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”

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

1 – Generalities Project founded by eContentplus Programme l

Other example Project founded by eContentplus Programme

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 m from the MSL of The Netherlands. As a result, contour lines are abruptly ending at the border. Project founded by eContentplus Programme

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

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

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

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

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

Contour levels Project founded by eContentplus Programme

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Vertex/triangle identifiers: example For database A –C.identifier = A.identifier For database B –C.identifier = B.identifier Intermediate zone –C.identifier = x Project founded by eContentplus Programme

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

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 See slides on lyon.fr/~laurini/resact/feder/FEDER.pdf lyon.fr/~laurini/resact/feder/FEDER.pdf