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Provision of interoperable datasets to open GI to EU communities
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Magistrato alle Acque di Venezia
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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
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1 – Generalities
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http://www.gug.bv.tum.de/seiten-e/technik/physik.htm l
Other example
http://www.kartografie.nl/geometrics/Reference%20surfaces/body.htm
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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
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http://www.bkg.bund.de/nn_159884/EN/FederalOffice/Products/Reference__sys/NatRefHeight/EN__Height03__node.html__nnn=true
Use Case Diagram
User
DatasetProvider #1
DatasetProvider #1
Wants a uniqueseamless terrain
Offers terrain #1
Offers terrain #2
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2 – Terrain Modeling
• TIN’s
• Orthogonal grids
• Level curves
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TIN
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Terrain
Triangles
Vertices
*
3-3
Terrain
Triangles
Segments
1-2
3-3
2-2
Vertices
2-nOther 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)
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Orthogonal grid
For instance, every 100 m
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Other point’s elevation estimationby bilinear interpolation
z = axy+bx+cy+d
Contourlevels
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Terrain
Level curvesz
Level curve piece
*
Verticesx, y
*
Other point’s elevation estimationbased on neighbors, f.i.
Gravity (Newton) interpolation
3 – Various Fragmentation
• Thematic fragmentation
• Zonal fragmentation
• Hybrid fragmentation
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Layer FragmentationThematic Partitioning
ElectricityDatabase
BuildingDatabase
ParcelDatabase
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Zonal FragmentationGeographic Partitioning
Zone ADatabase
Zone BDatabase
Zone CDatabase
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4 – Coordinate Transformation
X, YZ
X, Y
Z
Ellipsoid 2
Ellipsoid 1
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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
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5 – Cross-border integration
• Coordinate transformation, and then
• Same model– TIN– Grid– Contour levels
• Different models– General methodology
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TIN integration
• Construct a global TIN based on both TIN’s
• New triangles (green) are created having vertices in both TIN’s
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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
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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
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Different models
• Generic solution– Transform everything into TIN’s– Beware of intermediate triangles
• Example: TIN + Grid
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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
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Example of Terrain Integration TIN + Grid
Boundary of A
Intermediary zone
Boundary of B
Database A Database B
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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)
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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)
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Database Terrain MatchingTerrain Continuity
Excerp of 2 terrain databaseswhich are to be federated and matched
Matching 2 terrain databasesby transforming squares into triangles
and adding some intermediary triangles
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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)
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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
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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
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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
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