplus Programme

21. Grid integration Different steps (f.i. 100m, and 50 yards) Different orientations Two solutions: –Create a new grid by interpolating the previous grid Transform everything into TIN’s Project founded by eContentplus Programme

22. Contour levels Different Mean Sea level (origin of contour lines) Different interval Two solutions –Create new contour levels by interpolating –Transform everything into TIN’s Project founded by eContentplus Programme

23. Different models Generic solution –Transform everything into TIN’s –Beware of intermediate triangles Example: TIN + Grid Project founded by eContentplus Programme

24. Example for Terrain Integration Database A (Grid) Database B (TIN’s) Cross-border integration: Database AB –Transformation into TIN’s of database A by splitting square into triangles Project founded by eContentplus Programme

25. Example of Terrain Integration TIN + Grid Boundary of A Intermediary zone Boundary of B Database A Database B Project founded by eContentplus Programme

26. Database A Grid file representation UTM co-ordinates Type A ellipsoid Sea level (z=0) in Jackson Harbour Relations –A-Terrain (#terrain, #mesh) –A-Mash (#mesh, #nw-pt, #ne-pt, #se-pt, #sw.pt) –A-Point (#point, x, y, z) Project founded by eContentplus Programme

27. Database B TIN’s Gauss co-ordinates Type B ellipsoid Sea level (z=0) in Johnson Harbour Relations –B-Terrain (#terrain, #triangle) –B-Triangle (#triangle, #pt1, #pt2, #pt3) –B-Point (#point, x, y, z) Project founded by eContentplus Programme

28. Database Terrain Matching Terrain Continuity Excerp of 2 terrain databases which are to be federated and matched Matching 2 terrain databases by transforming squares into triangles and adding some intermediary triangles Project founded by eContentplus Programme

29. Database AB TIN’s Gauss co-ordinates Type B ellipsoid Sea level (z=0) in Johnson Harbour Global identifiers, even for additional triangles Relations –AB-Terrain (#terrain, #triangle) –AB-Triangle (#triangle, #pt1, #pt2, #pt3) –AB-Point (#point, x, y, z) Project founded by eContentplus Programme

30. Vertex/triangle identifiers: example For database A –C.identifier = 1 000 000 + A.identifier For database B –C.identifier = 2 000 000 + B.identifier Intermediate zone –C.identifier = 3 000 000 + x Project founded by eContentplus Programme

31. 6 – Final Remarks Cross-border integration for seamless terrains is very awkward Transformation of coordinates Transformation of models TIN is generally the best output model Necessity of creating a fresh database, or a view above existing datasets Problem of global identifiers Project founded by eContentplus Programme

32. References LAURINI R. (1998) Spatial Multidatabase Topological Continuity and Indexing: a Step towards Seamless GIS Data Interoperability. International Journal of Geographical Information Sciences. Vol. 12,4, June 1998, pp. 373-402. See slides on http://lisi.insa- lyon.fr/~laurini/resact/feder/FEDER.pdf http://lisi.insa- lyon.fr/~laurini/resact/feder/FEDER.pdf