{"id":"https://openalex.org/W2008162898","doi":"https://doi.org/10.1093/imamci/dni014","title":"Envelopes of splines in the projective plane","display_name":"Envelopes of splines in the projective plane","publication_year":2005,"publication_date":"2005-02-17","ids":{"openalex":"https://openalex.org/W2008162898","doi":"https://doi.org/10.1093/imamci/dni014","mag":"2008162898"},"language":"en","primary_location":{"id":"doi:10.1093/imamci/dni014","is_oa":false,"landing_page_url":"https://doi.org/10.1093/imamci/dni014","pdf_url":null,"source":{"id":"https://openalex.org/S162756791","display_name":"IMA Journal of Mathematical Control and Information","issn_l":"0265-0754","issn":["0265-0754","1471-6887"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IMA Journal of Mathematical Control and Information","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/A5008123701","display_name":"Krzysztof Krakowski","orcid":"https://orcid.org/0000-0001-9508-016X"},"institutions":[{"id":"https://openalex.org/I90745801","display_name":"University of New England","ror":"https://ror.org/04r659a56","country_code":"AU","type":"education","lineage":["https://openalex.org/I90745801"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"K. A. Krakowski","raw_affiliation_strings":["School of Mathematics, Statistics and Computer Science, The University of New England, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Statistics and Computer Science, The University of New England, Australia","institution_ids":["https://openalex.org/I90745801"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5008123701"],"corresponding_institution_ids":["https://openalex.org/I90745801"],"apc_list":{"value":2819,"currency":"GBP","value_usd":3718},"apc_paid":null,"fwci":1.487,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.80074061,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"22","issue":"2","first_page":"171","last_page":"180"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9993000030517578,"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":0.9993000030517578,"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":0.9305999875068665,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9108999967575073,"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/projective-plane","display_name":"Projective plane","score":0.5311682820320129},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.5216139554977417},{"id":"https://openalex.org/keywords/projective-test","display_name":"Projective test","score":0.4779377281665802},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42685651779174805},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34768354892730713},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3318920135498047},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2990924119949341}],"concepts":[{"id":"https://openalex.org/C39290043","wikidata":"https://www.wikidata.org/wiki/Q1475760","display_name":"Projective plane","level":3,"score":0.5311682820320129},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5216139554977417},{"id":"https://openalex.org/C177846678","wikidata":"https://www.wikidata.org/wiki/Q1501864","display_name":"Projective test","level":2,"score":0.4779377281665802},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42685651779174805},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34768354892730713},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3318920135498047},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2990924119949341},{"id":"https://openalex.org/C117220453","wikidata":"https://www.wikidata.org/wiki/Q5172842","display_name":"Correlation","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1093/imamci/dni014","is_oa":false,"landing_page_url":"https://doi.org/10.1093/imamci/dni014","pdf_url":null,"source":{"id":"https://openalex.org/S162756791","display_name":"IMA Journal of Mathematical Control and Information","issn_l":"0265-0754","issn":["0265-0754","1471-6887"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IMA Journal of Mathematical Control and Information","raw_type":"journal-article"},{"id":"pmh:oai:rune.une.edu.au:1959.11/3279","is_oa":false,"landing_page_url":"https://hdl.handle.net/1959.11/3279","pdf_url":null,"source":{"id":"https://openalex.org/S7407055448","display_name":"RUNE (Research UNE)","issn_l":null,"issn":null,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.6000000238418579,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W63727357","https://openalex.org/W588295442","https://openalex.org/W1518247801","https://openalex.org/W1949248870","https://openalex.org/W1973484256","https://openalex.org/W1986281772","https://openalex.org/W2001450374","https://openalex.org/W2030394252","https://openalex.org/W2030527848","https://openalex.org/W2036793545","https://openalex.org/W2062264317","https://openalex.org/W2091743831","https://openalex.org/W2108564727","https://openalex.org/W3129186208"],"related_works":["https://openalex.org/W2964292522","https://openalex.org/W2083539879","https://openalex.org/W2756329859","https://openalex.org/W2725952271","https://openalex.org/W2964145023","https://openalex.org/W2062228483","https://openalex.org/W2439115288","https://openalex.org/W2792779451","https://openalex.org/W168857003","https://openalex.org/W2044219908"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"a":[3,42,50],"family":[4],"of":[5,38],"curves\u2014Riemannian":[6],"cubics\u2014in":[7],"the":[8,12],"unit":[9],"sphere":[10],"and":[11],"real":[13],"projective":[14],"plane":[15],"is":[16,31,48],"investigated.":[17],"Riemannian":[18,28,43,51],"cubics":[19],"naturally":[20],"arise":[21],"as":[22],"solutions":[23],"to":[24,33],"variational":[25],"problems":[26],"in":[27,45,53],"spaces.":[29],"It":[30],"remarkable":[32],"find":[34],"that":[35],"an":[36],"envelope":[37],"lines":[39],"generated":[40],"by":[41],"cubic":[44,52],"one":[46],"space":[47],"(nearly)":[49],"another":[54],"space.":[55]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}