{"id":"https://openalex.org/W2093576171","doi":"https://doi.org/10.1016/s0167-8396(01)00015-2","title":"Transfinite interpolation over implicitly defined sets","display_name":"Transfinite interpolation over implicitly defined sets","publication_year":2001,"publication_date":"2001-04-01","ids":{"openalex":"https://openalex.org/W2093576171","doi":"https://doi.org/10.1016/s0167-8396(01)00015-2","mag":"2093576171"},"language":"en","primary_location":{"id":"doi:10.1016/s0167-8396(01)00015-2","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0167-8396(01)00015-2","pdf_url":null,"source":{"id":"https://openalex.org/S135221619","display_name":"Computer Aided Geometric Design","issn_l":"0167-8396","issn":["0167-8396","1879-2332"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer Aided Geometric Design","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/A5006175308","display_name":"V. L. Rvachev","orcid":null},"institutions":[{"id":"https://openalex.org/I4210121111","display_name":"Podgorny Institute for Mechanical Engineering Problems","ror":"https://ror.org/02ezqbp79","country_code":"UA","type":"facility","lineage":["https://openalex.org/I149851306","https://openalex.org/I4210121111"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"V.L. Rvachev","raw_affiliation_strings":["Institute for Problems in Machinery of the National Academy of Sciences, 2/10 Pozharsky Str., Kharkov, 61046 Ukraine"],"affiliations":[{"raw_affiliation_string":"Institute for Problems in Machinery of the National Academy of Sciences, 2/10 Pozharsky Str., Kharkov, 61046 Ukraine","institution_ids":["https://openalex.org/I4210121111"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002659426","display_name":"\u0422. \u0418. \u0428\u0435\u0439\u043a\u043e","orcid":null},"institutions":[{"id":"https://openalex.org/I4210121111","display_name":"Podgorny Institute for Mechanical Engineering Problems","ror":"https://ror.org/02ezqbp79","country_code":"UA","type":"facility","lineage":["https://openalex.org/I149851306","https://openalex.org/I4210121111"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"T.I. Sheiko","raw_affiliation_strings":["Institute for Problems in Machinery of the National Academy of Sciences, 2/10 Pozharsky Str., Kharkov, 61046 Ukraine"],"affiliations":[{"raw_affiliation_string":"Institute for Problems in Machinery of the National Academy of Sciences, 2/10 Pozharsky Str., Kharkov, 61046 Ukraine","institution_ids":["https://openalex.org/I4210121111"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111666256","display_name":"Vadim Shapiro","orcid":null},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"V. Shapiro","raw_affiliation_strings":["Spatial Automation Laboratory, University of Wisconsin\u2013Madison, 1513 University Avenue, Madison, WI, 53706, USA","Spatial Automation Laboratory, University of Wisconsin-Madison, 1513 University Avenue, Madison, WI 53706, USA"],"affiliations":[{"raw_affiliation_string":"Spatial Automation Laboratory, University of Wisconsin\u2013Madison, 1513 University Avenue, Madison, WI, 53706, USA","institution_ids":["https://openalex.org/I135310074"]},{"raw_affiliation_string":"Spatial Automation Laboratory, University of Wisconsin-Madison, 1513 University Avenue, Madison, WI 53706, USA","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067672785","display_name":"Igor Tsukanov","orcid":null},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"I. Tsukanov","raw_affiliation_strings":["Spatial Automation Laboratory, University of Wisconsin\u2013Madison, 1513 University Avenue, Madison, WI, 53706, USA","Spatial Automation Laboratory, University of Wisconsin-Madison, 1513 University Avenue, Madison, WI 53706, USA"],"affiliations":[{"raw_affiliation_string":"Spatial Automation Laboratory, University of Wisconsin\u2013Madison, 1513 University Avenue, Madison, WI, 53706, USA","institution_ids":["https://openalex.org/I135310074"]},{"raw_affiliation_string":"Spatial Automation Laboratory, University of Wisconsin-Madison, 1513 University Avenue, Madison, WI 53706, USA","institution_ids":["https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5111666256"],"corresponding_institution_ids":["https://openalex.org/I135310074"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":14.5289,"has_fulltext":false,"cited_by_count":121,"citation_normalized_percentile":{"value":0.99339689,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"18","issue":"3","first_page":"195","last_page":"220"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9994999766349792,"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/T11558","display_name":"Composite Material Mechanics","score":0.9941999912261963,"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/transfinite-number","display_name":"Transfinite number","score":0.8774785995483398},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8202083110809326},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.7457982897758484},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5148738622665405},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.4521496593952179},{"id":"https://openalex.org/keywords/nearest-neighbor-interpolation","display_name":"Nearest-neighbor interpolation","score":0.449806809425354},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.42642587423324585},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.4243921935558319},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3808324933052063},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3177962303161621},{"id":"https://openalex.org/keywords/linear-interpolation","display_name":"Linear interpolation","score":0.3057313561439514},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11528629064559937}],"concepts":[{"id":"https://openalex.org/C147358099","wikidata":"https://www.wikidata.org/wiki/Q1069891","display_name":"Transfinite number","level":2,"score":0.8774785995483398},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8202083110809326},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.7457982897758484},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5148738622665405},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.4521496593952179},{"id":"https://openalex.org/C207214200","wikidata":"https://www.wikidata.org/wiki/Q4202129","display_name":"Nearest-neighbor interpolation","level":4,"score":0.449806809425354},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.42642587423324585},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4243921935558319},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3808324933052063},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3177962303161621},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.3057313561439514},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11528629064559937},{"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/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1016/s0167-8396(01)00015-2","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0167-8396(01)00015-2","pdf_url":null,"source":{"id":"https://openalex.org/S135221619","display_name":"Computer Aided Geometric Design","issn_l":"0167-8396","issn":["0167-8396","1879-2332"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer Aided Geometric Design","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.4.4557","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.4.4557","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://sal-cnc.me.wisc.edu/publications/transfinite/interpolation.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W167920528","https://openalex.org/W1495295109","https://openalex.org/W1502632332","https://openalex.org/W1554511749","https://openalex.org/W1644886288","https://openalex.org/W1964673636","https://openalex.org/W1968757949","https://openalex.org/W1977252686","https://openalex.org/W1982471813","https://openalex.org/W1989519540","https://openalex.org/W1993590822","https://openalex.org/W2004085871","https://openalex.org/W2027899982","https://openalex.org/W2043122685","https://openalex.org/W2079976883","https://openalex.org/W2086545565","https://openalex.org/W2108142674","https://openalex.org/W2146968309","https://openalex.org/W2147169375","https://openalex.org/W2162148444","https://openalex.org/W2162870748","https://openalex.org/W2170120409","https://openalex.org/W2600643276","https://openalex.org/W2768498986","https://openalex.org/W2921636359","https://openalex.org/W4206360718","https://openalex.org/W6629995875","https://openalex.org/W6644344293","https://openalex.org/W6648545703","https://openalex.org/W6671891040","https://openalex.org/W6681742681"],"related_works":["https://openalex.org/W2364365984","https://openalex.org/W3157416991","https://openalex.org/W2532653122","https://openalex.org/W2139022416","https://openalex.org/W2378343395","https://openalex.org/W2105122052","https://openalex.org/W2142192217","https://openalex.org/W2161678290","https://openalex.org/W178094302","https://openalex.org/W1912636275"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
