{"id":"https://openalex.org/W2010030640","doi":"https://doi.org/10.1145/1141911.1141991","title":"Edge subdivision schemes and the construction of smooth vector fields","display_name":"Edge subdivision schemes and the construction of smooth vector fields","publication_year":2006,"publication_date":"2006-07-01","ids":{"openalex":"https://openalex.org/W2010030640","doi":"https://doi.org/10.1145/1141911.1141991","mag":"2010030640"},"language":"en","primary_location":{"id":"doi:10.1145/1141911.1141991","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1141911.1141991","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/A5073656495","display_name":"Ke Wang","orcid":"https://orcid.org/0000-0001-8128-3441"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ke Wang","raw_affiliation_strings":["Caltech","Caltech,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Caltech","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"Caltech,","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112622344","display_name":"Weiwei","orcid":null},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Weiwei","raw_affiliation_strings":["Caltech","Caltech,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Caltech","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"Caltech,","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042762771","display_name":"Yiying Tong","orcid":"https://orcid.org/0000-0002-7929-4333"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yiying Tong","raw_affiliation_strings":["Caltech","Caltech,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Caltech","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"Caltech,","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022153785","display_name":"Mathieu Desbrun","orcid":"https://orcid.org/0000-0003-3424-6079"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mathieu Desbrun","raw_affiliation_strings":["Caltech","Caltech,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Caltech","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"Caltech,","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051948556","display_name":"Peter Schr\u00f6der","orcid":"https://orcid.org/0000-0001-9084-7106"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Peter Schr\u00f6der","raw_affiliation_strings":["Caltech","Caltech,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Caltech","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"Caltech,","institution_ids":["https://openalex.org/I122411786"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.5241,"has_fulltext":false,"cited_by_count":49,"citation_normalized_percentile":{"value":0.95981252,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"25","issue":"3","first_page":"1041","last_page":"1048"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9818999767303467,"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":0.9458000063896179,"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-surface","display_name":"Subdivision surface","score":0.8608124256134033},{"id":"https://openalex.org/keywords/subdivision","display_name":"Subdivision","score":0.8217122554779053},{"id":"https://openalex.org/keywords/tangent-vector","display_name":"Tangent vector","score":0.6658543348312378},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6186652183532715},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5323498845100403},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.5001001358032227},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.4745897948741913},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.4569895267486572},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.45102187991142273},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.42015647888183594},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.41433802247047424},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2381819486618042},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2342444360256195},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.12268909811973572}],"concepts":[{"id":"https://openalex.org/C199686383","wikidata":"https://www.wikidata.org/wiki/Q1529124","display_name":"Subdivision surface","level":3,"score":0.8608124256134033},{"id":"https://openalex.org/C143392562","wikidata":"https://www.wikidata.org/wiki/Q449111","display_name":"Subdivision","level":2,"score":0.8217122554779053},{"id":"https://openalex.org/C47890412","wikidata":"https://www.wikidata.org/wiki/Q1179296","display_name":"Tangent vector","level":3,"score":0.6658543348312378},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6186652183532715},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5323498845100403},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5001001358032227},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.4745897948741913},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.4569895267486572},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.45102187991142273},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.42015647888183594},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.41433802247047424},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2381819486618042},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2342444360256195},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.12268909811973572},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"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/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/1141911.1141991","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1141911.1141991","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"},{"id":"pmh:oai:authors.library.caltech.edu:73243","is_oa":false,"landing_page_url":"https://resolver.caltech.edu/CaltechAUTHORS:20170104-161620229","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Book Section"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.62.4764","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.62.4764","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.multires.caltech.edu/pubs/FormSubdivision.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.6399999856948853,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W126840538","https://openalex.org/W1522382323","https://openalex.org/W1528814089","https://openalex.org/W1975807121","https://openalex.org/W1979650518","https://openalex.org/W1989480677","https://openalex.org/W2010030640","https://openalex.org/W2030232224","https://openalex.org/W2032325716","https://openalex.org/W2034833521","https://openalex.org/W2040692352","https://openalex.org/W2056816721","https://openalex.org/W2068264968","https://openalex.org/W2075492994","https://openalex.org/W2077244888","https://openalex.org/W2083574922","https://openalex.org/W2086906763","https://openalex.org/W2091620062","https://openalex.org/W2092929058","https://openalex.org/W2094963988","https://openalex.org/W2099945117","https://openalex.org/W2138486270","https://openalex.org/W2151406969","https://openalex.org/W2155457888","https://openalex.org/W2168206922","https://openalex.org/W2171815117","https://openalex.org/W2182932938","https://openalex.org/W2223141336","https://openalex.org/W2232880714","https://openalex.org/W2249925049","https://openalex.org/W4235034873","https://openalex.org/W4235062160","https://openalex.org/W4255193216","https://openalex.org/W4255747408","https://openalex.org/W4293102147"],"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/W2078522816"],"abstract_inverted_index":{"Vertex-":[0],"and":[1,12,15,39,72,86,94,121],"face-based":[2,87],"subdivision":[3,46,58,88,97,140,167],"schemes":[4,28,47,59,89],"are":[5,19,73],"now":[6],"routinely":[7],"used":[8],"in":[9,128],"geometric":[10],"modeling":[11],"computational":[13],"science,":[14],"their":[16],"primal/dual":[17],"relationships":[18],"well":[20],"studied.":[21],"In":[22],"this":[23,179],"paper,":[24],"we":[25,182],"interpret":[26],"these":[27],"as":[29,90,181],"defining":[30],"bases":[31,52],"for":[32,53,108,119,125,134],"discrete":[33,54],"differential":[34,55],"0-":[35],"resp.":[36],"2-forms":[37,126],",":[38],"complete":[40],"the":[41,50,66,69,76,100,109,154,165],"picture":[42],"by":[43],"introducing":[44],"edge-based":[45],"to":[48,68,75],"construct":[49],"missing":[51],"1-forms.":[56],"Such":[57],"map":[60],"scalar":[61,155],"coefficients":[62,157],"on":[63,82,164],"edges":[64],"from":[65],"coarse":[67],"refined":[70],"mesh":[71],"intrinsic":[74],"surface.":[77,168],"Our":[78],"construction":[79,107],"is":[80,152,174],"based":[81],"treating":[83],"vertex-,":[84],"edge-,":[85],"a":[91,129,150,159],"joint":[92],"triple":[93],"enforcing":[95],"that":[96],"commutes":[98],"with":[99,178],"topological":[101],"exterior":[102],"derivative.":[103],"We":[104,143],"demonstrate":[105],"our":[106],"case":[110],"of":[111,170],"arbitrary":[112],"topology":[113],"triangle":[114],"meshes.":[115],"Using":[116],"Loop's":[117],"scheme":[118,133],"0-forms":[120],"generalized":[122,131],"half-box":[123],"splines":[124],"results":[127],"unique":[130],"spline":[132],"1-forms,":[135],"easily":[136],"incorporated":[137],"into":[138],"standard":[139],"surface":[141],"codes.":[142],"also":[144],"provide":[145],"corresponding":[146],"boundary":[147],"stencils.":[148],"Once":[149],"metric":[151],"supplied,":[153],"1-form":[156],"define":[158],"smooth":[160],"tangent":[161,171],"vector":[162,172],"field":[163],"underlying":[166],"Design":[169],"fields":[173],"made":[175],"particularly":[176],"easy":[177],"machinery":[180],"demonstrate.":[183]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}