Conclusion
This project successfully implemented a comprehensive framework for terrain mesh generation and processing, utilizing both synthetic and real-world elevation data. The work focused on creating flexible and extensible methods to generate, refine, and visualize 3D terrain meshes.
1. Summary of achievements
Flexible terrain generation:
Two distinct terrain generation methods were developed:
-
The
LambdaGenerator
class, which uses user-defined lambda functions for synthetic terrain generation. -
The
GpsGenerator
class, which leverages real-world elevation data obtained from the Mapbox Terrain-RGB v1 API.
These approaches provided flexibility, allowing the generation of varied terrain shapes, from mathematically defined surfaces to accurate representations of real-world locations.
Contour line generation:
The ContourConstraint
class was developed
to generate contour lines, which play a critical role in enhancing the
mesh’s accuracy and detail. This process ensures that the mesh reflects
significant topographical features, providing a more realistic model.
Triangulation and refinement:
The Re-triangulation
process was efficiently handled by the
triangulateAssembledMesh
function,
which utilized the CGAL library’s Constrained_Delaunay_triangulation_2
class. This
ensured that the contour constraints were respected, resulting in high-quality
triangulated meshes suitable for further analysis.
Exporting and visualization:
The final meshes were exported in the MSH format and visualized using Gmsh, confirming the effectiveness of the methods employed. The visualizations showcased the accurate representation of both synthetic and real-world terrains, demonstrating the system’s capability to produce detailed and accurate terrain models.
2. Impact and future work
The methods and tools developed in this project have laid a solid foundation for generating high-quality terrain meshes, which are essential for various applications in urban planning, environmental simulations, and energy management. The framework’s flexibility allows it to be extended easily, enabling future work to incorporate additional terrain features, such as vegetation or building models, into the mesh.
Looking ahead, the next steps could involve:
-
Merging multiple tiles:
-
Expanding the framework to handle and merge multiple tiles of GPS data, as discussed in the Handling and merging multiple tiles section, would allow for the creation of larger, more complex terrain models.
-
-
Performance optimization:
-
Improving the performance of the mesh generation and triangulation processes to handle larger datasets more efficiently.
-
-
Integration of urban elemnts:
-
Integrating urban elements, like buildings and vegetation, as discussed in the Urban elements integration section, with the purpose of recreate a realistic 3D model of urban environments.
-
3. Final thoughts
This project has demonstrated the potential of combining advanced computational geometry techniques with flexible data-driven approaches to create accurate and detailed terrain models. The developed framework provides a robust foundation for future developments and applications, contributing to the broader goals of sustainable urban development and environmental conservation.
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.
-
[img:constrained-refined-mesh] Pierre Alliez, Senior Researcher and Team Leader at Inria, Image provided during personal communication. 2024.