{"id":"https://openalex.org/W3015720563","doi":"https://doi.org/10.3390/ijgi9040233","title":"General Method for Extending Discrete Global Grid Systems to Three Dimensions","display_name":"General Method for Extending Discrete Global Grid Systems to Three Dimensions","publication_year":2020,"publication_date":"2020-04-10","ids":{"openalex":"https://openalex.org/W3015720563","doi":"https://doi.org/10.3390/ijgi9040233","mag":"3015720563"},"language":"en","primary_location":{"id":"doi:10.3390/ijgi9040233","is_oa":true,"landing_page_url":"https://doi.org/10.3390/ijgi9040233","pdf_url":"https://www.mdpi.com/2220-9964/9/4/233/pdf?version=1586506220","source":{"id":"https://openalex.org/S2764431341","display_name":"ISPRS International Journal of Geo-Information","issn_l":"2220-9964","issn":["2220-9964"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ISPRS International Journal of Geo-Information","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2220-9964/9/4/233/pdf?version=1586506220","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019635236","display_name":"Benjamin Ulmer","orcid":"https://orcid.org/0000-0002-2387-8778"},"institutions":[{"id":"https://openalex.org/I168635309","display_name":"University of Calgary","ror":"https://ror.org/03yjb2x39","country_code":"CA","type":"education","lineage":["https://openalex.org/I168635309"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Benjamin Ulmer","raw_affiliation_strings":["Department of Computer Science, University of Calgary, Calgary, AB T2N 1N4, Canada"],"raw_orcid":"https://orcid.org/0000-0002-2387-8778","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Calgary, Calgary, AB T2N 1N4, Canada","institution_ids":["https://openalex.org/I168635309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073866991","display_name":"John Hall","orcid":"https://orcid.org/0000-0003-3861-1387"},"institutions":[{"id":"https://openalex.org/I168635309","display_name":"University of Calgary","ror":"https://ror.org/03yjb2x39","country_code":"CA","type":"education","lineage":["https://openalex.org/I168635309"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"John Hall","raw_affiliation_strings":["Department of Computer Science, University of Calgary, Calgary, AB T2N 1N4, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Calgary, Calgary, AB T2N 1N4, Canada","institution_ids":["https://openalex.org/I168635309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074643777","display_name":"Faramarz Samavati","orcid":"https://orcid.org/0000-0001-9440-7562"},"institutions":[{"id":"https://openalex.org/I168635309","display_name":"University of Calgary","ror":"https://ror.org/03yjb2x39","country_code":"CA","type":"education","lineage":["https://openalex.org/I168635309"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Faramarz Samavati","raw_affiliation_strings":["Department of Computer Science, University of Calgary, Calgary, AB T2N 1N4, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Calgary, Calgary, AB T2N 1N4, Canada","institution_ids":["https://openalex.org/I168635309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5019635236"],"corresponding_institution_ids":["https://openalex.org/I168635309"],"apc_list":{"value":1700,"currency":"CHF","value_usd":1893},"apc_paid":{"value":1700,"currency":"CHF","value_usd":1893},"fwci":0.6712,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.72618093,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"9","issue":"4","first_page":"233","last_page":"233"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10715","display_name":"Distributed and Parallel Computing Systems","score":0.9921000003814697,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10715","display_name":"Distributed and Parallel Computing Systems","score":0.9921000003814697,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11106","display_name":"Data Management and Algorithms","score":0.9915000200271606,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9702000021934509,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/geospatial-analysis","display_name":"Geospatial analysis","score":0.8055559992790222},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7629369497299194},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.7130791544914246},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5753107666969299},{"id":"https://openalex.org/keywords/encoding","display_name":"Encoding (memory)","score":0.5250375270843506},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.4984753131866455},{"id":"https://openalex.org/keywords/component","display_name":"Component (thermodynamics)","score":0.49836087226867676},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4592123031616211},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.4561365246772766},{"id":"https://openalex.org/keywords/search-engine-indexing","display_name":"Search engine indexing","score":0.43774980306625366},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.4362357258796692},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.4305139482021332},{"id":"https://openalex.org/keywords/distributed-computing","display_name":"Distributed computing","score":0.3831520676612854},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3576212227344513},{"id":"https://openalex.org/keywords/information-retrieval","display_name":"Information retrieval","score":0.2009732723236084},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.18256723880767822},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.12916076183319092},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.11897021532058716},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.09646978974342346},{"id":"https://openalex.org/keywords/cartography","display_name":"Cartography","score":0.08840516209602356}],"concepts":[{"id":"https://openalex.org/C9770341","wikidata":"https://www.wikidata.org/wiki/Q1938983","display_name":"Geospatial analysis","level":2,"score":0.8055559992790222},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7629369497299194},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.7130791544914246},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5753107666969299},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.5250375270843506},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4984753131866455},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.49836087226867676},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4592123031616211},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.4561365246772766},{"id":"https://openalex.org/C75165309","wikidata":"https://www.wikidata.org/wiki/Q2258979","display_name":"Search engine indexing","level":2,"score":0.43774980306625366},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.4362357258796692},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4305139482021332},{"id":"https://openalex.org/C120314980","wikidata":"https://www.wikidata.org/wiki/Q180634","display_name":"Distributed computing","level":1,"score":0.3831520676612854},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3576212227344513},{"id":"https://openalex.org/C23123220","wikidata":"https://www.wikidata.org/wiki/Q816826","display_name":"Information retrieval","level":1,"score":0.2009732723236084},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.18256723880767822},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.12916076183319092},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.11897021532058716},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.09646978974342346},{"id":"https://openalex.org/C58640448","wikidata":"https://www.wikidata.org/wiki/Q42515","display_name":"Cartography","level":1,"score":0.08840516209602356},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/ijgi9040233","is_oa":true,"landing_page_url":"https://doi.org/10.3390/ijgi9040233","pdf_url":"https://www.mdpi.com/2220-9964/9/4/233/pdf?version=1586506220","source":{"id":"https://openalex.org/S2764431341","display_name":"ISPRS International Journal of Geo-Information","issn_l":"2220-9964","issn":["2220-9964"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ISPRS International Journal of Geo-Information","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:d867285af501462ea422a329982262c6","is_oa":true,"landing_page_url":"https://doaj.org/article/d867285af501462ea422a329982262c6","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISPRS International Journal of Geo-Information, Vol 9, Iss 4, p 233 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2220-9964/9/4/233/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/ijgi9040233","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISPRS International Journal of Geo-Information","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/ijgi9040233","is_oa":true,"landing_page_url":"https://doi.org/10.3390/ijgi9040233","pdf_url":"https://www.mdpi.com/2220-9964/9/4/233/pdf?version=1586506220","source":{"id":"https://openalex.org/S2764431341","display_name":"ISPRS International Journal of Geo-Information","issn_l":"2220-9964","issn":["2220-9964"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ISPRS International Journal of Geo-Information","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3015720563.pdf","grobid_xml":"https://content.openalex.org/works/W3015720563.grobid-xml"},"referenced_works_count":51,"referenced_works":["https://openalex.org/W239093348","https://openalex.org/W1483854707","https://openalex.org/W1560515057","https://openalex.org/W1607838784","https://openalex.org/W1975843409","https://openalex.org/W1976579441","https://openalex.org/W1999515312","https://openalex.org/W2001703222","https://openalex.org/W2019762032","https://openalex.org/W2021160366","https://openalex.org/W2036409086","https://openalex.org/W2041300256","https://openalex.org/W2043375425","https://openalex.org/W2050812123","https://openalex.org/W2059802632","https://openalex.org/W2073431990","https://openalex.org/W2100773375","https://openalex.org/W2102635905","https://openalex.org/W2108039971","https://openalex.org/W2121462356","https://openalex.org/W2126165613","https://openalex.org/W2141944896","https://openalex.org/W2154327689","https://openalex.org/W2158142242","https://openalex.org/W2161460589","https://openalex.org/W2249958740","https://openalex.org/W2254454951","https://openalex.org/W2336991609","https://openalex.org/W2366872416","https://openalex.org/W2469144144","https://openalex.org/W2737926820","https://openalex.org/W2783777795","https://openalex.org/W2801993148","https://openalex.org/W2887173468","https://openalex.org/W2894323699","https://openalex.org/W2909812584","https://openalex.org/W2944590302","https://openalex.org/W2948909614","https://openalex.org/W2950080363","https://openalex.org/W2950100951","https://openalex.org/W2962117144","https://openalex.org/W2962855493","https://openalex.org/W2983403820","https://openalex.org/W2997077762","https://openalex.org/W3098507781","https://openalex.org/W3121813492","https://openalex.org/W4253655042","https://openalex.org/W6609269711","https://openalex.org/W6675760076","https://openalex.org/W6720181838","https://openalex.org/W6784716844"],"related_works":["https://openalex.org/W2004086023","https://openalex.org/W4367313141","https://openalex.org/W2733999579","https://openalex.org/W2910751785","https://openalex.org/W2110217573","https://openalex.org/W4366547507","https://openalex.org/W4283374591","https://openalex.org/W4387891126","https://openalex.org/W1595427329","https://openalex.org/W1848641581"],"abstract_inverted_index":{"Geospatial":[0],"sensors":[1],"are":[2,16,43],"generating":[3],"increasing":[4],"amounts":[5],"of":[6,118,126,132,189],"three-dimensional":[7],"(3D)":[8],"data.":[9,31],"While":[10],"Discrete":[11],"Global":[12],"Grid":[13],"Systems":[14],"(DGGS)":[15],"a":[17,54,69,100,127,130,141,148],"useful":[18],"tool":[19],"for":[20,29,115,162,186],"integrating":[21],"geospatial":[22],"data,":[23],"they":[24],"provide":[25],"no":[26],"native":[27],"support":[28,185],"3D":[30,34,70,111,124,159,176],"Several":[32],"different":[33,158],"global":[35,177],"grids":[36,178],"have":[37],"been":[38],"proposed;":[39],"however,":[40],"these":[41],"approaches":[42],"not":[44],"consistent":[45],"with":[46],"state-of-the-art":[47],"DGGSs.":[48],"In":[49],"this":[50],"paper,":[51],"we":[52,134],"propose":[53],"general":[55],"method":[56,154],"that":[57,102,139],"can":[58,82],"extend":[59],"any":[60,79],"DGGS":[61,81,108],"to":[62,66,77,173],"the":[63,106,110,121],"third":[64],"dimension":[65],"operate":[67],"as":[68,144,184],"DGGS.":[71,128,150],"This":[72],"extension":[73],"is":[74],"done":[75],"carefully":[76],"ensure":[78],"valid":[80],"be":[83],"supported,":[84],"including":[85],"all":[86],"refinement":[87],"factors":[88],"and":[89,96,109,123,195],"non-congruent":[90],"refinement.":[91],"We":[92,151],"define":[93],"encoding,":[94],"decoding,":[95],"indexing":[97],"operations":[98],"in":[99,147],"way":[101],"splits":[103],"responsibility":[104],"between":[105,120,193],"surface":[107],"component,":[112],"which":[113],"allows":[114],"easy":[116],"transference":[117],"data":[119],"2D":[122],"versions":[125],"As":[129],"part":[131],"this,":[133],"use":[135,165,168],"radial":[136],"mapping":[137],"functions":[138],"serve":[140],"similar":[142],"purpose":[143],"polyhedral":[145],"projection":[146],"conventional":[149],"validate":[152],"our":[153,171],"by":[155],"creating":[156],"three":[157,163],"DGGSs":[160],"tailored":[161],"specific":[164],"cases.":[166],"These":[167],"cases":[169],"demonstrate":[170],"ability":[172],"quickly":[174],"generate":[175],"while":[179],"achieving":[180],"desired":[181],"properties":[182],"such":[183],"large":[187],"ranges":[188],"altitudes,":[190],"volume":[191],"preservation":[192],"cells,":[194],"custom":[196],"cell":[197],"aspect":[198],"ratio.":[199]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":2}],"updated_date":"2026-08-10T07:06:39.071514","created_date":"2025-10-10T00:00:00"}