{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T04:02:23Z","timestamp":1768708943020,"version":"3.49.0"},"reference-count":35,"publisher":"University of Toronto Press Inc. (UTPress)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Cartographica"],"published-print":{"date-parts":[[2019,3]]},"abstract":"<jats:p> Hexagonal discrete global grid systems (DGGSs) with integer spatial indexes are a promising new approach to designing geospatial data structures and location reference systems. Central place indexing (CPI) is a class of multi-precision hierarchical linear spatial indexing systems for pure and mixed-aperture hexagonal DGGSs. Definitions for CPI systems are given both on the plane and on the polyhedral surfaces of geodesic DGGSs, and examples of real-world DGGSs indexed using CPI are described. The semantic advantages of CPI systems are discussed, including their ability to exactly represent their own geometries. <\/jats:p>","DOI":"10.3138\/cart.54.1.2018-0022","type":"journal-article","created":{"date-parts":[[2019,3,28]],"date-time":"2019-03-28T23:08:50Z","timestamp":1553814530000},"page":"16-29","source":"Crossref","is-referenced-by-count":27,"title":["Central Place Indexing: Hierarchical Linear Indexing Systems for Mixed-Aperture Hexagonal Discrete Global Grid Systems"],"prefix":"10.3138","volume":"54","author":[{"given":"Kevin","family":"Sahr","sequence":"first","affiliation":[{"name":"Department of Computer Science \/ Southern Oregon University \/ Ashland \/ OR \/ USA"}]}],"member":"1696","reference":[{"issue":"4","key":"r1","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/0262-8856(83)90020-3","volume":"1","author":"Bell S.B.M.","year":"1983","journal-title":"Image and Vision Computing"},{"issue":"5","key":"r2","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1016\/0262-8856(91)90036-O","volume":"9","author":"Bell S.B.M.","year":"1991","journal-title":"Image and Vision Computing"},{"issue":"2","key":"r3","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1007\/s11430-017-9111-y","volume":"61","author":"Ben J.","year":"2018","journal-title":"Science China: Earth Sciences"},{"key":"r4","unstructured":"Brodsky, I. 2018. \u201cH3: Uber\u2019s Hexagonal Hierarchical Spatial Index.\u201d Available at https:\/\/eng.uber.com\/h3\/."},{"issue":"3","key":"r5","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1016\/0146-664X(80)90056-8","volume":"14","author":"Burt P.J.","year":"1980","journal-title":"Computer Graphics and Image Processing"},{"key":"r6","volume-title":"Central Places in Southern Germany","author":"Christaller W.","year":"1966"},{"key":"r7","unstructured":"Csillag, F. 1991. \u201cResolution Revisited.\u201d In Proceedings of the Tenth International Symposium on Computer-Assisted Cartography: Auto-Carto 10, ed. American Society for Photogrammetry and Remote Sensing and American Congress on Surveying and Mapping, 15\u201329. Bethesda, MD: American Society for Photogrammetry and Remote Sensing and American Congress on Surveying and Mapping."},{"issue":"2","key":"r8","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1080\/04353684.1965.11879288","volume":"47","author":"Dacey M.F.","year":"1965","journal-title":"Geografiska Annaler: Series B, Human Geography"},{"key":"r9","volume-title":"Spatial Data Processing Using Tesseral Methods: Collected Papers from Tesseral Workshops 1 and 2","author":"Diaz B.","year":"1986"},{"key":"r10","volume-title":"A Hierarchical Coordinate System for Geoprocessing and Cartography","author":"Dutton G.","year":"1999"},{"key":"r11","doi-asserted-by":"crossref","unstructured":"Fekete, G., and L. Treinish. 1990. \u201cSphere Quadtrees: A New Data Structure to Support Farrell, SPIE, and SPSE, 242\u201350. Bellingham, WA: SPIE.","DOI":"10.1117\/12.19991"},{"issue":"4","key":"r12","doi-asserted-by":"crossref","first-page":"605","DOI":"10.2307\/209914","volume":"33","author":"Fisher I.","year":"1943","journal-title":"Geographical Review"},{"key":"r13","volume-title":"Synergetics","author":"Fuller R.B","year":"1975"},{"issue":"12","key":"r14","doi-asserted-by":"crossref","first-page":"905","DOI":"10.1145\/358728.358741","volume":"25","author":"Gargantini I.","year":"1982","journal-title":"Communications of the ACM"},{"key":"r15","unstructured":"Gibson, L., and D. Lucas. 1982. \u201cSpatial Data Processing Using Generalized Balanced Ternary.\u201d In Proceedings of the IEEE Computer Society Conference on Pattern Recognition and Image Processing, 566\u201371. Piscataway, NJ: IEEE."},{"issue":"1","key":"r16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/19475683.2018.1424737","volume":"24","author":"Goodchild M.F.","year":"2018","journal-title":"Annals of GIS"},{"issue":"28","key":"r17","doi-asserted-by":"crossref","first-page":"11088","DOI":"10.1073\/pnas.1202383109","volume":"109","author":"Goodchild M.F.","year":"2012","journal-title":"Proceedings of the National Academy of Sciences of the United States of America"},{"issue":"3","key":"r18","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1016\/j.compenvurbsys.2008.03.001","volume":"32","author":"Kiester A.R.","year":"2008","journal-title":"Computers, Environment and Urban Systems"},{"key":"r19","volume-title":"The Art of Computer Programming","volume":"2","author":"Knuth D.","year":"1998"},{"key":"r20","unstructured":"Mark, D., and M.F. Goodchild. 1986. \u201cOn the Ordering of Two-Dimensional Space: Introduction and Relation to Tesseral Principles.\u201d In Spatial Data Processing Using Tesseral Methods: Collected Papers from Tesseral Workshops 1 and 2, ed. B. Diaz and S. Bell, 179\u201392. Reading, UK: Natural Environment Research Council."},{"key":"r21","unstructured":"Open Geospatial Consortium. 2017. \u201cTopic 21: Discrete Global Grid Systems Abstract Specification.\u201d Available at http:\/\/docs.opengeospatial.org\/as\/15-104r5\/15-104r5.html."},{"issue":"3","key":"r22","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1016\/j.compenvurbsys.2007.11.005","volume":"32","author":"Sahr K.","year":"2008","journal-title":"Computers, Environment and Urban Systems"},{"key":"r23","unstructured":"Sahr, K. 2010. \u201cCentral Place Indexing Systems.\u201d U.S. Patent 9,311,350, filed October 28, 2010, and issued April 12, 2016."},{"key":"r24","first-page":"363","volume":"22","author":"Sahr K.","year":"2011","journal-title":"Archives of Photogrammetry, Cartography and Remote Sensing"},{"issue":"2","key":"r25","first-page":"1","volume":"4","author":"Sahr K.","year":"2013","journal-title":"International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences"},{"key":"r26","unstructured":"Sahr, K. 2018a. \u201cDGGRID Users.\u201d Available at http:\/\/www.discreteglobalgrids.org\/dggrid-users\/."},{"key":"r27","unstructured":"Sahr, K. 2018b. \u201cDGGRID version 6.4: User Documentation for Discrete Global Grid Generation Software.\u201d Available at http:\/\/webpages.sou.edu\/~sahrk\/docs\/dggridManualV64.pdf."},{"key":"r28","unstructured":"Sahr, K., M. Dumas, and N. Chaudhuri. 2015. \u201cThe PlanetRisk Discrete Global Grid System.\u201d Available at https:\/\/webpages.sou.edu\/~sahrk\/docs\/PlanetRiskDGGS.pdf."},{"key":"r29","unstructured":"Sahr, K., and D. White. 2010. \u201cThe Superfund_500m Discrete Global Grid.\u201d Available at https:\/\/webpages.sou.edu\/~sahrk\/docs\/superfund_500m_020719.pdf."},{"issue":"2","key":"r30","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1559\/152304003100011090","volume":"30","author":"Sahr K.","year":"2003","journal-title":"Cartography and Geographic Information Science"},{"issue":"1","key":"r31","doi-asserted-by":"crossref","first-page":"10","DOI":"10.3138\/27H7-8K88-4882-1752","volume":"29","author":"Snyder J. P.","year":"1992","journal-title":"Cartographica"},{"key":"r32","doi-asserted-by":"crossref","unstructured":"Tong, X., J. Ben, and Y. Wang. 2010. \u201cA New Effective Hexagonal Discrete Global Grid System: Hexagonal Quad Balanced Structure.\u201d In Proceedings of the 18th International Conference on Geoinformatics, 1\u20136. Piscataway, NJ : IEEE.","DOI":"10.1109\/GEOINFORMATICS.2010.5567908"},{"key":"r33","unstructured":"Uber Technologies Inc. 2018. \u201cWalkthrough of h3ToGeoBoundary.\u201d Available at https:\/\/uber.github.io\/h3\/#\/documentation\/core-library\/walkthrough-of-h3togeoboundary."},{"issue":"7","key":"r34","first-page":"161","volume":"2","author":"Wang R.","year":"2017","journal-title":"International Archives of the Photogrammetry, Remote Sensing & Spatial Information Sciences"},{"issue":"1","key":"r35","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1559\/152304092783786636","volume":"19","author":"White D.","year":"1992","journal-title":"Cartography and Geographic Information Systems"}],"container-title":["Cartographica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/utppublishing.com\/doi\/pdf\/10.3138\/cart.54.1.2018-0022","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,13]],"date-time":"2025-03-13T12:52:39Z","timestamp":1741870359000},"score":1,"resource":{"primary":{"URL":"https:\/\/utppublishing.com\/doi\/10.3138\/cart.54.1.2018-0022"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3]]},"references-count":35,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,3]]}},"alternative-id":["10.3138\/cart.54.1.2018-0022"],"URL":"https:\/\/doi.org\/10.3138\/cart.54.1.2018-0022","relation":{},"ISSN":["0317-7173","1911-9925"],"issn-type":[{"value":"0317-7173","type":"print"},{"value":"1911-9925","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,3]]}}}