Large Scale Constraint Delaunay Triangulation for Virtual Globe Rendering

Part of the Lecture Notes in Geoinformation and Cartography book series (LNGC)


A technique to create a Delaunay triangulation for terrain visualization on a virtual globe is presented. This method can be used to process large scale elevation datasets with billions of points by using little RAM during data processing. All data is being transformed to a global spatial reference system. If grid based elevation data is used as input, a reduced TIN can be calculated. Furthermore, a level of detail approach for large scale out-of-core spherical terrain rendering for virtual globes is presented using the previously created TIN.


Delaunay Triangulation Edge Point Elevation Data Mercator Projection Virtual Globe 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Devillers, O., Devillers, Pion, S., Pion, S., Prisme, P.: Efficient exact geometric predicates for Delaunay triangulations. In: Proceedings of the 5th Workshop Algorithm Engineering and Experiments. pp. 37–44. Baltimore (2003)Google Scholar
  2. Dick, C., Schneider, J., Westermann, R.: Efficient geometry compression for GPU- based decoding in realtime terrain rendering. Comp. Graph. Forum 28(1), 67–83 (2009)CrossRefGoogle Scholar
  3. Fowler, R.E., Samberg, A., Flood, M., Greaves, T.J.: Modeling mobile terrestrial LiDAR to vector based models. In: Maune, D. F. (ed.) Digital Elevation Model Technologies and Applications: The DEM Users Manual, chap. Topographic and Terrestrial Lidar. pp. 199–252. American Society of Photogrammetry and Remote Sensing, Bethesda (1997)Google Scholar
  4. Gerstner, T.: Multiresolution visualization and compression of global topographic data. Tech. rep., GeoInformatica (1999)Google Scholar
  5. Google: Earth,
  6. Google: Google Earth API Developer’s Guide,
  7. Guibas, L.J., Stolfi, J.: Primitives for the manipulation of general subdivisions and the computation of voronoi diagrams. In: STOC’ 83: Proceedings of the Fifteenth Annual ACM Symposium on Theory of Computing. pp. 221–234. ACM, New York (1983)Google Scholar
  8. Guibas, L.J., Stolfi, J.: Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams. ACM Trans. Graph. 4, 74–123 (1985)CrossRefGoogle Scholar
  9. Heller, M.: Triangulation algorithms for adaptive terrain modeling. In: Proceedings of the 4th International Symposium on Spatial Data Handling. pp. 163–174. Zurich, Switzerland (1990)Google Scholar
  10. Hjelle, O., Daehlen, M.: Triangulations and Applications (Mathematics and Visualization). Springer-Verlag New York, Secaucus, NJ (2006)Google Scholar
  11. Hoppe, H.: Smooth view-dependent level-of-detail control and its application to terrain rendering. In: VIS ’98: Proceedings of the Conference on Visualization ’98. pp. 35–42. IEEE Computer Society Press, Los Alamitos (1998)Google Scholar
  12. Isenburg, M., Liu, Y., Shewchuk, J., Snoeyink, J.: Streaming computation of Delaunay triangulations. ACM Trans. Graph. 25(3), 1049–1056 (2006)CrossRefGoogle Scholar
  13. Isenburg, M., Shewchuk, J.: Visualizing LIDAR in Google Earth. In: Proceedings of the 17th International Conference on Geoinformatics. Fairfax (2009)Google Scholar
  14. Lee, J.: A drop heuristic conversion method for extracting irregular networks for digital elevation models. In: Proceedings of the GIS/LIS ’89. pp. 30–39. Orlando (1989)Google Scholar
  15. Lindstrom, P., Cohen, J.D.: On-the-fly decompression and rendering of multiresolution terrain. In: I3D ’10: Proceedings of the 2010 ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games. pp. 65–73. ACM, New York (2010)Google Scholar
  16. Livny, Y., Kogan, Z., El-Sana, J.: Seamless patches for GPU-based terrain rendering. Vis. Comput. 25(3), 197–208 (2009)CrossRefGoogle Scholar
  17. Microsoft: Bing Maps 3d,
  18. Morton, G.: A computer oriented geodetic data base and a new technique in file sequencing. Tech. Rep. IBM Ltd., Ottawa, Ontario, Canada (1966)Google Scholar
  19. Mostafavi, M.A., Gold, C., Dakowicz, M.: Delete and insert operations in Voronoi/Delaunay methods and applications. Comput. Geosci. 29(4), 523–530 (2003)CrossRefGoogle Scholar
  20. Nebiker, S., Christen, M., Eugster, H., Flückiger, K., Stierli, C.: Integrating mobile geo sensors into collaborative virtual globes – design and implementation issues. Paper presented at the Mobile Mapping Technologies Symposium MMT 2007, Padua (2007)Google Scholar
  21. Nebiker, S., Bleisch, S., Christen, M.: Rich point clouds in virtual globes a new paradigm in city modeling? Computers, Environment and Urban Systems (June 2010),
  22. Open Geospatial Consortium, Inc: OpenGIS® city geography markup language (CityGML) – encoding standard (ogc 08-007r1). (p. 218): Open Geospatial Consortium Inc. (2010)Google Scholar
  23. Pajarola, R., Gobbetti, E.: Survey of semi-regular multiresolution models for interactive terrain rendering. Vis. Comput. 23(8), 583–605 (2007)CrossRefGoogle Scholar
  24. Pajarola, R., Antonijuan, M., Lario, R.: Quadtin: quadtree based triangulated irregular networks. In: VIS ’02: Proceedings of the Conference on Visualization ’02. pp. 395–402. IEEE Computer Society, Washington, DC (2002)Google Scholar
  25. Shan, J., Toth, C.: Topographic laser ranging and scanning. CRC Press, Boca Raton (2009)Google Scholar
  26. Shewchuk, J.R.: Adaptive precision floating-point arithmetic and fast robust geometric predicates. Discrete Comput. Geometry 18, 305–363 (1996)CrossRefGoogle Scholar
  27. Snyder, J.P.: Map Projections: A Working Manual. U.S. Geological Survey Professional Paper 1395, U.S. Geological Survey, (1987)
  28. Szalay, A.S., Gray, J., Fekete, G., Kunszt, P.Z., Kukol, P., Thakar, A.: Indexing the sphere with the hierarchical triangular mesh. CoRR abs/cs/0701164 (2007)Google Scholar
  29. Weiler, K.: Edge-based data structures for solid modeling in curved-surface environments. IEEE Comput. Graph. Appl. 5(1), 21–40 (1985)CrossRefGoogle Scholar
  30. Zhou, Q., Lees, B., Tang, G.A.: Lecture Notes in Geoinformation and Cartography, chap. A Seamless and Adaptive LOD Model of the Global Terrain Based on the QTM. pp. 85–103. Springer Berlin Heidelberg, New York (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Institute of Geomatics EngineeringUniversity of Applied Sciences Northwestern SwitzerlandMuttenzSwitzerland

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