{"id":"https://openalex.org/W2041765521","doi":"https://doi.org/10.1145/2661229.2661270","title":"Skinning cubic B\u00e9zier splines and Catmull-Clark subdivision surfaces","display_name":"Skinning cubic B\u00e9zier splines and Catmull-Clark subdivision surfaces","publication_year":2014,"publication_date":"2014-11-18","ids":{"openalex":"https://openalex.org/W2041765521","doi":"https://doi.org/10.1145/2661229.2661270","mag":"2041765521"},"language":"en","primary_location":{"id":"doi:10.1145/2661229.2661270","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2661229.2661270","pdf_url":null,"source":{"id":"https://openalex.org/S185367456","display_name":"ACM Transactions on Graphics","issn_l":"0730-0301","issn":["0730-0301","1557-7368"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Graphics","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/A5051846523","display_name":"Songrun Liu","orcid":"https://orcid.org/0000-0003-4846-8932"},"institutions":[{"id":"https://openalex.org/I162714631","display_name":"George Mason University","ror":"https://ror.org/02jqj7156","country_code":"US","type":"education","lineage":["https://openalex.org/I162714631"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Songrun Liu","raw_affiliation_strings":["George Mason University"],"affiliations":[{"raw_affiliation_string":"George Mason University","institution_ids":["https://openalex.org/I162714631"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060647975","display_name":"Alec Jacobson","orcid":"https://orcid.org/0000-0003-4603-7143"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alec Jacobson","raw_affiliation_strings":["Columbia University"],"affiliations":[{"raw_affiliation_string":"Columbia University","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036366808","display_name":"Yotam Gingold","orcid":"https://orcid.org/0000-0002-5381-2104"},"institutions":[{"id":"https://openalex.org/I162714631","display_name":"George Mason University","ror":"https://ror.org/02jqj7156","country_code":"US","type":"education","lineage":["https://openalex.org/I162714631"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yotam Gingold","raw_affiliation_strings":["George Mason University"],"affiliations":[{"raw_affiliation_string":"George Mason University","institution_ids":["https://openalex.org/I162714631"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5051846523"],"corresponding_institution_ids":["https://openalex.org/I162714631"],"apc_list":null,"apc_paid":null,"fwci":2.523,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.88067239,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"33","issue":"6","first_page":"1","last_page":"9"},"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9991999864578247,"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/T10531","display_name":"Advanced Vision and Imaging","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/skinning","display_name":"Skinning","score":0.9771453142166138},{"id":"https://openalex.org/keywords/b\u00e9zier-curve","display_name":"B\u00e9zier curve","score":0.7171587347984314},{"id":"https://openalex.org/keywords/subdivision","display_name":"Subdivision","score":0.631098210811615},{"id":"https://openalex.org/keywords/subdivision-surface","display_name":"Subdivision surface","score":0.604689359664917},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5428043603897095},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics (images)","score":0.5374525189399719},{"id":"https://openalex.org/keywords/animation","display_name":"Animation","score":0.5219963788986206},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39016789197921753},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3749952018260956},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3440369963645935},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.08152133226394653}],"concepts":[{"id":"https://openalex.org/C2777685762","wikidata":"https://www.wikidata.org/wiki/Q780654","display_name":"Skinning","level":2,"score":0.9771453142166138},{"id":"https://openalex.org/C206423108","wikidata":"https://www.wikidata.org/wiki/Q214728","display_name":"B\u00e9zier curve","level":2,"score":0.7171587347984314},{"id":"https://openalex.org/C143392562","wikidata":"https://www.wikidata.org/wiki/Q449111","display_name":"Subdivision","level":2,"score":0.631098210811615},{"id":"https://openalex.org/C199686383","wikidata":"https://www.wikidata.org/wiki/Q1529124","display_name":"Subdivision surface","level":3,"score":0.604689359664917},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5428043603897095},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.5374525189399719},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.5219963788986206},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39016789197921753},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3749952018260956},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3440369963645935},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.08152133226394653},{"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/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2661229.2661270","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2661229.2661270","pdf_url":null,"source":{"id":"https://openalex.org/S185367456","display_name":"ACM Transactions on Graphics","issn_l":"0730-0301","issn":["0730-0301","1557-7368"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Graphics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.7599999904632568}],"awards":[{"id":"https://openalex.org/G6665073100","display_name":null,"funder_award_id":"IIS-1451198","funder_id":"https://openalex.org/F4320337389","funder_display_name":"Division of Information and Intelligent Systems"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320307102","display_name":"Intel Corporation","ror":"https://ror.org/01ek73717"},{"id":"https://openalex.org/F4320307897","display_name":"Autodesk","ror":"https://ror.org/00pkt4594"},{"id":"https://openalex.org/F4320308011","display_name":"Walt Disney Company","ror":"https://ror.org/04eg47h42"},{"id":"https://openalex.org/F4320309327","display_name":"Google","ror":"https://ror.org/00njsd438"},{"id":"https://openalex.org/F4320337389","display_name":"Division of Information and Intelligent Systems","ror":"https://ror.org/053a2cp42"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W10311529","https://openalex.org/W82705568","https://openalex.org/W120045745","https://openalex.org/W1977148430","https://openalex.org/W1987841290","https://openalex.org/W1993689907","https://openalex.org/W1999284314","https://openalex.org/W2008535862","https://openalex.org/W2008647155","https://openalex.org/W2013982170","https://openalex.org/W2015475217","https://openalex.org/W2023950391","https://openalex.org/W2024395588","https://openalex.org/W2030798836","https://openalex.org/W2031362888","https://openalex.org/W2038110879","https://openalex.org/W2045503467","https://openalex.org/W2046911213","https://openalex.org/W2047594593","https://openalex.org/W2050448951","https://openalex.org/W2052286413","https://openalex.org/W2052728883","https://openalex.org/W2053762489","https://openalex.org/W2055373760","https://openalex.org/W2059017188","https://openalex.org/W2063155970","https://openalex.org/W2071063243","https://openalex.org/W2076897996","https://openalex.org/W2079209697","https://openalex.org/W2101468456","https://openalex.org/W2104480174","https://openalex.org/W2108546419","https://openalex.org/W2108672708","https://openalex.org/W2113275166","https://openalex.org/W2119878875","https://openalex.org/W2129412583","https://openalex.org/W2135170744","https://openalex.org/W2135454631","https://openalex.org/W2135785391","https://openalex.org/W2137742453","https://openalex.org/W2139182243","https://openalex.org/W2144461711","https://openalex.org/W2147169375","https://openalex.org/W2170474669","https://openalex.org/W2171786315","https://openalex.org/W2293537096","https://openalex.org/W2561675875","https://openalex.org/W2913279420","https://openalex.org/W3003157036","https://openalex.org/W3136375062","https://openalex.org/W3137158176","https://openalex.org/W3138390653","https://openalex.org/W3138581055","https://openalex.org/W4256534192","https://openalex.org/W6680916133"],"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/W3083116488","https://openalex.org/W2143665433","https://openalex.org/W2062151580"],"abstract_inverted_index":{"Smooth":[0],"space":[1],"deformation":[2,96],"has":[3],"become":[4],"a":[5,64,92,120,144],"vital":[6],"tool":[7],"for":[8,33,163],"the":[9,21,29,50,69,102,116,152],"animation":[10,167],"and":[11,15,76,135,157,166],"design":[12],"of":[13,24,72,104,119,154,168],"2D":[14,56],"3D":[16,34],"shapes.":[17,170],"Linear":[18],"methods,":[19],"under":[20],"umbrella":[22],"term":[23],"\"linear":[25],"blend":[26,94,106],"skinning\",":[27],"are":[28],"de":[30],"facto":[31],"standard":[32],"animations.":[35],"Unfortunately":[36],"such":[37,48],"approaches":[38],"do":[39],"not":[40],"trivially":[41],"extend":[42],"to":[43,67,151],"deforming":[44],"vector":[45],"graphics":[46],",":[47,128,131,134],"as":[49,97,99],"cubic":[51,73],"B\u00e9zier":[52,74,141],"splines":[53,75],"prevalent":[54],"in":[55,60,143],"or":[57,84,88],"subdivision":[58,78,82],"surfaces":[59,89],"3D.":[61],"We":[62,124],"propose":[63],"variational":[65],"approach":[66],"reposition":[68],"control":[70],"points":[71],"Catmull-Clark":[77],"surfaces---or":[79],"any":[80],"linear":[81,93,105],"curves":[83,87,142,156],"surfaces---to":[85],"produce":[86],"which":[90],"match":[91],"skinning":[95],"closely":[98],"possible.":[100],"Exploiting":[101],"linearity":[103],"skinning,":[107],"we":[108],"show":[109],"how":[110],"this":[111],"optimization":[112],"collapses":[113],"neatly":[114],"into":[115],"repeated":[117],"multiplication":[118],"matrix":[121],"per":[122],"handle.":[123],"support":[125],"C":[126,129],"0":[127],"1":[130,133],"G":[132],"fixed-angle":[136],"continuity":[137],"constraints":[138],"between":[139],"adjacent":[140],"spline.":[145],"Complexity":[146],"scales":[147],"linearly":[148],"with":[149],"respect":[150],"number":[153],"input":[155],"run-time":[158],"performance":[159],"is":[160],"fast":[161],"enough":[162],"real-time":[164],"editing":[165],"high-resolution":[169]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
