Categorization and conversions for indexing methods of discrete global grid systems

ISPRS International Journal of Geo-Information

Volumn 4, Issue 1, 2015, Pages 320-336

  Amiri, Ali Mahdavi ^a   Samavati, Faramarz ^a   Peterson, Perry ^b  

^a UNIVERSITY OF CALGARY   (Canada)

^b PYXIS Innovation Inc   (Canada)

Author keywords

Digital Earth; Hierarchy; Indexing method; Space filling curves

Indexed keywords

EID: 84947762370     PISSN: None     EISSN: 22209964     Source Type: Journal    
DOI: 10.3390/ijgi4010320     Document Type: Article

References (38)

1. Goodchild, M.F. Discrete global grids for Digital Earth. In Proceedings of the 1 st International Conference on Discrete Global Grids, Santa Barbara, CA, USA, 26-28 March 2000.
2. Sahr, K., White, D., Kimerling, A.J. Geodesic discrete global grid systems. Cartogr. Geogr. Inf. Sci. 2003, 30, 121-134.
3. Tong, X., Ben, J., Qing, Z., Zhang, Y. The hexagonal discrete global grid system appropriate for remote sensing spatial data. Proc. SPIE 2000, 7146, 10.1117/12.813110.
4. Tong, X., Ben, J., Wang, Y., Zhang, Y., Pei, T. Efficient encoding and spatial operation scheme for aperture 4 hexagonal discrete global grid system. Int. J. Geogr. Inf. Sci. 2013, 27, 898-921.
5. Sahr, K. Location coding on icosahedral aperture 3 hexagon discrete global grids. Comput. Environ. Urban Syst. 2008, 32, 174-187.
6. Peterson, P. Close-Packed, Uniformly Adjacent, Multiresolutional, Overlapping Spatial Data Ordering. U.S. Patent US 20,060,265,197 A1, 23 November 2006.
7. Vince, A., Zheng, X. Arithmetic and Fourier transform for the PYXIS multi-resolution digital Earth model. Int. J. Digit. Earth 2009, 2, 59-79.
8. White, D. Global grids from recursive diamond subdivisions of the surface of an octahedron or icosahedron. Environ. Monit. Assess. 2000, 64, 93-103.
9. Alborzi, H., Samet, H. Augmenting SAND with a spherical data model. In Proceedings of the First International Conference on Discrete Global Grids, Santa Barbara, CA, USA, 26-28 March 2000.
10. Mahdavi-Amiri, A., Bhojani, F., Samavati, F. One-To-Two Digital Earth. In Advances in Visual Computing, Lecture Notes in Computer Science, Proceedings of 9th International Symposium on Visual Computing, Rethymnon, Crete, Greece, 29-31 July 2013; Bebis, G., Boyle, R., Parvin, B., Koracin, D., Li, B., Porikli, F., Zordan, V., Klosowski, J., Coquillart, S., Luo, X., et al., Eds., Springer: Berlin, Germany, 2013; pp. 681-692.
11. Górski, K.M., Hivon, E., Banday, A.J., Wandelt, B.D., Hansen, F.K., Reinecke, M., Bartelmann, M. HEALPix: A framework for high-resolution discretization and fast analysis of data distributed on the sphere. Astrophys. J. 2005, 622, 759-771.
12. Gibb, R., Raichev, A., Speth, M. The rHEALPIX Discrete Global Grid System. Available online: http://raichev.net/files/rhealpix-dggs-preprint.pdf (accessed on 15 January 2013).
13. Cozzi, P., Ring, K. 3D Engine Design for Virtual Globes, 1st ed., A. K. Peters, Ltd.: Natick, MA, USA, 2011.
14. Dutton, G. A Hierarchical Coordinate System for Geoprocessing and Cartography: With 85 Figures, 16 Tables and 2 Foldouts. In Lecture Notes in Earth Sciences Series; Springer-Verlag: Berlin, Germany, 1999.
15. Vince, A. Indexing the aperture 3 hexagonal discrete global grid. J. Vis. Commun. Image Represent. 2006, 17, 1227-1236.
16. Ben, J., Tong, X., Chen, R. A spatial indexing method for the hexagon discrete global grid system. In Proceedings of the 2010 18th International Conference on Geoinformatics, Beijing, China, 18-20 June 2010; pp. 1-5.
17. Wickman, F.E., Elvers, E., Edvarson, K. A system of domains for global sampling problems. Geogr. Ann. Ser. A Phys. Geogr. 1974, 56, 201-212.
18. Bartholdi, J.J., III; Goldsman, P. Continuous indexing of hierarchical subdivisions of the globe. Int. J. Geogr. Inf. Sci. 2000, 15, 489-522.
19. Goodchild, M.F., Shiren, Y. A hierarchical spatial data structure for global geographic information systems. CVGIP: Graph. Models Image Process. 1992, 54, 31-44.
20. Mahdavi-Amiri, A., Harrison, E., Samavati, F. Hexagonal connectivity maps for Digital Earth. Int. J. Digit. Earth 2014, 10.1080/17538947.2014.927597.
21. Sahr, K. Hexagonal discrete global grid systems for geospatial computing. Arch. Photogramm. Cartogr. Remote Sens. 2011, 22, 363-376.
22. Tong, X., Ben, J., Wang, Y., Zhang, Y., Pei, T. Efficient encoding and spatial operation scheme for aperture 4 hexagonal discrete global grid system. Int. J. Geogr. Inf. Sci. 2013, 27, 898-921.
23. Szalay, A.S., Gray, J., Fekete, G., Kunszt, P.Z., Kukol, P., Thakar, A. Indexing the Sphere with the Hierarchical Triangular Mesh; TechReport MSR-TR-2005-123; Microsoft Research: Redmond, WA, USA, 2005.
24. Gibson, L., Lucas, D. Spatial data processing using generalized balanced ternary. In Proceedings of the IEEE Computer Society on Pattern Recognition and Image Processing, Las Vegas, NV, USA, 14-17 June 1982; pp. 566-572.
25. Kennedy, M., Koop, S., Environmental Systems Research Institute. Understanding map projections: GIS by Esri. In ArcGIS 8 Concept Guides; Environmental Systems Research Institute: Redlands, CA, USA, 2000.
26. Hormann, K., Levy, B., Sheffer, A. Mesh parameterization: Theory and practice video files associated with this course are available from the citation page. In Proceedings of the ACM SIGGRAPH 2007 Courses (SIGGRAPH 07), Special Interest Group on Computer Graphics and Interactive Techniques Conference, San Diego, CA, USA, 5-9 August 2007.
27. Snyder, J.P. An equal area map projection for polyhedral globes. Cartographica 1992, 29, 10-21.
28. Roşca, D., Plonka, G. Uniform spherical grids via equal area projection from the cube to the sphere. J. Comput. Appl. Math. 2011, 236, 1033-1041.
29. Samet, H. Foundations of Multidimensional and Metric Data Structures (The Morgan Kaufmann Series in Computer Graphics and Geometric Modeling); Morgan Kaufmann Publishers Inc.: San Francisco, CA, USA, 2005.
30. Faust, N., Ribarsky,W., Jiang, T.;Wasilewski, T. Real-Time global data model for the Digital Earth. In Proceedings of the International Conference on Discrete Global Grid, Santa Barbara, CA, USA, 26-28 March 2000.
31. Gargantini, I. An effective way to represent quadtrees. ACM Commun. 1982, 25, 905-910.
32. Bai, J., Zhao, X., Chen, J. Indexing of the discrete global grid using linear quadtree. In Proceedings of ISPRS Hangzhou 2005 Workshop on Service and Application of Spatial Data Infrastructure, Hangzhou, China, 14-16 October 2005; pp. 267-270.
33. Pharr, M., Fernando, R. GPU Gems 2: Programming techniques for high-performance graphics and general-purpose computation. In Chapter Terrain Rendering Using GPU-Based Geometry Clipmaps; Addison-Wesley: Boston, MA, USA, 2005.
34. Hwa, L.M., Duchaineau, M.A., Joy, K.I. Real-Time optimal adaptation for planetary geometry and texture: 4-8 tile hierarchies. IEEE Trans. Vis. Comput. Graph. 2005, 11, 355-368.
35. Lawder, J. The Application of Space-Filling Curves to the Storage and Retrieval of Multi-Dimensional Data. Ph.D. Thesis, University of London, London, UK, 2000.
36. Lindstrom, P., Pascucci, V. Terrain simplification simplified: A general framework for view-dependent out-of-core visualization. IEEE Trans. Vis. Comput. Graph. 2002, 8, 239-254.
37. Mahdavi-Amiri, A., Samavati, F. Connectivity maps for subdivision surfaces. In Proceedings of the GRAPP/IVAPP, Rome, Italy, 24-26 February, 2012; pp. 26-37.
38. Mahdavi-Amiri, A., Samavati, F. Atlas of connectivity maps. Comput. Graph. 2014, 39, 1-11.