{"id":"https://openalex.org/W2747062268","doi":"https://doi.org/10.1137/16m1076794","title":"A Flexible $C^2$ Subdivision Scheme on the Sphere: With Application to Biomembrane Modelling","display_name":"A Flexible $C^2$ Subdivision Scheme on the Sphere: With Application to Biomembrane Modelling","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2747062268","doi":"https://doi.org/10.1137/16m1076794","mag":"2747062268"},"language":"en","primary_location":{"id":"doi:10.1137/16m1076794","is_oa":true,"landing_page_url":"https://doi.org/10.1137/16m1076794","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/16M1076794","source":{"id":"https://openalex.org/S2996807011","display_name":"SIAM Journal on Applied Algebra and Geometry","issn_l":"2470-6566","issn":["2470-6566"],"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 Applied Algebra and Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://epubs.siam.org/doi/pdf/10.1137/16M1076794","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090901796","display_name":"Jingmin Chen","orcid":"https://orcid.org/0000-0001-6336-5427"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jingmin Chen","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074036913","display_name":"Sara Grundel","orcid":"https://orcid.org/0000-0002-0209-6566"},"institutions":[{"id":"https://openalex.org/I4210127568","display_name":"Max Planck Institute for Dynamics of Complex Technical Systems","ror":"https://ror.org/030h7k016","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210127568"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Sara Grundel","raw_affiliation_strings":["Max Planck Institute for Dynamics of Complex Technical Systems, 39106 Magdeburg, Germany"],"affiliations":[{"raw_affiliation_string":"Max Planck Institute for Dynamics of Complex Technical Systems, 39106 Magdeburg, Germany","institution_ids":["https://openalex.org/I4210127568"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006903519","display_name":"Thomas Yu","orcid":"https://orcid.org/0000-0002-4800-0822"},"institutions":[{"id":"https://openalex.org/I72816309","display_name":"Drexel University","ror":"https://ror.org/04bdffz58","country_code":"US","type":"education","lineage":["https://openalex.org/I72816309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Thomas P. Y. Yu","raw_affiliation_strings":["Department of Mathematics, Drexel University, Philadelphia, PA 19104"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Drexel University, Philadelphia, PA 19104","institution_ids":["https://openalex.org/I72816309"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5090901796"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7203,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.68938218,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"1","issue":"1","first_page":"459","last_page":"483"},"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9757999777793884,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9660999774932861,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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":0.7883319854736328},{"id":"https://openalex.org/keywords/subdivision","display_name":"Subdivision","score":0.745751678943634},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4891364872455597},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.4839508831501007},{"id":"https://openalex.org/keywords/tetrahedron","display_name":"Tetrahedron","score":0.44724905490875244},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44122976064682007},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.4365423023700714},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4345186948776245},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3236953020095825},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.2722015380859375},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.2554570436477661},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1857326328754425},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17800167202949524},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.16290226578712463},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.11588573455810547}],"concepts":[{"id":"https://openalex.org/C199686383","wikidata":"https://www.wikidata.org/wiki/Q1529124","display_name":"Subdivision surface","level":3,"score":0.7883319854736328},{"id":"https://openalex.org/C143392562","wikidata":"https://www.wikidata.org/wiki/Q449111","display_name":"Subdivision","level":2,"score":0.745751678943634},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4891364872455597},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4839508831501007},{"id":"https://openalex.org/C105239961","wikidata":"https://www.wikidata.org/wiki/Q160003","display_name":"Tetrahedron","level":2,"score":0.44724905490875244},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44122976064682007},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4365423023700714},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4345186948776245},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3236953020095825},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.2722015380859375},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2554570436477661},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1857326328754425},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17800167202949524},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.16290226578712463},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.11588573455810547},{"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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/16m1076794","is_oa":true,"landing_page_url":"https://doi.org/10.1137/16m1076794","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/16M1076794","source":{"id":"https://openalex.org/S2996807011","display_name":"SIAM Journal on Applied Algebra and Geometry","issn_l":"2470-6566","issn":["2470-6566"],"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 Applied Algebra and Geometry","raw_type":"journal-article"},{"id":"pmh:oai:escidoc.org:escidoc:2498696","is_oa":true,"landing_page_url":"http://hdl.handle.net/11858/00-001M-0000-002E-2CD4-7","pdf_url":null,"source":{"id":"https://openalex.org/S7407052962","display_name":"Max Planck Digital Library","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1137/16m1076794","is_oa":true,"landing_page_url":"https://doi.org/10.1137/16m1076794","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/16M1076794","source":{"id":"https://openalex.org/S2996807011","display_name":"SIAM Journal on Applied Algebra and Geometry","issn_l":"2470-6566","issn":["2470-6566"],"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 Applied Algebra and Geometry","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.7900000214576721}],"awards":[{"id":"https://openalex.org/G2858194323","display_name":null,"funder_award_id":"DMS 0714321","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2913313590","display_name":null,"funder_award_id":"DMS 0915068","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6960184300","display_name":null,"funder_award_id":"DMS 0512673","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2747062268.pdf","grobid_xml":"https://content.openalex.org/works/W2747062268.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1165615","https://openalex.org/W126840538","https://openalex.org/W1525296983","https://openalex.org/W1528814089","https://openalex.org/W1578723177","https://openalex.org/W1953218957","https://openalex.org/W1973890908","https://openalex.org/W1986725116","https://openalex.org/W2000545789","https://openalex.org/W2001972447","https://openalex.org/W2007035075","https://openalex.org/W2012909180","https://openalex.org/W2015707217","https://openalex.org/W2025402290","https://openalex.org/W2030232224","https://openalex.org/W2067257899","https://openalex.org/W2083574922","https://openalex.org/W2086906763","https://openalex.org/W2094672957","https://openalex.org/W2155457888","https://openalex.org/W2165122923","https://openalex.org/W2264936970","https://openalex.org/W2341241031","https://openalex.org/W2525604031","https://openalex.org/W2911524037","https://openalex.org/W4233115509"],"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/W2296482608"],"abstract_inverted_index":{"We":[0,162],"construct":[1],"a":[2,16,19,24,33,58,81,129,145],"$C^2$":[3,21,35],"multiscale":[4],"approximation":[5],"scheme":[6,22,37,48,86,98,122],"for":[7,43,110,168],"functions":[8],"defined":[9],"on":[10,15,57],"the":[11,70,76,97,103,107,116,120,124,137,170,179],"(Riemann)":[12],"sphere.":[13],"Based":[14],"three-directional":[17],"box-spline,":[18],"flexible":[20,34],"over":[23],"valence":[25,64],"3":[26,65],"extraordinary":[27],"vertex":[28],"can":[29,49,88,99,151],"be":[30,41,50,89,100,154],"constructed.":[31],"Such":[32],"subdivision":[36,47,79,121,139],"is":[38,189],"known":[39],"to":[40,52,75,91,156,178],"impossible":[42],"arbitrary":[44],"valences.":[45],"The":[46],"used":[51,101],"model":[53],"spherical":[54,111],"surfaces":[55,140],"based":[56],"recursively":[59],"subdivided":[60],"tetrahedron,":[61],"with":[62,128,144,176],"only":[63],"and":[66,112,173,187],"6":[67],"vertices":[68],"in":[69,102,133,152,159],"resulted":[71],"triangulations.":[72],"This":[73,132],"adds":[74],"toolbox":[77],"of":[78,106,119],"methods":[80],"high":[82,84],"order,":[83],"regularity":[85],"which":[87,150],"beneficial":[90],"scientific":[92],"computing":[93,169],"applications.":[94],"For":[95],"instance,":[96],"numerical":[104],"solution":[105],"Canham--Helfrich--Evans":[108],"models":[109],"toroidal":[113],"biomembranes.":[114],"Moreover,":[115],"characteristic":[117],"maps":[118],"endow":[123],"underlying":[125],"simplicial":[126],"complex":[127],"conformal":[130],"structure.":[131],"particular":[134],"means":[135],"that":[136],"special":[138],"constructed":[141],"here":[142],"comes":[143],"well-defined":[146],"harmonic":[147,171],"energy":[148,172],"functional,":[149],"turn":[153],"exploited":[155],"promote":[157],"conformality":[158],"surface":[160],"parameterizations.":[161],"develop":[163],"an":[164],"efficient":[165],"parallel":[166],"algorithm":[167],"its":[174],"gradient":[175],"respect":[177],"control":[180],"vertices.":[181],"A":[182],"software":[183],"implementation":[184],"(in":[185],"CUDA":[186],"MATLAB)":[188],"provided.":[190]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
