{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T03:56:48Z","timestamp":1773374208463,"version":"3.50.1"},"reference-count":38,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2015,2,25]],"date-time":"2015-02-25T00:00:00Z","timestamp":1424822400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"PYXIS Innovation"},{"DOI":"10.13039\/501100000038","name":"NSERC","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>Digital Earth frameworks provide a tool to receive, send and interact with large location-based datasets, organized usually according to Discrete Global Grid Systems (DGGS). In DGGS, an indexing method is used to assign a unique index to each cell of a global grid, and the datasets corresponding to these cells are retrieved or allocated using this unique index. There exist many methods to index cells of DGGS. Toward facility, interoperability and also defining a \u201cstandard\u201d for DGGS, a conversion is needed to translate a dataset from one DGGS to another. In this paper, we first propose a categorization of indexing methods of DGGS and then define a general conversion method from one indexing to another. Several examples are presented to describe the method.<\/jats:p>","DOI":"10.3390\/ijgi4010320","type":"journal-article","created":{"date-parts":[[2015,2,25]],"date-time":"2015-02-25T05:28:04Z","timestamp":1424842084000},"page":"320-336","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":60,"title":["Categorization and Conversions for Indexing Methods of Discrete Global Grid Systems"],"prefix":"10.3390","volume":"4","author":[{"given":"Ali","family":"Amiri","sequence":"first","affiliation":[{"name":"Department of Computer Science, University of Calgary, 2500 University Drive N.W., Calgary, AB T2N 1N4, Canada"}]},{"given":"Faramarz","family":"Samavati","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Calgary, 2500 University Drive N.W., Calgary, AB T2N 1N4, Canada"}]},{"given":"Perry","family":"Peterson","sequence":"additional","affiliation":[{"name":"PYXIS Innovation Inc., 13, Windsor Street, Kingston, ON K7M 4K4, Canada"}]}],"member":"1968","published-online":{"date-parts":[[2015,2,25]]},"reference":[{"key":"ref_1","unstructured":"Goodchild, M.F. (2000, January 26\u201328). Discrete global grids for Digital Earth, Santa Barbara, CA, USA."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1559\/152304003100011090","article-title":"Geodesic discrete global grid systems","volume":"30","author":"Sahr","year":"2003","journal-title":"Cartogr. Geogr. Inf. Sci."},{"key":"ref_3","unstructured":"Tong, X., Ben, J., Qing, Z., and Zhang, Y. (2000). The hexagonal discrete global grid system appropriate for remote sensing spatial data. Proc. SPIE., 7146."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"898","DOI":"10.1080\/13658816.2012.725474","article-title":"Efficient encoding and spatial operation scheme for aperture 4 hexagonal discrete global grid system","volume":"27","author":"Tong","year":"2013","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1016\/j.compenvurbsys.2007.11.005","article-title":"Location coding on icosahedral aperture 3 hexagon discrete global grids","volume":"32","author":"Sahr","year":"2008","journal-title":"Comput. Environ. Urban Syst"},{"key":"ref_6","unstructured":"Peterson, P. (2006). Close-Packed, Uniformly Adjacent, Multiresolutional, Overlapping Spatial Data Ordering. (20,060,265,197 A1), U.S. Patent US."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1080\/17538940802657694","article-title":"Arithmetic and Fourier transform for the PYXIS multi-resolution digital Earth model","volume":"2","author":"Vince","year":"2009","journal-title":"Int. J. Digit. Earth."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1023\/A:1006407023786","article-title":"Global grids from recursive diamond subdivisions of the surface of an octahedron or icosahedron","volume":"64","author":"White","year":"2000","journal-title":"Environ. Monit. Assess."},{"key":"ref_9","unstructured":"Alborzi, H., and Samet, H. (2000, January 26\u201328). Augmenting SAND with a spherical data model, Santa Barbara, CA, USA."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Bebis, G., Boyle, R., Parvin, B., Koracin, D., Li, B., Porikli, F., Zordan, V., Klosowski, J., Coquillart, S., and Luo, X. (2013, January 29\u201331). One-to-Two Digital Earth. Advances in Visual Computing, Lecture Notes in Computer Science, Rethymnon, Crete, Greece.","DOI":"10.1007\/978-3-642-41939-3"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"759","DOI":"10.1086\/427976","article-title":"HEALPix: A framework for high-resolution discretization and fast analysis of data distributed on the sphere","volume":"622","author":"Hivon","year":"2005","journal-title":"Astrophys. J."},{"key":"ref_12","unstructured":"Gibb, R., Raichev, A., and Speth, M. Available online: http:\/\/raichev.net\/files\/rhealpix_dggs_preprint.pdf."},{"key":"ref_13","unstructured":"Peters, A. K. (2011). 3D Engine Design for Virtual Globes, Ltd. [1st ed.]."},{"key":"ref_14","unstructured":"Dutton, G. (1999). Lecture Notes in Earth Sciences Series, Springer-Verlag."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1227","DOI":"10.1016\/j.jvcir.2006.04.003","article-title":"Indexing the aperture 3 hexagonal discrete global grid","volume":"17","author":"Vince","year":"2006","journal-title":"J. Vis. Commun. Image Represent"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Ben, J., Tong, X., and Chen, R. (2010, January 18\u201320). A spatial indexing method for the hexagon discrete global grid system, Beijing, China.","DOI":"10.1109\/GEOINFORMATICS.2010.5567972"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1080\/04353676.1974.11879899","article-title":"A system of domains for global sampling problems","volume":"56","author":"Wickman","year":"1974","journal-title":"Geogr. Ann. Ser. A Phys. Geogr."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1080\/13658810110043603","article-title":"Continuous indexing of hierarchical subdivisions of the globe","volume":"15","author":"Bartholdi","year":"2000","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Goodchild, M.F., and Shiren, Y. (1992). A hierarchical spatial data structure for global geographic information systems. CVGIP: Graph. Models Image Process, 31\u201344.","DOI":"10.1016\/1049-9652(92)90032-S"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Mahdavi-Amiri, A., Harrison, E., and Samavati, F. (2014). Hexagonal connectivity maps for Digital Earth. Int. J. Digit. Earth.","DOI":"10.1080\/17538947.2014.927597"},{"key":"ref_21","first-page":"363","article-title":"Hexagonal discrete global grid systems for geospatial computing","volume":"22","author":"Sahr","year":"2011","journal-title":"Arch. Photogramm. Cartogr. Remote Sens"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"898","DOI":"10.1080\/13658816.2012.725474","article-title":"Efficient encoding and spatial operation scheme for aperture 4 hexagonal discrete global grid system","volume":"27","author":"Tong","year":"2013","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_23","unstructured":"Szalay, A.S., Gray, J., Fekete, G., Kunszt, P.Z., Kukol, P., and Thakar, A. (2005). Indexing the Sphere with the Hierarchical Triangular Mesh, Microsoft Research."},{"key":"ref_24","unstructured":"Gibson, L., and Lucas, D. (1982, January 14\u201317). Spatial data processing using generalized balanced ternary, Las Vegas, NV, USA."},{"key":"ref_25","unstructured":"Kennedy, M., and Koop, S. (2000). ArcGIS 8 Concept Guides, Environmental Systems Research Institute."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Hormann, K., L\u00e9vy, B., and Sheffer, A. (2007, January 5\u20139). Mesh parameterization: Theory and practice video files associated with this course are available from the citation page, San Diego, CA, USA.","DOI":"10.1145\/1281500.1281510"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"10","DOI":"10.3138\/27H7-8K88-4882-1752","article-title":"An equal area map projection for polyhedral globes","volume":"29","author":"Snyder","year":"1992","journal-title":"Cartographica"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1033","DOI":"10.1016\/j.cam.2011.07.009","article-title":"Uniform spherical grids via equal area projection from the cube to the sphere","volume":"236","author":"Plonka","year":"2011","journal-title":"J. Comput. Appl. Math."},{"key":"ref_29","unstructured":"Samet, H. (2005). Foundations of Multidimensional and Metric Data Structures (The Morgan Kaufmann Series in Computer Graphics and Geometric Modeling), Morgan Kaufmann Publishers Inc."},{"key":"ref_30","unstructured":"Faust, N., Ribarsky, W., Jiang, T., and Wasilewski, T. (2000, January 26\u201328). Real-time global data model for the Digital Earth, Santa Barbara, CA, USA."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"905","DOI":"10.1145\/358728.358741","article-title":"An effective way to represent quadtrees","volume":"25","author":"Gargantini","year":"1982","journal-title":"ACM Commun"},{"key":"ref_32","unstructured":"Bai, J., Zhao, X., and Chen, J. (2005, January 14\u201316). Indexing of the discrete global grid using linear quadtree, Hangzhou, China."},{"key":"ref_33","unstructured":"Pharr, M., and Fernando, R. (2005). Chapter Terrain Rendering Using GPU-Based Geometry Clipmaps, Addison-Wesley."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1109\/TVCG.2005.65","article-title":"Real-time optimal adaptation for planetary geometry and texture: 4-8 tile hierarchies","volume":"11","author":"Hwa","year":"2005","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_35","unstructured":"Lawder, J. (2000). Ph.D. Thesis, University of London."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1109\/TVCG.2002.1021577","article-title":"Terrain simplification simplified: A general framework for view-dependent out-of-core visualization","volume":"8","author":"Lindstrom","year":"2002","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Mahdavi-Amiri, A., and Samavati, F. (2012, January 24\u201326). Connectivity maps for subdivision surfaces, Rome, Italy.","DOI":"10.5220\/0003814200260037"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.cag.2014.01.001","article-title":"Atlas of connectivity maps","volume":"39","author":"Samavati","year":"2014","journal-title":"Comput. 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