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Smooth SSC Creation and 3D Vario-Scale Implementation for Topological Area Partitioning

This document discusses the technique of creating smooth Space Scale Cubes (SSC) and implementing 3D vario-scale for topological area partitioning. It covers the process of creating smooth SSCs, utilizing SSCs, and transitioning between shock and smooth changes within the SSC structure. The conclusion highlights the advantages of vario-scale mapping in terms of integrity, efficiency, and cost optimization. The patent-pending method ensures accurate representation and integration of space, scale, and time in multi-dimensional maps without overlaps or gaps.

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Smooth SSC Creation and 3D Vario-Scale Implementation for Topological Area Partitioning

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  1. Vario-scale (and nD extension): results and work in progress Martijn Meijers STW User Committee meeting, Utrecht, 19 September, 2012

  2. Contents • Creating smooth SSC • Using SSC • 3D vario-scale • Conclusion tGAP = topological Generalized Area Partitioning (2D) SSC = Space Scale Cube

  3. Smooth simplify Simplified  • Shock change: • 2 rectangles • 1 triangle • Smooth change: • 3 triangles Transition  Original line 

  4. Smooth merge for convex neighbour • make #nodes shared top and target bnd equal (n) view • connect node pairs • 2 triangles + n-3 quadrangles • if non-flat  space-split quadrangle scaleinto 2 triangle view • Merge planar neighbours

  5. b_o (opposite boundary) LS_o = 1+3+1 = 5 b_s (shared boundary) LS_s = 7 Alternative (without adding nodes) • Create triangle base at one sideand top at other side at scale s2, from s1 to s2, at scale s1

  6. Non-convex neighbour subdivide in convex parts m-shaped neighbour neighbour with hole (note: smooth collapse/split similar to smooth merge)

  7. Implementation: simplification

  8. Contents • Creating smooth SSC • Using SSC • 3D vario-scale • Conclusion tGAP = topological Generalized Area Partitioning (2D) SSC = Space Scale Cube

  9. Selection based on (n+1)D overlap from space-scale cube Simple initial map Progressive initial map (sorting lowerhigher detail) Low LoD s High LoD y x

  10. Selection based on (n+1)D overlap from space-scale cube Simple initial map Progressive initial map (sorting lowerhigher detail) s y x

  11. (n+1)D overlap selection for zooming Progressive zoom-in Progressive zoom-out (normal sorting order) (reverse sorting order)

  12. (n+1)D overlap selection for panning Normal panning Progressive panning (normal sorting order)

  13. Streaming of importance range(and first compared with a cut) A cut (or slice) of single importance A ordered range of importance values select face_id as id, '101' as impLevel, RETURN_POLYGON(face_id, 101) as geom from tgap_face where imp_low <= 101 and 101 < imp_high; select face_id as id, imp_high as impLevel, imp_low, imp_high, RETURN_POLYGON(face_id,imp_high) as geom from tgap_face where imp_high >= imp_high order by imp_high desc;

  14. Extension to OGC/ISO WFS It is possible to specify imp range in Filter part of GetFeature request and using ogc:SortBy Not ideal because it is not clear that this is about scale, streaming, progressive transfer/refinement Deeper integration in WFS (called WFS-Refinement): GetCapabilities should indicate if server supports progressive refinement Reporting of the min and max imp of a theme New request type GetFeatureByImportance

  15. Example WFS-R request <wfs:GetFeatureByImportanceservice="WFS" version="1.0.0" outputFormat="GML2" ...> <wfs:Query typeName='tgap_face' minImp='5' maxImp=‘8'> <ogc:Filter> <ogc:BBOX> <ogc:PropertyName>geom</ogc:PropertyName> <gml:Box srsName=“…epsg.xml#28992"> <gml:coordinates> 136931,416574 139382,418904 </gml:coordinates> </gml:Box> </ogc:BBOX> </ogc:Filter> <ogc:SortBy>gdmc:imp_high D</ogc:SortBy> </wfs:Query> </wfs:GetFeatureByImportance>

  16. Contents • Creating smooth SSC • Using SSC • 3D vario-scale • Conclusion tGAP = topological Generalized Area Partitioning (2D) SSC = Space Scale Cube

  17. zii’’ zii’ zii ZII zi’’ zi’ zi 3D smooth merge No ZI

  18. Opposite boundary (5 faces) zii’ 3 (top) C 3 (top) B c 3 b 4 (back) 4 (back) 5 (left) 4 zi’ zii 5 (left) 5 zi 2 d 2 (front) 2 (front) a f D 1 A 1 (bottom) e 1 (bottom) Equator (ring) Generic 3D smooth merge Low detail High detail zii’’ zi’’

  19. ZII 3D Smooth simplify • Simplify boundary of merged object, two options: • 1. Keep block shape • 2. Tilted roof shape ZII’ ZII’’

  20. z y x s Pseudo 4D-view s1 s2 Zone zi shown for reference purpose ZII’’ zii zi

  21. Step-wise approach

  22. Contents • Creating SSC • Using SSC • 3D vario-scale • Conclusion tGAP = topological Generalized Area Partitioning (2D) SSC = Space Scale Cube

  23. Conclusion, advantages vario-scale maps Map producers: more integrity, less manpower needed for the production of maps (=less cost) Map providers: more efficiency, less data = less storage capacity, less energy, high transmission speed Map users: more functionality at less cost and higher speed Patent pending nr. OCNL 2006630

  24. Conclusions, true vario-scale • True vario-scale nD maps based on (n+1)D representations and slicing (selecting) with hyperplanes: • tGAP structure translates 2D space and 1D scale in an integrated 3D topological representation: no overlaps and no gaps (in space and scale) • Starting with 3D space and adding scale results in 4D • Starting with 3D space and time (history) and adding scale results in 5D topological structure (again no gaps/overlaps in space, time or scale), well defined neighbors in space, time and scale directions

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