{"id":"https://openalex.org/W2030362796","doi":"https://doi.org/10.1137/060669759","title":"Smoothness Analysis of Subdivision Schemes on Regular Grids by Proximity","display_name":"Smoothness Analysis of Subdivision Schemes on Regular Grids by Proximity","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2030362796","doi":"https://doi.org/10.1137/060669759","mag":"2030362796"},"language":"en","primary_location":{"id":"doi:10.1137/060669759","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060669759","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","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/A5023888160","display_name":"Philipp Grohs","orcid":"https://orcid.org/0000-0001-9205-0969"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Philipp Grohs","raw_affiliation_strings":["grohs@geometrie.tuwien.ac.at#TAB#"],"affiliations":[{"raw_affiliation_string":"grohs@geometrie.tuwien.ac.at#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5023888160"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.966,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.95493051,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"46","issue":"4","first_page":"2169","last_page":"2182"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":1.0,"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":1.0,"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":0.9959999918937683,"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9958000183105469,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/subdivision","display_name":"Subdivision","score":0.9320799112319946},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.8575581908226013},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7519292831420898},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5922892093658447},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.5710694193840027},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5572618246078491},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.4541782736778259},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.43817681074142456},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4054623246192932},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37166810035705566},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34074950218200684},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3225868344306946},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1789267361164093}],"concepts":[{"id":"https://openalex.org/C143392562","wikidata":"https://www.wikidata.org/wiki/Q449111","display_name":"Subdivision","level":2,"score":0.9320799112319946},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.8575581908226013},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7519292831420898},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5922892093658447},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5710694193840027},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5572618246078491},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.4541782736778259},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.43817681074142456},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4054623246192932},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37166810035705566},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34074950218200684},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3225868344306946},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1789267361164093},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/060669759","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060669759","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.143.8077","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.143.8077","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.dmg.tuwien.ac.at/geom/grohs/sassrg.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.187.3055","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.187.3055","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.geometrie.tuwien.ac.at/grohs/papers/sassrg.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W20914128","https://openalex.org/W1528814089","https://openalex.org/W1587069887","https://openalex.org/W2030136249","https://openalex.org/W2034940548","https://openalex.org/W2043571611","https://openalex.org/W2043809413","https://openalex.org/W2044060118","https://openalex.org/W2057217736","https://openalex.org/W2057823172","https://openalex.org/W2060971311","https://openalex.org/W2064445894","https://openalex.org/W2075492994","https://openalex.org/W2096610373","https://openalex.org/W2126142334","https://openalex.org/W2157787988","https://openalex.org/W2341241031","https://openalex.org/W4242771523"],"related_works":["https://openalex.org/W2384806462","https://openalex.org/W4389950792","https://openalex.org/W2375549870","https://openalex.org/W1994442929","https://openalex.org/W2791987989","https://openalex.org/W2076215172","https://openalex.org/W1819043602","https://openalex.org/W4296528831","https://openalex.org/W2952407034","https://openalex.org/W2292573552"],"abstract_inverted_index":{"Subdivision":[0,78],"is":[1,47,65,71,99,134],"a":[2,7,12,34,49,54,96,101,112,139,146,177],"powerful":[3],"way":[4,129],"of":[5,18,66,111,130,176,180],"approximating":[6],"continuous":[8,59],"object":[9,60],"$f(x,y)$":[10,61],"by":[11,63],"sequence":[13],"$(":[14],"(S^lp_{i,j})_{i,j\\in":[15],"\\mathbb{Z}})_{l\\in":[16],"\\mathbb{N}}$":[17],"discrete":[19],"data":[20,92,108],"on":[21,33,41],"finer":[22,24,44],"and":[23,123,143],"grids.":[25],"The":[26,166],"rule":[27],"S":[28,57,64,70],"that":[29,158],"maps":[30],"an":[31],"approximation":[32,40],"coarse":[35],"grid":[36,45],"$S^lp$":[37],"to":[38,73,126,135,138,144,172],"the":[39,42,91,151,159,163,174],"next":[43],"$S^{l+1}p$":[46],"called":[48],"subdivision":[50,119],"scheme.":[51],"If":[52],"for":[53,88],"given":[55,140],"scheme":[56,142],"every":[58],"constructed":[62],"$C^k$":[67],"smoothness,":[68],"then":[69],"said":[72],"have":[74,93],"smoothness":[75],"order":[76],"k.":[77],"schemes":[79,120,133,161],"are":[80,85,109],"well":[81],"understood":[82],"if":[83],"they":[84],"linear.":[86],"However,":[87],"various":[89],"applications":[90],"values":[94],"in":[95,156],"manifold":[97],"which":[98,154],"not":[100],"vector":[102],"space":[103],"(for":[104],"example,":[105],"when":[106],"our":[107],"positions":[110],"moving":[113],"rigid":[114],"body).":[115],"Under":[116],"these":[117],"circumstances,":[118],"become":[121],"nonlinear":[122,181],"much":[124],"harder":[125],"analyze.":[127],"One":[128],"analyzing":[131],"such":[132],"relate":[136],"them":[137],"linear":[141],"establish":[145],"so-called":[147],"proximity":[148],"condition":[149],"between":[150],"two":[152,160],"schemes,":[153],"helps":[155],"proving":[157],"share":[162],"same":[164],"smoothness.":[165],"present":[167],"paper":[168],"uses":[169],"this":[170],"method":[171],"show":[173],"$C^1$-smoothness":[175],"wide":[178],"class":[179],"multivariate":[182],"schemes.":[183]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}