{"id":"https://openalex.org/W2020570805","doi":"https://doi.org/10.1111/1467-8659.t01-1-00605","title":"Slow Growing Subdivision (SGS) in Any Dimension: Towards Removing the Curse of Dimensionality","display_name":"Slow Growing Subdivision (SGS) in Any Dimension: Towards Removing the Curse of Dimensionality","publication_year":2002,"publication_date":"2002-09-01","ids":{"openalex":"https://openalex.org/W2020570805","doi":"https://doi.org/10.1111/1467-8659.t01-1-00605","mag":"2020570805"},"language":"en","primary_location":{"id":"doi:10.1111/1467-8659.t01-1-00605","is_oa":false,"landing_page_url":"https://doi.org/10.1111/1467-8659.t01-1-00605","pdf_url":null,"source":{"id":"https://openalex.org/S67831204","display_name":"Computer Graphics Forum","issn_l":"0167-7055","issn":["0167-7055","1467-8659"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer Graphics Forum","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009460413","display_name":"Valerio Pascucci","orcid":"https://orcid.org/0000-0002-8877-2042"},"institutions":[{"id":"https://openalex.org/I1282311441","display_name":"Lawrence Livermore National Laboratory","ror":"https://ror.org/041nk4h53","country_code":"US","type":"facility","lineage":["https://openalex.org/I1282311441","https://openalex.org/I1330989302","https://openalex.org/I198811213","https://openalex.org/I4210138311"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"V. Pascucci","raw_affiliation_strings":["Center for Applied Scientific Computing\n Lawrence Livermore National Laboratory, Livermore, CA","\u2020 This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract no. W-7405-Eng-48"],"affiliations":[{"raw_affiliation_string":"Center for Applied Scientific Computing\n Lawrence Livermore National Laboratory, Livermore, CA","institution_ids":["https://openalex.org/I1282311441"]},{"raw_affiliation_string":"\u2020 This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract no. W-7405-Eng-48","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5009460413"],"corresponding_institution_ids":["https://openalex.org/I1282311441"],"apc_list":{"value":3710,"currency":"USD","value_usd":3710},"apc_paid":null,"fwci":9.2858,"has_fulltext":false,"cited_by_count":46,"citation_normalized_percentile":{"value":0.9838288,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"21","issue":"3","first_page":"451","last_page":"460"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9983000159263611,"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"}},{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9973999857902527,"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/subdivision-surface","display_name":"Subdivision surface","score":0.8601300120353699},{"id":"https://openalex.org/keywords/subdivision","display_name":"Subdivision","score":0.8123204112052917},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.8076655864715576},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.646580696105957},{"id":"https://openalex.org/keywords/t-vertices","display_name":"T-vertices","score":0.4898928999900818},{"id":"https://openalex.org/keywords/mesh-generation","display_name":"Mesh generation","score":0.46634289622306824},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics","score":0.45532655715942383},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.43597540259361267},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4221591353416443},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.4199162423610687},{"id":"https://openalex.org/keywords/graphics-hardware","display_name":"Graphics hardware","score":0.41912198066711426},{"id":"https://openalex.org/keywords/visualization","display_name":"Visualization","score":0.41654539108276367},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39179107546806335},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3792528808116913},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics (images)","score":0.3151480555534363},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.31047937273979187},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.22277739644050598},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.20282068848609924},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1633644998073578}],"concepts":[{"id":"https://openalex.org/C199686383","wikidata":"https://www.wikidata.org/wiki/Q1529124","display_name":"Subdivision surface","level":3,"score":0.8601300120353699},{"id":"https://openalex.org/C143392562","wikidata":"https://www.wikidata.org/wiki/Q449111","display_name":"Subdivision","level":2,"score":0.8123204112052917},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.8076655864715576},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.646580696105957},{"id":"https://openalex.org/C160403270","wikidata":"https://www.wikidata.org/wiki/Q7667943","display_name":"T-vertices","level":4,"score":0.4898928999900818},{"id":"https://openalex.org/C181145010","wikidata":"https://www.wikidata.org/wiki/Q4418033","display_name":"Mesh generation","level":3,"score":0.46634289622306824},{"id":"https://openalex.org/C77660652","wikidata":"https://www.wikidata.org/wiki/Q150971","display_name":"Computer graphics","level":2,"score":0.45532655715942383},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.43597540259361267},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4221591353416443},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.4199162423610687},{"id":"https://openalex.org/C18945957","wikidata":"https://www.wikidata.org/wiki/Q5597193","display_name":"Graphics hardware","level":3,"score":0.41912198066711426},{"id":"https://openalex.org/C36464697","wikidata":"https://www.wikidata.org/wiki/Q451553","display_name":"Visualization","level":2,"score":0.41654539108276367},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39179107546806335},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3792528808116913},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.3151480555534363},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31047937273979187},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.22277739644050598},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.20282068848609924},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1633644998073578},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1111/1467-8659.t01-1-00605","is_oa":false,"landing_page_url":"https://doi.org/10.1111/1467-8659.t01-1-00605","pdf_url":null,"source":{"id":"https://openalex.org/S67831204","display_name":"Computer Graphics Forum","issn_l":"0167-7055","issn":["0167-7055","1467-8659"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer Graphics Forum","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W1494985239","https://openalex.org/W1504064795","https://openalex.org/W1966495409","https://openalex.org/W1976731160","https://openalex.org/W1989850389","https://openalex.org/W1994030546","https://openalex.org/W1998372843","https://openalex.org/W2012909180","https://openalex.org/W2016040834","https://openalex.org/W2022408614","https://openalex.org/W2025398554","https://openalex.org/W2028576613","https://openalex.org/W2032325716","https://openalex.org/W2043571611","https://openalex.org/W2056816721","https://openalex.org/W2058478206","https://openalex.org/W2063305179","https://openalex.org/W2065661959","https://openalex.org/W2072067430","https://openalex.org/W2081357081","https://openalex.org/W2099787816","https://openalex.org/W2159938896","https://openalex.org/W2163324644","https://openalex.org/W2170716456","https://openalex.org/W2232880714","https://openalex.org/W2237767100","https://openalex.org/W2237825899","https://openalex.org/W3022636055","https://openalex.org/W3149831928","https://openalex.org/W4238792553","https://openalex.org/W4249479708","https://openalex.org/W6644595922","https://openalex.org/W6647704911","https://openalex.org/W6656096504","https://openalex.org/W6656671217","https://openalex.org/W6664794628","https://openalex.org/W6668541951"],"related_works":["https://openalex.org/W2387884585","https://openalex.org/W2365894372","https://openalex.org/W646807382","https://openalex.org/W2078248985","https://openalex.org/W2377450293","https://openalex.org/W2359772210","https://openalex.org/W2041572753","https://openalex.org/W2165448222","https://openalex.org/W2393452129","https://openalex.org/W2026887492"],"abstract_inverted_index":{"In":[0,76],"recent":[1],"years":[2],"subdivision":[3,90,115,234],"methods":[4],"have":[5,154],"been":[6],"one":[7],"of":[8,20,38,57,61,69,72,85,106,113,121,129,135,149,162,181,195,199,211],"the":[9,15,27,55,58,62,67,70,73,82,86,101,119,127,130,136,147,150,179,182,190,196,200,209],"most":[10],"successful":[11],"techniques":[12,25,205],"applied":[13,177],"to":[14,26,94,178,185,219],"multi-resolution":[16],"representation":[17],"and":[18,45,65,96,158,215,228],"visualization":[19,44],"surface":[21],"meshes.":[22],"Extension":[23],"these":[24],"volumetric":[28],"case":[29],"would":[30],"enable":[31],"their":[32],"use":[33,170],"in":[34,54,66],"a":[35,89,171],"broad":[36],"class":[37],"applications":[39],"including":[40],"solid":[41],"modeling,":[42],"scientific":[43],"mesh":[46,137,183],"generation.":[47],"Unfortunately,":[48],"major":[49],"challenges":[50],"remain":[51],"unsolved":[52],"both":[53],"generalization":[56],"combinatorial":[59],"structure":[60],"refinement":[63,122,134],"procedure":[64,116],"analysis":[68,204],"smoothness":[71,198],"limit":[74,197],"mesh.":[75,191],"this":[77,212],"paper":[78],"we":[79],"mainly":[80],"tackle":[81],"first":[83],"part":[84],"problem":[87],"introducing":[88,141],"scheme":[91],"that":[92,175,206],"generalizes":[93],"3D":[95],"higher":[97],"dimensional":[98],"meshes":[99,152],"without":[100,140],"excessive":[102],"vertex":[103],"proliferation":[104],"typical":[105],"tensor-product":[107],"refinements.":[108],"The":[109,192],"main":[110],"four":[111],"qualities":[112],"our":[114],"are:":[117],"(i)":[118],"rate":[120],"does":[123],"not":[124],"grow":[125],"with":[126],"dimension":[128],"mesh,":[131],"(ii)":[132],"adaptive":[133],"is":[138,176],"possible":[139],"special":[142],"temporary":[143],"cell":[144],"decompositions,":[145],"(iii)":[146],"cells":[148],"base":[151],"can":[153,165],"virtually":[155],"unrestricted":[156],"topology,":[157],"(iv)":[159],"``sharp''":[160],"features":[161],"different":[163],"dimensions":[164],"be":[166],"incorporated":[167],"naturally.":[168],"We":[169],"narrow":[172],"averaging":[173],"mask":[174],"vertices":[180],"and/or":[184],"eventual":[186],"functions":[187],"defined":[188],"on":[189],"general":[193],"study":[194],"approach":[201],"requires":[202],"new":[203],"are":[207],"beyond":[208],"scope":[210],"paper.":[213],"Categories":[214],"Subject":[216],"Descriptors":[217],"(according":[218],"ACM":[220],"CCS):":[221],"I.3.5":[222],"[Computer":[223],"Graphics]:":[224],"Curve,":[225],"surface,":[226],"solid,":[227],"object":[229],"representations.":[230],"Volumetric":[231],"meshes,":[232],"recursive":[233],"methods.":[235]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
