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Large Scale Constraint Delaunay Triangulation for Virtual Globe Rendering

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

Abstract

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.

Keywords

  • 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.

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References

  • 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 

  • 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)

    CrossRef  Google Scholar 

  • 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 

  • Gerstner, T.: Multiresolution visualization and compression of global topographic data. Tech. rep., GeoInformatica (1999)

    Google Scholar 

  • Google: Earth, http://earth.google.com

  • Google: Google Earth API Developer’s Guide, http://code.google.com/apis/earth/documentation/

  • 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 

  • 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)

    CrossRef  Google Scholar 

  • 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 

  • Hjelle, O., Daehlen, M.: Triangulations and Applications (Mathematics and Visualization). Springer-Verlag New York, Secaucus, NJ (2006)

    Google Scholar 

  • 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 

  • Isenburg, M., Liu, Y., Shewchuk, J., Snoeyink, J.: Streaming computation of Delaunay triangulations. ACM Trans. Graph. 25(3), 1049–1056 (2006)

    CrossRef  Google Scholar 

  • Isenburg, M., Shewchuk, J.: Visualizing LIDAR in Google Earth. In: Proceedings of the 17th International Conference on Geoinformatics. Fairfax (2009)

    Google Scholar 

  • 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 

  • 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 

  • Livny, Y., Kogan, Z., El-Sana, J.: Seamless patches for GPU-based terrain rendering. Vis. Comput. 25(3), 197–208 (2009)

    CrossRef  Google Scholar 

  • Microsoft: Bing Maps 3d, http://www.bing.com/maps

  • Microsoft: Bing Maps Tile System, http://msdn.microsoft.com/en-us/library/bb259689.aspx

  • 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 

  • Mostafavi, M.A., Gold, C., Dakowicz, M.: Delete and insert operations in Voronoi/Delaunay methods and applications. Comput. Geosci. 29(4), 523–530 (2003)

    CrossRef  Google Scholar 

  • 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 

  • 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), http://dx.doi.org/10.1016/j.compenvurbsys.2010.05.002

  • Open Geospatial Consortium, Inc: OpenGIS® city geography markup language (CityGML) – encoding standard (ogc 08-007r1). (p. 218): Open Geospatial Consortium Inc. (2010)

    Google Scholar 

  • Pajarola, R., Gobbetti, E.: Survey of semi-regular multiresolution models for interactive terrain rendering. Vis. Comput. 23(8), 583–605 (2007)

    CrossRef  Google Scholar 

  • 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 

  • Shan, J., Toth, C.: Topographic laser ranging and scanning. CRC Press, Boca Raton (2009)

    Google Scholar 

  • Shewchuk, J.R.: Adaptive precision floating-point arithmetic and fast robust geometric predicates. Discrete Comput. Geometry 18, 305–363 (1996)

    CrossRef  Google Scholar 

  • Snyder, J.P.: Map Projections: A Working Manual. U.S. Geological Survey Professional Paper 1395, U.S. Geological Survey, http://pubs.er.usgs.gov/usgspubs/pp/pp1395 (1987)

  • 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 

  • Weiler, K.: Edge-based data structures for solid modeling in curved-surface environments. IEEE Comput. Graph. Appl. 5(1), 21–40 (1985)

    CrossRef  Google Scholar 

  • 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 

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Correspondence to M. Christen .

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Christen, M., Nebiker, S. (2011). Large Scale Constraint Delaunay Triangulation for Virtual Globe Rendering. In: Kolbe, T., König, G., Nagel, C. (eds) Advances in 3D Geo-Information Sciences. Lecture Notes in Geoinformation and Cartography(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12670-3_4

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