{"id":"https://openalex.org/W7124513824","doi":"https://doi.org/10.1111/cgf.70515","title":"Phong\u2010Rodrigues Extrinsic Vector\u2010Field Processing","display_name":"Phong\u2010Rodrigues Extrinsic Vector\u2010Field Processing","publication_year":2026,"publication_date":"2026-08-13","ids":{"openalex":"https://openalex.org/W7124513824","doi":"https://doi.org/10.1111/cgf.70515"},"language":"en","primary_location":{"id":"doi:10.1111/cgf.70515","is_oa":true,"landing_page_url":"https://doi.org/10.1111/cgf.70515","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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer Graphics Forum","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1111/cgf.70515","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100622143","display_name":"Hongyi Liu","orcid":"https://orcid.org/0000-0003-4156-4788"},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hongyi Liu","raw_affiliation_strings":["Johns Hopkins University  USA"],"raw_orcid":"https://orcid.org/0000-0002-5908-4822","affiliations":[{"raw_affiliation_string":"Johns Hopkins University  USA","institution_ids":["https://openalex.org/I145311948"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000788307","display_name":"Oded Stein","orcid":"https://orcid.org/0000-0001-9741-3175"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Oded Stein","raw_affiliation_strings":["Technion \u2010 Israel Institute of Technology  Israel"],"raw_orcid":"https://orcid.org/0000-0001-9741-3175","affiliations":[{"raw_affiliation_string":"Technion \u2010 Israel Institute of Technology  Israel","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003150364","display_name":"Amir Vaxman","orcid":"https://orcid.org/0000-0001-6998-6689"},"institutions":[{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Amir Vaxman","raw_affiliation_strings":["University of Edinburgh  UK"],"raw_orcid":"https://orcid.org/0000-0001-6998-6689","affiliations":[{"raw_affiliation_string":"University of Edinburgh  UK","institution_ids":["https://openalex.org/I98677209"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5123170549","display_name":"Mirela Ben-Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Mirela Ben\u2010Chen","raw_affiliation_strings":["Technion \u2010 Israel Institute of Technology  Israel"],"raw_orcid":"https://orcid.org/0000-0002-1732-2327","affiliations":[{"raw_affiliation_string":"Technion \u2010 Israel Institute of Technology  Israel","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001385960","display_name":"Misha Kazhdan","orcid":"https://orcid.org/0000-0002-6904-2167"},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Misha Kazhdan","raw_affiliation_strings":["Johns Hopkins University  USA"],"raw_orcid":"https://orcid.org/0000-0002-6904-2167","affiliations":[{"raw_affiliation_string":"Johns Hopkins University  USA","institution_ids":["https://openalex.org/I145311948"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"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":0.07243511,"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.43479999899864197,"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.43479999899864197,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.08569999784231186,"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"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.05790000036358833,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/covariant-derivative","display_name":"Covariant derivative","score":0.7770000100135803},{"id":"https://openalex.org/keywords/covariant-transformation","display_name":"Covariant transformation","score":0.7390999794006348},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.7354999780654907},{"id":"https://openalex.org/keywords/tangent-vector","display_name":"Tangent vector","score":0.6973999738693237},{"id":"https://openalex.org/keywords/lie-derivative","display_name":"Lie derivative","score":0.6884999871253967},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.5527999997138977},{"id":"https://openalex.org/keywords/tangent-space","display_name":"Tangent space","score":0.5169000029563904},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.4875999987125397},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.45660001039505005},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4496999979019165}],"concepts":[{"id":"https://openalex.org/C19492387","wikidata":"https://www.wikidata.org/wiki/Q2287715","display_name":"Covariant derivative","level":2,"score":0.7770000100135803},{"id":"https://openalex.org/C9136319","wikidata":"https://www.wikidata.org/wiki/Q362640","display_name":"Covariant transformation","level":2,"score":0.7390999794006348},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.7354999780654907},{"id":"https://openalex.org/C47890412","wikidata":"https://www.wikidata.org/wiki/Q1179296","display_name":"Tangent vector","level":3,"score":0.6973999738693237},{"id":"https://openalex.org/C187519435","wikidata":"https://www.wikidata.org/wiki/Q579267","display_name":"Lie derivative","level":5,"score":0.6884999871253967},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6348999738693237},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.5527999997138977},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.5169000029563904},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.4875999987125397},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4602000117301941},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.45660001039505005},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4496999979019165},{"id":"https://openalex.org/C28903235","wikidata":"https://www.wikidata.org/wiki/Q746550","display_name":"Tangent bundle","level":3,"score":0.44909998774528503},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.38940000534057617},{"id":"https://openalex.org/C7451433","wikidata":"https://www.wikidata.org/wiki/Q1265039","display_name":"Solenoidal vector field","level":3,"score":0.3856000006198883},{"id":"https://openalex.org/C102650682","wikidata":"https://www.wikidata.org/wiki/Q5527631","display_name":"Gauge covariant derivative","level":5,"score":0.3801000118255615},{"id":"https://openalex.org/C148047603","wikidata":"https://www.wikidata.org/wiki/Q1014612","display_name":"Parallelizable manifold","level":2,"score":0.37869998812675476},{"id":"https://openalex.org/C112280298","wikidata":"https://www.wikidata.org/wiki/Q5156582","display_name":"Complex lamellar vector field","level":4,"score":0.3743000030517578},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.3614000082015991},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.3587000072002411},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.35830000042915344},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.33379998803138733},{"id":"https://openalex.org/C166077713","wikidata":"https://www.wikidata.org/wiki/Q1758924","display_name":"Tensor field","level":3,"score":0.325300008058548},{"id":"https://openalex.org/C2027888","wikidata":"https://www.wikidata.org/wiki/Q521126","display_name":"Vector potential","level":3,"score":0.3237000107765198},{"id":"https://openalex.org/C84316537","wikidata":"https://www.wikidata.org/wiki/Q36255","display_name":"Unit vector","level":2,"score":0.3221000134944916},{"id":"https://openalex.org/C14344131","wikidata":"https://www.wikidata.org/wiki/Q5478310","display_name":"Lie bracket of vector fields","level":5,"score":0.32010000944137573},{"id":"https://openalex.org/C2011187","wikidata":"https://www.wikidata.org/wiki/Q383851","display_name":"Directional derivative","level":2,"score":0.3156000077724457},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.30640000104904175},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.30250000953674316},{"id":"https://openalex.org/C106953101","wikidata":"https://www.wikidata.org/wiki/Q1814838","display_name":"Parallel transport","level":2,"score":0.3005000054836273},{"id":"https://openalex.org/C17685861","wikidata":"https://www.wikidata.org/wiki/Q6960532","display_name":"Time derivative","level":2,"score":0.2896000146865845},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2847000062465668},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.2671999931335449},{"id":"https://openalex.org/C42519931","wikidata":"https://www.wikidata.org/wiki/Q1200279","display_name":"Killing vector field","level":2,"score":0.25519999861717224}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1111/cgf.70515","is_oa":true,"landing_page_url":"https://doi.org/10.1111/cgf.70515","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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer Graphics Forum","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2601.10621","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2601.10621","pdf_url":"https://arxiv.org/pdf/2601.10621","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"doi:10.1111/cgf.70515","is_oa":true,"landing_page_url":"https://doi.org/10.1111/cgf.70515","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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer Graphics Forum","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.5433844923973083}],"awards":[{"id":"https://openalex.org/G186564067","display_name":null,"funder_award_id":"1073/21","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"We":[1,33],"introduce":[2],"a":[3,38,131],"new":[4],"extrinsic":[5,160],"discretization":[6,105,156],"of":[7,30,109,169,172],"tangent":[8,56],"vector":[9,162],"fields":[10],"on":[11,140],"triangle":[12,59],"meshes":[13],"that":[14,20,90,157],"is":[15,83,153],"continuous,":[16],"with":[17],"bounded":[18,164],"derivatives":[19,75],"are":[21],"continuous":[22,39,161],"almost":[23],"everywhere,":[24],"supporting":[25,142],"pointwise":[26,84,147,167],"evaluation":[27,168],"and":[28,48,86,101,117,124,133,146,166],"integration":[29],"differential":[31],"operators.":[32,173],"achieve":[34],"this":[35,170],"by":[36],"building":[37],"normal":[40],"field":[41],"over":[42],"the":[43,71,88,91,107,115,125,154],"mesh":[44],"via":[45],"Phong":[46],"interpolation":[47],"using":[49,87],"minimal":[50],"Rodrigues":[51],"rotations":[52],"to":[53,73],"transport":[54],"vertex\u2010based":[55],"vectors":[57],"into":[58,97],"interiors.":[60],"Unlike":[61],"most":[62],"existing":[63],"discretizations,":[64],"which":[65],"typically":[66],"sacrifice":[67],"either":[68],"continuity":[69],"or":[70],"ability":[72],"evaluate":[74],"pointwise,":[76],"our":[77,104,150],"approach":[78],"supports":[79,106],"both.":[80],"Because":[81],"it":[82],"evaluatable,":[85],"fact":[89],"covariant":[92],"derivative":[93],"can":[94],"be":[95],"decomposed":[96],"its":[98],"symmetric,":[99],"antisymmetric,":[100],"scalar":[102],"components,":[103],"construction":[108],"standard":[110],"vector\u2010field":[111,138],"processing":[112,139],"operators":[113,145],"including":[114],"connection":[116],"Hodge":[118],"Laplacians,":[119],"Killing":[120],"energy,":[121],"divergence,":[122],"curl,":[123],"Lie":[126],"bracket.":[127],"This":[128],"framework":[129],"provides":[130],"simple":[132],"practical":[134],"finite\u2010element":[135],"formulation":[136],"for":[137],"meshes,":[141],"both":[143],"integration\u2010based":[144],"queries.":[148],"To":[149],"knowledge,":[151],"ours":[152],"first":[155],"jointly":[158],"enables":[159],"fields,":[163],"derivatives,":[165],"collection":[171]},"counts_by_year":[],"updated_date":"2026-08-15T07:11:24.734988","created_date":"2026-01-17T00:00:00"}