{"id":"https://openalex.org/W7162300353","doi":"https://doi.org/10.1111/cgf.70566","title":"Closing Trajectories: Equation\u2010Free Cyclic Animation via Koopman Surrogates","display_name":"Closing Trajectories: Equation\u2010Free Cyclic Animation via Koopman Surrogates","publication_year":2026,"publication_date":"2026-08-12","ids":{"openalex":"https://openalex.org/W7162300353","doi":"https://doi.org/10.1111/cgf.70566"},"language":"en","primary_location":{"id":"doi:10.1111/cgf.70566","is_oa":true,"landing_page_url":"https://doi.org/10.1111/cgf.70566","pdf_url":null,"source":{"id":"https://openalex.org/S67831204","display_name":"Computer Graphics Forum","issn_l":"0167-7055","issn":["0167-7055","1467-8659"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer Graphics Forum","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1111/cgf.70566","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136909068","display_name":"Shixun Huang","orcid":null},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]},{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Shixun Huang","raw_affiliation_strings":["University of British Columbia Vancouver Canada","University of Toronto Toronto Canada"],"raw_orcid":"https://orcid.org/0009-0002-2463-1133","affiliations":[{"raw_affiliation_string":"University of British Columbia Vancouver Canada","institution_ids":["https://openalex.org/I141945490"]},{"raw_affiliation_string":"University of Toronto Toronto Canada","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136986820","display_name":"Siyuan Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Siyuan Chen","raw_affiliation_strings":["University of British Columbia Vancouver Canada"],"raw_orcid":"https://orcid.org/0009-0009-4309-862X","affiliations":[{"raw_affiliation_string":"University of British Columbia Vancouver Canada","institution_ids":["https://openalex.org/I141945490"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128910420","display_name":"Yue Chang","orcid":null},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Yue Chang","raw_affiliation_strings":["University of Toronto Toronto Canada"],"raw_orcid":"https://orcid.org/0000-0002-2587-827X","affiliations":[{"raw_affiliation_string":"University of Toronto Toronto Canada","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136954758","display_name":"Zhecheng Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Zhecheng Wang","raw_affiliation_strings":["University of Toronto Toronto Canada"],"raw_orcid":"https://orcid.org/0000-0003-4989-6971","affiliations":[{"raw_affiliation_string":"University of Toronto Toronto Canada","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5136945998","display_name":"Peter Yichen Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Peter Yichen Chen","raw_affiliation_strings":["University of British Columbia Vancouver Canada"],"raw_orcid":"https://orcid.org/0000-0003-1919-5437","affiliations":[{"raw_affiliation_string":"University of British Columbia Vancouver Canada","institution_ids":["https://openalex.org/I141945490"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5136945998","https://openalex.org/A5136986820"],"corresponding_institution_ids":["https://openalex.org/I141945490"],"apc_list":{"value":3710,"currency":"USD","value_usd":3710},"apc_paid":{"value":3710,"currency":"USD","value_usd":3710},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.49307437,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12290","display_name":"Human Motion and Animation","score":0.4260999858379364,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T12290","display_name":"Human Motion and Animation","score":0.4260999858379364,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T11206","display_name":"Model Reduction and Neural Networks","score":0.08190000057220459,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10719","display_name":"3D Shape Modeling and Analysis","score":0.07029999792575836,"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/trajectory","display_name":"Trajectory","score":0.690500020980835},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.642799973487854},{"id":"https://openalex.org/keywords/karush\u2013kuhn\u2013tucker-conditions","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","score":0.6305999755859375},{"id":"https://openalex.org/keywords/animation","display_name":"Animation","score":0.6111000180244446},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5379999876022339},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics","score":0.5041000247001648},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.4821000099182129},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.4372999966144562},{"id":"https://openalex.org/keywords/computer-animation","display_name":"Computer animation","score":0.43140000104904175}],"concepts":[{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.690500020980835},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6819999814033508},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.642799973487854},{"id":"https://openalex.org/C50454189","wikidata":"https://www.wikidata.org/wiki/Q2075125","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","level":2,"score":0.6305999755859375},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.6111000180244446},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.5600000023841858},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5379999876022339},{"id":"https://openalex.org/C77660652","wikidata":"https://www.wikidata.org/wiki/Q150971","display_name":"Computer graphics","level":2,"score":0.5041000247001648},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.4821000099182129},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44690001010894775},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.4372999966144562},{"id":"https://openalex.org/C69369342","wikidata":"https://www.wikidata.org/wiki/Q1401416","display_name":"Computer animation","level":3,"score":0.43140000104904175},{"id":"https://openalex.org/C21442007","wikidata":"https://www.wikidata.org/wiki/Q1027879","display_name":"Graphics","level":2,"score":0.4307999908924103},{"id":"https://openalex.org/C2778775528","wikidata":"https://www.wikidata.org/wiki/Q5135432","display_name":"Closing (real estate)","level":2,"score":0.41620001196861267},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3804999887943268},{"id":"https://openalex.org/C66629338","wikidata":"https://www.wikidata.org/wiki/Q189177","display_name":"3D computer graphics","level":3,"score":0.3659000098705292},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.33230000734329224},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.32829999923706055},{"id":"https://openalex.org/C126766683","wikidata":"https://www.wikidata.org/wiki/Q6896006","display_name":"Molecular graphics","level":3,"score":0.32089999318122864},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.30390000343322754},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.301800012588501},{"id":"https://openalex.org/C2776235265","wikidata":"https://www.wikidata.org/wiki/Q18392052","display_name":"Fragment (logic)","level":2,"score":0.30140000581741333},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2957000136375427},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.29269999265670776},{"id":"https://openalex.org/C199639397","wikidata":"https://www.wikidata.org/wiki/Q1788588","display_name":"Engineering drawing","level":1,"score":0.2922999858856201},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.2906000018119812},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.262800008058548},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.257999986410141},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.25600001215934753},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.25369998812675476}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1111/cgf.70566","is_oa":true,"landing_page_url":"https://doi.org/10.1111/cgf.70566","pdf_url":null,"source":{"id":"https://openalex.org/S67831204","display_name":"Computer Graphics Forum","issn_l":"0167-7055","issn":["0167-7055","1467-8659"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer Graphics Forum","raw_type":"journal-article"},{"id":"doi:10.48550/arxiv.2605.23462","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.23462","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.1111/cgf.70566","is_oa":true,"landing_page_url":"https://doi.org/10.1111/cgf.70566","pdf_url":null,"source":{"id":"https://openalex.org/S67831204","display_name":"Computer Graphics Forum","issn_l":"0167-7055","issn":["0167-7055","1467-8659"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer Graphics Forum","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Life below water","score":0.7020204663276672,"id":"https://metadata.un.org/sdg/14"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320309480","display_name":"Nvidia","ror":"https://ror.org/03jdj4y14"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1723433682","https://openalex.org/W1967494143","https://openalex.org/W1970797733","https://openalex.org/W1997054581","https://openalex.org/W2014356541","https://openalex.org/W2045459928","https://openalex.org/W2062740692","https://openalex.org/W2075605912","https://openalex.org/W2076897996","https://openalex.org/W2089182646","https://openalex.org/W2134389879","https://openalex.org/W2293545866","https://openalex.org/W2791693147","https://openalex.org/W2804898937","https://openalex.org/W2964119648","https://openalex.org/W3035965352","https://openalex.org/W3111036211","https://openalex.org/W4206829704","https://openalex.org/W4231947169","https://openalex.org/W4246308730","https://openalex.org/W4286611287","https://openalex.org/W4286611302","https://openalex.org/W4386141917","https://openalex.org/W4389575012","https://openalex.org/W4400573507","https://openalex.org/W4400702585","https://openalex.org/W4402816868","https://openalex.org/W4404525443","https://openalex.org/W4410166062","https://openalex.org/W4412673659","https://openalex.org/W4417000505","https://openalex.org/W4417000867"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"Cyclic":[1],"animation":[2],"is":[3,40,121],"widely":[4],"used":[5],"in":[6,16],"computer":[7],"graphics":[8],"and":[9,19,53,79],"interactive":[10,20],"content.":[11],"It":[12],"supports":[13],"seamless":[14,38],"playback":[15],"games,":[17],"VR,":[18],"simulation,":[21],"where":[22],"short":[23],"clips":[24],"must":[25],"repeat":[26],"smoothly":[27],"over":[28],"long":[29],"durations.":[30],"Converting":[31],"an":[32,67],"observed":[33,48,77],"non\u2010cyclic":[34],"trajectory":[35,78,83],"into":[36],"a":[37,72,81,86,92,104,115,124],"loop":[39],"challenging":[41],"because":[42],"the":[43,47,54,58,76],"endpoint":[44],"states":[45],"of":[46,57,127],"sequence":[49],"rarely":[50],"match":[51],"exactly,":[52],"governing":[55],"equations":[56],"underlying":[59],"system":[60],"are":[61],"often":[62],"unavailable.":[63],"We":[64],"therefore":[65],"propose":[66],"equation\u2010free":[68],"framework":[69],"that":[70,109],"identifies":[71],"Koopman":[73],"surrogate":[74],"from":[75],"computes":[80],"cyclic":[82,101],"by":[84],"applying":[85],"Fourier\u2010parameterized,":[87],"time\u2010varying":[88],"control":[89],"input":[90],"under":[91],"hard":[93],"temporal":[94],"periodicity":[95],"constraint.":[96],"The":[97],"resulting":[98],"formulation":[99],"reduces":[100],"synthesis":[102],"to":[103,123],"linearly":[105],"constrained":[106],"quadratic":[107],"program":[108],"can":[110],"be":[111],"solved":[112],"efficiently":[113],"through":[114],"structured":[116],"KKT":[117],"system.":[118],"Our":[119],"method":[120],"applicable":[122],"diverse":[125],"range":[126],"examples,":[128],"including":[129],"N\u2010body":[130],"systems,":[131],"cloth,":[132],"deformable":[133],"objects,":[134],"shallow":[135],"water,":[136],"etc.":[137]},"counts_by_year":[],"updated_date":"2026-08-14T07:06:38.338062","created_date":"2026-05-26T00:00:00"}