Handling and merging multiple tiles
As we aim to model extensive urban environments, a single terrain tile often is not enough due to the large geographical area that needs to be covered. Instead, the terrain is divided into multiple smaller tiles, each representing a portion of the overall area. These tiles must be individually processed and then seamlessly merged to form a cohesive, continuous mesh. This process, while straightforward for a single tile, presents significant challenges when applied to multiple tiles, particularly in maintaining data consistency and ensuring integration.
1. Challenges in merging multiple miles
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Integration: One of the primary challenges is ensuring that the boundaries between adjacent tiles align perfectly. Any discontinuities at the tile edges can lead to visible seams, gaps, or overlaps in the final mesh, which would significantly degrade the quality of the terrain model.
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Consistent elevation data: Different tiles may be sourced from varying datasets or processed independently, leading to inconsistencies in elevation data at the tile boundaries. Ensuring that the elevation values match across tile borders is essential for a smooth, continuous terrain surface.
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Handling projection and alignment: Each tile is typically aligned with a specific geographic projection, and differences in projection between tiles can lead to distortions when merging them. Correctly aligning tiles, especially across different regions, is crucial for maintaining the accuracy of the terrain model.
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Consistency of contour lines: When merging tiles, it’s important to ensure that contour lines remain consistent across tile boundaries. This involves aligning the contour lines from adjacent tiles and ensuring that the triangulation process respects these constraints, even across multiple tiles.
2. Strategies for merging multiple tiles
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Edge matching and smoothing: To ensure seamless transitions between tiles, edge matching techniques can be employed. This involves adjusting the vertices at the tile boundaries to ensure they align perfectly. Additionally, smoothing algorithms can be applied across tile boundaries to create a more natural transition, reducing any visible seams.
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Preprocessing of elevation data: Before merging tiles, preprocessing steps can be taken to normalize the elevation data. This could involve interpolating values at the tile edges or applying filters to ensure consistency across adjacent tiles, minimizing the potential for mismatches.
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Adaptive refinement at boundaries: To improve the quality of the mesh at tile boundaries, adaptive refinement techniques can be applied. This involves refining the mesh at the edges of tiles to better match the elevation data of adjacent tiles, ensuring a more accurate and seamless integration.
References
-
[cemosis] Cemosis. Center for Modeling and Simulation in Strasbourg. 2024. (www.cemosis.fr)
-
[irma] IRMA. Institut de recherche mathématique avancée. 2024 (irma.math.unistra.fr)
-
[unistra] University of Strasbourg. 2024. (en.unistra.fr)
-
[numpex] PEPR Numpex. Priority Research Program and Equipment for Numerical Exascale computing. 2024. (numpex.org/numpex-program)
-
[exama] Exa-MA. Methods and Algorithms for Exascale. 2024. (numpex.org/exama-methods-and-algorithms-for-exascale)
-
[ktirio] Ktirio Urban Building application. Prud’homme Christophe. Expanding horizons: Ktirio and the urban building vision in Hidalgo2. October 2023. 2024. (github.com/orgs/feelpp/discussions/2167)
-
[hidalgo2] CoE Hidalgo2. HPC and big data technologies for global challenges. 2024. (www.hidalgo2.eu/about)
-
[ubm] CoE Hidalgo2. The Urban Building Model 2024. (www.hidalgo2.eu/urban-building-model)
-
[inria] Inria. National Institute for Research in Digital Science and Technology. 2024. (www.inria.fr/en)
-
[eea1] European Environment Agency. Greenhouse gas emissions from energy use in buildings in Europe. Octber 2023. 2024. (www.eea.europa.eu/en/analysis/indicators/greenhouse-gas-emissions-from-energy?activeAccordion=546a7c35-9188-4d23-94ee-005d97c26f2b)
-
[eea2] European Environment Agency. Accelerating the energy efficiency renovation of residential buildings — a behavioural approach. June 2023. 2024. (www.eea.europa.eu/publications/accelerating-the-energy-efficiency)
-
[ec1] European Commission. 2050 long-term strategy. 2024. (climate.ec.europa.eu/eu-action/climate-strategies-targets/2050-long-term-strategy_en#:~:text=Striving%20to%20become%20the%20world’s%20first%20climate%2Dneutral%20continent%20by%202050.&text=The%20EU%20aims%20to%20be,to%20the%20European%20Climate%20Law%20.)
-
[ec2] European Commission. The European Green Deal. 2024. (commission.europa.eu/strategy-and-policy/priorities-2019-2024/european-green-deal_en)
-
[ec3] European Commission. European Climate Law. 2024. (climate.ec.europa.eu/eu-action/european-climate-law_en)
-
[ubp] Urban Building Pilot. Prud’homme Christophe. CoE Hidalgo2 Urban Building Pilot at NumPEx workshop on Discretization@Exascale. November 2023. 2024. (github.com/orgs/feelpp/discussions/2188)
-
[eurohpc] EuroHPC JU. The European High Performance Computing Joint Undertaking. 2024. (eurohpc-ju.europa.eu/index_en)
-
[mapbox] Wikipedia contributors. Mapbox. Wikipedia, The Free Encyclopedia. August 2024. 2024. (en.wikipedia.org/wiki/Mapbox)
-
[mapbox-terrain-rgb] Mapbox. Mapbox Terrain-RGB v1. Mapbox Documentation. 2024. (docs.mapbox.com/data/tilesets/reference/mapbox-terrain-rgb-v1)
-
[mapbox-raster-tiles] Mapbox. Mapbox Raster Tiles API. Mapbox Documentation. 2024. (docs.mapbox.com/api/maps/raster-tiles)
-
[json-nlohmann] Lohmann, Niels. JSON for Modern C++. 2024. (json.nlohmann.me)
-
[curl] Stenberg, Daniel. cURL: A Command Line Tool and Library for Transferring Data with URLs. 2024. (curl.se)
-
[libpng] libpng: The Official PNG Reference Library. 2024. (www.libpng.org/pub/png/libpng.html)
-
[cgal] CGAL: The Computational Geometry Algorithms Library. 2024. (www.cgal.org)
-
[stl] STL (STereoLithography) File Format Specification. 2024. (www.fabbers.com/tech/STL_Format)
-
[gmsh] Geuzaine Christophe, and Jean-François Remacle. Gmsh: A 3D Finite Element Mesh Generator with Built-in Pre- and Post-Processing Facilities. Version 4.10, 2024. (gmsh.info)
-
[msh] MSH: The Gmsh Mesh File Format. 2024. (gmsh.info/doc/texinfo/gmsh.html#MSH-file-format)
-
[img:lat-lon] Latitude and Longitude. BBC Bitesize. 2024. (www.bbc.co.uk/bitesize/guides/ztqtyrd/revision/1)
-
[world-geodetic-system] Wikipedia contributors. World Geodetic System. Wikipedia, The Free Encyclopedia. 2024. (en.wikipedia.org/wiki/World_Geodetic_System)
-
[marcator-projection] Wikipedia contributors. Mercator projection. Wikipedia, The Free Encyclopedia. 2024. (en.wikipedia.org/wiki/Mercator_projection)
-
[web-marcator-projection] Wikipedia contributors. Web Mercator projection. Wikipedia, The Free Encyclopedia. 2024. (en.wikipedia.org/wiki/Web_Mercator_projection)
-
[cdt1] Wikipedia contributors. Constrained Delaunay triangulation. Wikipedia, The Free Encyclopedia. 2024. (en.wikipedia.org/wiki/Constrained_Delaunay_triangulation)
-
[cdt2] L. Paul Chew. Constrained Delaunay Triangulations. Dartmouth College. 1987. 2024. (www.cs.jhu.edu/~misha/Spring16/Chew87.pdf)
-
[dt] Wikipedia contributors. Delaunay triangulation. Wikipedia, The Free Encyclopedia. 2024. (en.wikipedia.org/wiki/Voronoi_diagram)
-
[voronoi] Wikipedia contributors. Voronoi diagram. Wikipedia, The Free Encyclopedia. 2024. ()
-
[tiled-web-map] Wikipedia contributors. Tiled web map. Wikipedia, The Free Encyclopedia. 2024. (en.wikipedia.org/wiki/Tiled_web_map)
-
[img:tiles-coordinates] XYZ Tiles coordinate numbers. Wikipedia, The Free Encyclopedia. 2024. (en.wikipedia.org/wiki/File:XYZ_Tiles.png)
-
[img:tiled-web-map] Tiled Web Map. Wikipedia, The Free Encyclopedia. 2024. (en.wikipedia.org/wiki/Tiled_web_map#/media/File:Tiled_web_map_Stevage.png)
-
[img:dt] Delaunay triangulation. Wikipedia, The Free Encyclopedia. 2024. (en.wikipedia.org/wiki/Delaunay_triangulation#/media/File:Delaunay_circumcircles_vectorial.svg)
-
[img:dt-centers] Delaunay triangulation with all the circumcircles and their centers. Wikipedia, The Free Encyclopedia. 2024. (en.wikipedia.org/wiki/Delaunay_triangulation#/media/File:Delaunay_circumcircles_centers.svg)
-
[img:dt-voronoi] Delaunay triangulation and its Voronoi diagram. Wikipedia, The Free Encyclopedia. 2024. (en.wikipedia.org/wiki/Delaunay_triangulation#/media/File:Delaunay_Voronoi.svg)
-
[img:constrained-mesh] Pierre Alliez, Senior Researcher and Team Leader at Inria, Image provided during personal communication. 2024.
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[img:constrained-refined-mesh] Pierre Alliez, Senior Researcher and Team Leader at Inria, Image provided during personal communication. 2024.