{"id":"https://openalex.org/W4399493344","doi":"https://doi.org/10.3390/axioms13060390","title":"Bicubic Splines for Fast-Contracting Control Nets","display_name":"Bicubic Splines for Fast-Contracting Control Nets","publication_year":2024,"publication_date":"2024-06-09","ids":{"openalex":"https://openalex.org/W4399493344","doi":"https://doi.org/10.3390/axioms13060390"},"language":"en","primary_location":{"id":"doi:10.3390/axioms13060390","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13060390","pdf_url":"https://www.mdpi.com/2075-1680/13/6/390/pdf?version=1717922982","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/13/6/390/pdf?version=1717922982","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030292229","display_name":"K\u0229stutis Kar\u010diauskas","orcid":"https://orcid.org/0000-0002-9398-6424"},"institutions":[{"id":"https://openalex.org/I173212132","display_name":"Vilnius University","ror":"https://ror.org/03nadee84","country_code":"LT","type":"education","lineage":["https://openalex.org/I173212132"]}],"countries":["LT"],"is_corresponding":false,"raw_author_name":"K\u0229stutis Kar\u010diauskas","raw_affiliation_strings":["Institute of Mathematics, Vilnius University, LT-03225 Vilnius, Lithuania"],"raw_orcid":"https://orcid.org/0000-0002-9398-6424","affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Vilnius University, LT-03225 Vilnius, Lithuania","institution_ids":["https://openalex.org/I173212132"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058288671","display_name":"Kyle Shih-Huang Lo","orcid":"https://orcid.org/0000-0002-0338-6469"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kyle Shih-Huang Lo","raw_affiliation_strings":["Department of Computer and Information Sciences and Engineering, University of Florida, Gainesville, FL 32611, USA"],"raw_orcid":"https://orcid.org/0000-0002-0338-6469","affiliations":[{"raw_affiliation_string":"Department of Computer and Information Sciences and Engineering, University of Florida, Gainesville, FL 32611, USA","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046517594","display_name":"Erkan G\u00fcnp\u0131nar","orcid":"https://orcid.org/0000-0002-0266-5546"},"institutions":[{"id":"https://openalex.org/I48912391","display_name":"Istanbul Technical University","ror":"https://ror.org/059636586","country_code":"TR","type":"education","lineage":["https://openalex.org/I48912391"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Erkan Gunpinar","raw_affiliation_strings":["Department of Mechanical Engineering, Istanbul Technical University, 34437 Istanbul, T\u00fcrkiye"],"raw_orcid":"https://orcid.org/0000-0002-0266-5546","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Istanbul Technical University, 34437 Istanbul, T\u00fcrkiye","institution_ids":["https://openalex.org/I48912391"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027686327","display_name":"J\u00f6rg Peters","orcid":"https://orcid.org/0000-0002-2499-1529"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"J\u00f6rg Peters","raw_affiliation_strings":["Department of Computer and Information Sciences and Engineering, University of Florida, Gainesville, FL 32611, USA"],"raw_orcid":"https://orcid.org/0000-0002-2499-1529","affiliations":[{"raw_affiliation_string":"Department of Computer and Information Sciences and Engineering, University of Florida, Gainesville, FL 32611, USA","institution_ids":["https://openalex.org/I33213144"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5027686327"],"corresponding_institution_ids":["https://openalex.org/I33213144"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.901,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.67687315,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"13","issue":"6","first_page":"390","last_page":"390"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9991999864578247,"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":0.9991999864578247,"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/T11138","display_name":"Tribology and Lubrication Engineering","score":0.9861000180244446,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9787999987602234,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.649876594543457},{"id":"https://openalex.org/keywords/merge","display_name":"Merge (version control)","score":0.5215559005737305},{"id":"https://openalex.org/keywords/spline","display_name":"Spline (mechanical)","score":0.47638291120529175},{"id":"https://openalex.org/keywords/bicubic-interpolation","display_name":"Bicubic interpolation","score":0.4546445310115814},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4532212018966675},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.45003411173820496},{"id":"https://openalex.org/keywords/isotropy","display_name":"Isotropy","score":0.44957906007766724},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43125107884407043},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.4277811646461487},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42442551255226135},{"id":"https://openalex.org/keywords/spline-interpolation","display_name":"Spline interpolation","score":0.41765788197517395},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3410336375236511},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33981502056121826},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3311440646648407},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.27741315960884094},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21921375393867493},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.18721550703048706},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.13359922170639038},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.11406916379928589},{"id":"https://openalex.org/keywords/linear-interpolation","display_name":"Linear interpolation","score":0.10243317484855652},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.08322188258171082},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.08172622323036194}],"concepts":[{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.649876594543457},{"id":"https://openalex.org/C197129107","wikidata":"https://www.wikidata.org/wiki/Q1921621","display_name":"Merge (version control)","level":2,"score":0.5215559005737305},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.47638291120529175},{"id":"https://openalex.org/C49608258","wikidata":"https://www.wikidata.org/wiki/Q611705","display_name":"Bicubic interpolation","level":4,"score":0.4546445310115814},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4532212018966675},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.45003411173820496},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.44957906007766724},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43125107884407043},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.4277811646461487},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42442551255226135},{"id":"https://openalex.org/C31447003","wikidata":"https://www.wikidata.org/wiki/Q545002","display_name":"Spline interpolation","level":3,"score":0.41765788197517395},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3410336375236511},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33981502056121826},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3311440646648407},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.27741315960884094},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21921375393867493},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.18721550703048706},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.13359922170639038},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.11406916379928589},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.10243317484855652},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.08322188258171082},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.08172622323036194},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms13060390","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13060390","pdf_url":"https://www.mdpi.com/2075-1680/13/6/390/pdf?version=1717922982","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:92eee2d21460462a9c4e3efb5dd17f3a","is_oa":true,"landing_page_url":"https://doaj.org/article/92eee2d21460462a9c4e3efb5dd17f3a","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 13, Iss 6, p 390 (2024)","raw_type":"article"},{"id":"pmh:oai:polen.itu.edu.tr:11527/50559","is_oa":false,"landing_page_url":"https://hdl.handle.net/11527/50559","pdf_url":null,"source":{"id":"https://openalex.org/S4306400460","display_name":"Istanbul Technical University Academic Open Archive (Istanbul Technical University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I48912391","host_organization_name":"Istanbul Technical University","host_organization_lineage":["https://openalex.org/I48912391"],"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":"Article"}],"best_oa_location":{"id":"doi:10.3390/axioms13060390","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13060390","pdf_url":"https://www.mdpi.com/2075-1680/13/6/390/pdf?version=1717922982","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.6100000143051147,"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4399493344.pdf"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W115996756","https://openalex.org/W168805139","https://openalex.org/W1186497850","https://openalex.org/W1972866868","https://openalex.org/W1973730326","https://openalex.org/W1991967767","https://openalex.org/W2002667544","https://openalex.org/W2009369335","https://openalex.org/W2011129566","https://openalex.org/W2029119997","https://openalex.org/W2032325716","https://openalex.org/W2043772115","https://openalex.org/W2047131312","https://openalex.org/W2059085479","https://openalex.org/W2091620062","https://openalex.org/W2159770071","https://openalex.org/W2174386445","https://openalex.org/W2293903326","https://openalex.org/W2295183215","https://openalex.org/W2550160097","https://openalex.org/W2580302988","https://openalex.org/W2736383202","https://openalex.org/W2739447304","https://openalex.org/W2884447654","https://openalex.org/W2947230571","https://openalex.org/W3003572695","https://openalex.org/W3022241089","https://openalex.org/W3034225756","https://openalex.org/W3088452382","https://openalex.org/W4249019869","https://openalex.org/W4253976794","https://openalex.org/W4280514842","https://openalex.org/W4281775632","https://openalex.org/W4283693964","https://openalex.org/W4299672679","https://openalex.org/W4307887065","https://openalex.org/W4328029555","https://openalex.org/W4377832112","https://openalex.org/W4385766035","https://openalex.org/W4396831286","https://openalex.org/W6625727892"],"related_works":["https://openalex.org/W2035908164","https://openalex.org/W2092836869","https://openalex.org/W1965605760","https://openalex.org/W2089774915","https://openalex.org/W2046026412","https://openalex.org/W2036543038","https://openalex.org/W2014956377","https://openalex.org/W2394087716","https://openalex.org/W2002288548","https://openalex.org/W2009426420"],"abstract_inverted_index":{"Merging":[0],"parallel":[1],"quad":[2],"strips":[3],"facilitates":[4],"narrowing":[5],"surface":[6,23,79],"passages,":[7],"and":[8,106],"allows":[9],"a":[10,15,19,39,53],"design":[11],"to":[12,14,101,111],"transition":[13],"simpler":[16],"shape.":[17],"While":[18],"number":[20],"of":[21,66],"spline":[22,36,69],"constructions":[24,37],"exist":[25],"for":[26,42,56],"the":[27,64,82,103],"isotropic":[28],"case":[29],"where":[30],"n":[31],"pieces":[32,109],"join,":[33],"few":[34],"existing":[35,112],"deliver":[38],"good":[40,54],"shape":[41,55],"control":[43,59,73],"nets":[44],"that":[45],"merge":[46],"parameter":[47],"lines.":[48],"Additionally,":[49],"untilrecently,":[50],"none":[51],"provided":[52],"fast-contracting":[57,72,77],"polyhedral":[58],"nets.":[60,74],"This":[61],"work":[62],"improves":[63],"state-of-the-art":[65],"piecewise":[67],"polynomial":[68],"surfaces":[70,89],"accommodating":[71],"The":[75,88],"new":[76],"(FC)":[78],"algorithm":[80],"yields":[81],"industry-preferred":[83],"uniform":[84],"degree":[85],"bi-3":[86],"(bi-cubic).":[87],"are":[90],"by":[91],"default":[92],"differentiable,":[93],"have":[94],"an":[95],"improved":[96],"shape,":[97],"measured":[98],"empirically":[99],"as":[100],"highlight":[102],"line":[104],"distribution,":[105],"require":[107],"fewer":[108],"compared":[110],"methods.":[113]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
