provision of interoperable datasets to open gi to eu communities

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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

Contour levels

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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