{"id":"https://openalex.org/W2145935788","doi":"https://doi.org/10.1109/cadcg.2009.5246889","title":"Unified subdivision generalizing 2- and 4-direction box splines","display_name":"Unified subdivision generalizing 2- and 4-direction box splines","publication_year":2009,"publication_date":"2009-08-01","ids":{"openalex":"https://openalex.org/W2145935788","doi":"https://doi.org/10.1109/cadcg.2009.5246889","mag":"2145935788"},"language":"en","primary_location":{"id":"doi:10.1109/cadcg.2009.5246889","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cadcg.2009.5246889","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 11th IEEE International Conference on Computer-Aided Design and Computer Graphics","raw_type":"proceedings-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/A5046869223","display_name":"Canjiang Ren","orcid":null},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]},{"id":"https://openalex.org/I90610280","display_name":"South China University of Technology","ror":"https://ror.org/0530pts50","country_code":"CN","type":"education","lineage":["https://openalex.org/I90610280"]}],"countries":["CN","HK"],"is_corresponding":true,"raw_author_name":"Canjiang Ren","raw_affiliation_strings":["Department of CSE, South China University of Technology, Guangzhou, China","Department of MEEM, City University of Hong Kong, Hong Kong, China"],"affiliations":[{"raw_affiliation_string":"Department of CSE, South China University of Technology, Guangzhou, China","institution_ids":["https://openalex.org/I90610280"]},{"raw_affiliation_string":"Department of MEEM, City University of Hong Kong, Hong Kong, China","institution_ids":["https://openalex.org/I168719708"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067363489","display_name":"Guiqing Li","orcid":"https://orcid.org/0000-0002-4598-1522"},"institutions":[{"id":"https://openalex.org/I90610280","display_name":"South China University of Technology","ror":"https://ror.org/0530pts50","country_code":"CN","type":"education","lineage":["https://openalex.org/I90610280"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guiqing Li","raw_affiliation_strings":["Department of CSE, South China University of Technology, Guangzhou, China"],"affiliations":[{"raw_affiliation_string":"Department of CSE, South China University of Technology, Guangzhou, China","institution_ids":["https://openalex.org/I90610280"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053587889","display_name":"Weiyin Ma","orcid":"https://orcid.org/0000-0001-9760-7789"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Weiyin Ma","raw_affiliation_strings":["Department of MEEM, City University of Hong Kong, Hong Kong, China"],"affiliations":[{"raw_affiliation_string":"Department of MEEM, City University of Hong Kong, Hong Kong, China","institution_ids":["https://openalex.org/I168719708"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5046869223"],"corresponding_institution_ids":["https://openalex.org/I168719708","https://openalex.org/I90610280"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.18484483,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"292","last_page":"299"},"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/T10188","display_name":"Advanced machining processes and optimization","score":0.9753000140190125,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9524000287055969,"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","display_name":"Subdivision","score":0.9367853403091431},{"id":"https://openalex.org/keywords/box-spline","display_name":"Box spline","score":0.7742983102798462},{"id":"https://openalex.org/keywords/subdivision-surface","display_name":"Subdivision surface","score":0.7346442937850952},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6783177852630615},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.585925817489624},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5518664121627808},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5019321441650391},{"id":"https://openalex.org/keywords/box-model","display_name":"Box model","score":0.43287256360054016},{"id":"https://openalex.org/keywords/spline","display_name":"Spline (mechanical)","score":0.42655065655708313},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.42039626836776733},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39274686574935913},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3706528842449188},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3429032266139984},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics (images)","score":0.19114020466804504},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.0993693470954895},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.08435770869255066},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07783478498458862},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.0734337866306305},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.06446659564971924}],"concepts":[{"id":"https://openalex.org/C143392562","wikidata":"https://www.wikidata.org/wiki/Q449111","display_name":"Subdivision","level":2,"score":0.9367853403091431},{"id":"https://openalex.org/C78383375","wikidata":"https://www.wikidata.org/wiki/Q4951620","display_name":"Box spline","level":4,"score":0.7742983102798462},{"id":"https://openalex.org/C199686383","wikidata":"https://www.wikidata.org/wiki/Q1529124","display_name":"Subdivision surface","level":3,"score":0.7346442937850952},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6783177852630615},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.585925817489624},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5518664121627808},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5019321441650391},{"id":"https://openalex.org/C2992995325","wikidata":"https://www.wikidata.org/wiki/Q4951592","display_name":"Box model","level":2,"score":0.43287256360054016},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.42655065655708313},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.42039626836776733},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39274686574935913},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3706528842449188},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3429032266139984},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.19114020466804504},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0993693470954895},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.08435770869255066},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07783478498458862},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0734337866306305},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.06446659564971924},{"id":"https://openalex.org/C147176958","wikidata":"https://www.wikidata.org/wiki/Q77590","display_name":"Civil engineering","level":1,"score":0.0},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0},{"id":"https://openalex.org/C31447003","wikidata":"https://www.wikidata.org/wiki/Q545002","display_name":"Spline interpolation","level":3,"score":0.0},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cadcg.2009.5246889","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cadcg.2009.5246889","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 11th IEEE International Conference on Computer-Aided Design and Computer Graphics","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W126840538","https://openalex.org/W1528814089","https://openalex.org/W1531573944","https://openalex.org/W1966495409","https://openalex.org/W2001562259","https://openalex.org/W2017068862","https://openalex.org/W2020263524","https://openalex.org/W2032325716","https://openalex.org/W2043571611","https://openalex.org/W2068264968","https://openalex.org/W2084023406","https://openalex.org/W2091620062","https://openalex.org/W2094963988","https://openalex.org/W2127372291","https://openalex.org/W2167979983"],"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/W2370429828","https://openalex.org/W2415051010","https://openalex.org/W2145935788","https://openalex.org/W2953374956","https://openalex.org/W4321104946"],"abstract_inverted_index":{"This":[0],"paper":[1],"applies":[2],"a":[3,27,41,50,59],"modified":[4],"composite":[5],"radic(2)":[6],"subdivision":[7,32,53],"framework":[8,72],"to":[9,22],"an":[10],"extensive":[11],"family":[12],"of":[13,29,33,44,61],"box":[14,20,64],"splines,":[15],"and":[16,35,79],"therefore":[17],"generalizes":[18],"these":[19],"splines":[21],"irregular":[23],"control":[24],"meshes.":[25],"Particularly,":[26],"variant":[28],"the":[30,45,67,70],"quad":[31],"Peters":[34],"Shiue":[36],"(2004)":[37],"is":[38,55,73],"shown":[39],"as":[40,58],"special":[42,63],"case":[43],"new":[46,51],"framework.":[47],"In":[48],"addition,":[49],"dual":[52],"scheme":[54],"also":[56,74],"derived,":[57],"generalization":[60],"some":[62],"splines.":[65],"Towards":[66],"practical":[68],"use,":[69],"unified":[71],"extended":[75],"for":[76],"modelling":[77],"boundary":[78],"crease":[80],"features.":[81]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
