{"id":"https://openalex.org/W4292768201","doi":"https://doi.org/10.1142/s0218195922500030","title":"Non-Rational and Rational Transfinite Interpolation Using Bernstein Polynomials","display_name":"Non-Rational and Rational Transfinite Interpolation Using Bernstein Polynomials","publication_year":2022,"publication_date":"2022-03-01","ids":{"openalex":"https://openalex.org/W4292768201","doi":"https://doi.org/10.1142/s0218195922500030"},"language":"en","primary_location":{"id":"doi:10.1142/s0218195922500030","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195922500030","pdf_url":null,"source":{"id":"https://openalex.org/S25827807","display_name":"International Journal of Computational Geometry & Applications","issn_l":"0218-1959","issn":["0218-1959","1793-6357"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Geometry &amp; Applications","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/A5049793842","display_name":"Christopher G. Provatidis","orcid":"https://orcid.org/0000-0002-1845-9245"},"institutions":[{"id":"https://openalex.org/I174458059","display_name":"National Technical University of Athens","ror":"https://ror.org/03cx6bg69","country_code":"GR","type":"education","lineage":["https://openalex.org/I174458059"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"Christopher G. Provatidis","raw_affiliation_strings":["School of Mechanical Engineering, National Technical University of Athens, Zografou Campus, 9, Iroon Polytechniou Str., 15780 Zografou, Greece"],"raw_orcid":"https://orcid.org/0000-0002-1845-9245","affiliations":[{"raw_affiliation_string":"School of Mechanical Engineering, National Technical University of Athens, Zografou Campus, 9, Iroon Polytechniou Str., 15780 Zografou, Greece","institution_ids":["https://openalex.org/I174458059"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5049793842"],"corresponding_institution_ids":["https://openalex.org/I174458059"],"apc_list":null,"apc_paid":null,"fwci":1.1111,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.72012589,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"32","issue":"01n02","first_page":"55","last_page":"89"},"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/T10188","display_name":"Advanced machining processes and optimization","score":0.9902999997138977,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T10221","display_name":"Composite Structure Analysis and Optimization","score":0.9781000018119812,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/mathematics","display_name":"Mathematics","score":0.7900995016098022},{"id":"https://openalex.org/keywords/quadric","display_name":"Quadric","score":0.5998257994651794},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5122095942497253},{"id":"https://openalex.org/keywords/transfinite-number","display_name":"Transfinite number","score":0.5094776749610901},{"id":"https://openalex.org/keywords/lagrange-polynomial","display_name":"Lagrange polynomial","score":0.4798840582370758},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.44673773646354675},{"id":"https://openalex.org/keywords/bernstein-polynomial","display_name":"Bernstein polynomial","score":0.43359100818634033},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3465648293495178},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3401058316230774},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33852267265319824},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.27981871366500854},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10414308309555054}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7900995016098022},{"id":"https://openalex.org/C2779219049","wikidata":"https://www.wikidata.org/wiki/Q852117","display_name":"Quadric","level":2,"score":0.5998257994651794},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5122095942497253},{"id":"https://openalex.org/C147358099","wikidata":"https://www.wikidata.org/wiki/Q1069891","display_name":"Transfinite number","level":2,"score":0.5094776749610901},{"id":"https://openalex.org/C64208722","wikidata":"https://www.wikidata.org/wiki/Q861606","display_name":"Lagrange polynomial","level":3,"score":0.4798840582370758},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.44673773646354675},{"id":"https://openalex.org/C34179328","wikidata":"https://www.wikidata.org/wiki/Q826841","display_name":"Bernstein polynomial","level":2,"score":0.43359100818634033},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3465648293495178},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3401058316230774},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33852267265319824},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.27981871366500854},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10414308309555054},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218195922500030","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195922500030","pdf_url":null,"source":{"id":"https://openalex.org/S25827807","display_name":"International Journal of Computational Geometry & Applications","issn_l":"0218-1959","issn":["0218-1959","1793-6357"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Geometry &amp; Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.6200000047683716}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1963729634","https://openalex.org/W1977182911","https://openalex.org/W2001483770","https://openalex.org/W2031357298","https://openalex.org/W2058111044","https://openalex.org/W2094689827","https://openalex.org/W2138784103","https://openalex.org/W2503549878","https://openalex.org/W3007654668","https://openalex.org/W3135117475","https://openalex.org/W4200244989","https://openalex.org/W4237713727","https://openalex.org/W4300929448"],"related_works":["https://openalex.org/W2951364565","https://openalex.org/W2963803326","https://openalex.org/W2093857802","https://openalex.org/W4302313139","https://openalex.org/W1975449259","https://openalex.org/W1968435904","https://openalex.org/W2953102570","https://openalex.org/W4296472263","https://openalex.org/W2614747680","https://openalex.org/W4292768201"],"abstract_inverted_index":{"It":[0],"is":[1,25,38,138],"shown":[2],"that":[3,93],"the":[4,27,31,36,40,44,55,61,65,70,74,78,89,113,135,141,152,182,191,199],"standard":[5,114],"transfinite":[6],"interpolation":[7],"in":[8,14],"quadrilateral":[9],"patches":[10],"may":[11,94],"be":[12],"written":[13],"terms":[15],"of":[16,19,26,39,54,64,69,80,91,98,103,144,185,202],"two":[17],"sets":[18],"Bernstein":[20,75],"polynomials.":[21],"The":[22,67,109],"former":[23],"set":[24],"same":[28,41],"degree":[29,42],"with":[30,43,127,163],"corresponding":[32],"blending":[33],"functions":[34,51,194],"while":[35],"latter":[37,153],"Lagrange":[45,71],"polynomials":[46,72],"which":[47,117,173],"operate":[48],"like":[49],"trial":[50],"along":[52],"each":[53],"four":[56],"edges":[57],"as":[58,60],"well":[59],"additional":[62],"inter-boundaries":[63],"patch.":[66,150],"replacement":[68],"by":[73],"ones":[76],"allows":[77,88],"use":[79],"control":[81,177],"points":[82,178],"useful":[83],"for":[84,181],"design.":[85],"Also":[86],"it":[87],"determination":[90],"weights":[92,175],"ensure":[95],"accurate":[96,183],"representation":[97,143,184],"quadric":[99],"surfaces":[100],"including":[101],"those":[102],"revolution":[104],"(spheres,":[105],"ellipsoids,":[106],"hyperboloids,":[107],"etc).":[108],"presentation":[110],"restricts":[111],"to":[112,119,123,140,167,198],"Gordon":[115],"formulation,":[116],"refers":[118],"structured":[120],"stencils,":[121],"similar":[122],"rectangular":[124],"plates":[125],"reinforced":[126],"longitudinal":[128],"and":[129,147,176],"transverse":[130],"stiffeners.":[131],"As":[132],"an":[133],"example,":[134],"proposed":[136],"formula":[137],"applied":[139,197],"geometric":[142],"a":[145,148,155,168,186,203],"cylindrical":[146],"spherical":[149,187],"In":[151,189],"case":[154],"nonlinear":[156],"programming":[157],"optimization":[158],"technique":[159],"was":[160],"applied,":[161],"starting":[162],"initial":[164],"data":[165],"pertinent":[166],"tensor":[169],"product":[170],"surface,":[171],"from":[172],"original":[174],"were":[179,195],"obtained":[180],"cap.":[188],"addition,":[190],"involved":[192],"shape":[193],"successfully":[196],"numerical":[200],"solution":[201],"boundary":[204],"value":[205],"problem.":[206]},"counts_by_year":[{"year":2025,"cited_by_count":7}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
