{"id":"https://openalex.org/W4406632491","doi":"https://doi.org/10.3390/axioms14010072","title":"From Topological Optimization to Spline Layouts: An Approach for Industrial Real-Wise Parts","display_name":"From Topological Optimization to Spline Layouts: An Approach for Industrial Real-Wise Parts","publication_year":2025,"publication_date":"2025-01-20","ids":{"openalex":"https://openalex.org/W4406632491","doi":"https://doi.org/10.3390/axioms14010072"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14010072","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14010072","pdf_url":"https://www.mdpi.com/2075-1680/14/1/72/pdf?version=1737359538","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/2075-1680/14/1/72/pdf?version=1737359538","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004945435","display_name":"Carolina Vittoria Beccari","orcid":"https://orcid.org/0000-0002-0048-6034"},"institutions":[{"id":"https://openalex.org/I9360294","display_name":"University of Bologna","ror":"https://ror.org/01111rn36","country_code":"IT","type":"education","lineage":["https://openalex.org/I9360294"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Carolina Vittoria Beccari","raw_affiliation_strings":["Department of Mathematics, University of Bologna, Piazza di Porta San Donato 5, 40126 Bologna, Italy"],"raw_orcid":"https://orcid.org/0000-0002-0048-6034","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Bologna, Piazza di Porta San Donato 5, 40126 Bologna, Italy","institution_ids":["https://openalex.org/I9360294"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063333786","display_name":"Alessandro Ceruti","orcid":"https://orcid.org/0000-0001-7947-3932"},"institutions":[{"id":"https://openalex.org/I9360294","display_name":"University of Bologna","ror":"https://ror.org/01111rn36","country_code":"IT","type":"education","lineage":["https://openalex.org/I9360294"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Alessandro Ceruti","raw_affiliation_strings":["Department of Industrial Engineering, University of Bologna, Viale del Risorgimento 2, 40136 Bologna, Italy"],"raw_orcid":"https://orcid.org/0000-0001-7947-3932","affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering, University of Bologna, Viale del Risorgimento 2, 40136 Bologna, Italy","institution_ids":["https://openalex.org/I9360294"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051724422","display_name":"Filip Chudy","orcid":"https://orcid.org/0000-0002-6174-9109"},"institutions":[{"id":"https://openalex.org/I219388962","display_name":"University of Wroc\u0142aw","ror":"https://ror.org/00yae6e25","country_code":"PL","type":"education","lineage":["https://openalex.org/I219388962"]},{"id":"https://openalex.org/I4210087266","display_name":"Institute of Computer Science","ror":"https://ror.org/003fvp964","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210087266","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I9360294","display_name":"University of Bologna","ror":"https://ror.org/01111rn36","country_code":"IT","type":"education","lineage":["https://openalex.org/I9360294"]}],"countries":["IT","PL"],"is_corresponding":false,"raw_author_name":"Filip Chudy","raw_affiliation_strings":["Department of Mathematics, University of Bologna, Piazza di Porta San Donato 5, 40126 Bologna, Italy","Institute of Computer Science, University of Wroc\u0142aw, ul. Joliot-Curie 15, 50-383 Wroc\u0142aw, Poland"],"raw_orcid":"https://orcid.org/0000-0002-6174-9109","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Bologna, Piazza di Porta San Donato 5, 40126 Bologna, Italy","institution_ids":["https://openalex.org/I9360294"]},{"raw_affiliation_string":"Institute of Computer Science, University of Wroc\u0142aw, ul. Joliot-Curie 15, 50-383 Wroc\u0142aw, Poland","institution_ids":["https://openalex.org/I219388962","https://openalex.org/I4210087266"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5004945435"],"corresponding_institution_ids":["https://openalex.org/I9360294"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.0627,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.7485557,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"14","issue":"1","first_page":"72","last_page":"72"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11159","display_name":"Manufacturing Process and Optimization","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"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/T11159","display_name":"Manufacturing Process and Optimization","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing 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/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/T10783","display_name":"Additive Manufacturing and 3D Printing Technologies","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/2203","display_name":"Automotive Engineering"},"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/spline","display_name":"Spline (mechanical)","score":0.5790756940841675},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45503780245780945},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.41700947284698486},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.40075579285621643},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3579411506652832},{"id":"https://openalex.org/keywords/engineering-drawing","display_name":"Engineering drawing","score":0.3372041881084442},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.2596970796585083},{"id":"https://openalex.org/keywords/mechanical-engineering","display_name":"Mechanical engineering","score":0.17745688557624817},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.10356858372688293}],"concepts":[{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.5790756940841675},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45503780245780945},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.41700947284698486},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40075579285621643},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3579411506652832},{"id":"https://openalex.org/C199639397","wikidata":"https://www.wikidata.org/wiki/Q1788588","display_name":"Engineering drawing","level":1,"score":0.3372041881084442},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.2596970796585083},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.17745688557624817},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.10356858372688293}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms14010072","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14010072","pdf_url":"https://www.mdpi.com/2075-1680/14/1/72/pdf?version=1737359538","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:cris.unibo.it:11585/1004669","is_oa":true,"landing_page_url":"https://hdl.handle.net/11585/1004669","pdf_url":"https://cris.unibo.it/bitstream/11585/1004669/1/axioms-14-00072.pdf","source":{"id":"https://openalex.org/S4306402579","display_name":"Archivio istituzionale della ricerca (Alma Mater Studiorum Universit\u00e0 di Bologna)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210117483","host_organization_name":"Istituto di Ematologia di Bologna","host_organization_lineage":["https://openalex.org/I4210117483"],"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":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:032303ce58e24673856842738be10800","is_oa":true,"landing_page_url":"https://doaj.org/article/032303ce58e24673856842738be10800","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 14, Iss 1, p 72 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14010072","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14010072","pdf_url":"https://www.mdpi.com/2075-1680/14/1/72/pdf?version=1737359538","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":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320323553","display_name":"Universit\u00e0 di Bologna","ror":"https://ror.org/01111rn36"},{"id":"https://openalex.org/F4320334079","display_name":"Gruppo Nazionale per il Calcolo Scientifico","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4406632491.pdf"},"referenced_works_count":40,"referenced_works":["https://openalex.org/W1969944427","https://openalex.org/W1990119681","https://openalex.org/W2000214666","https://openalex.org/W2025606830","https://openalex.org/W2030596220","https://openalex.org/W2030977254","https://openalex.org/W2034538896","https://openalex.org/W2059210098","https://openalex.org/W2072627393","https://openalex.org/W2072707490","https://openalex.org/W2075010828","https://openalex.org/W2092801729","https://openalex.org/W2112311198","https://openalex.org/W2119876572","https://openalex.org/W2135634705","https://openalex.org/W2197700944","https://openalex.org/W2267893120","https://openalex.org/W2612666967","https://openalex.org/W2737514381","https://openalex.org/W2806513993","https://openalex.org/W2950425749","https://openalex.org/W2969633497","https://openalex.org/W3016496727","https://openalex.org/W3138619098","https://openalex.org/W3155898734","https://openalex.org/W3185735817","https://openalex.org/W3195339082","https://openalex.org/W4200172275","https://openalex.org/W4205649593","https://openalex.org/W4256379935","https://openalex.org/W4380324170","https://openalex.org/W4398164505","https://openalex.org/W4400249180","https://openalex.org/W4402456039","https://openalex.org/W4404169984","https://openalex.org/W6629634115","https://openalex.org/W6681751655","https://openalex.org/W6687094287","https://openalex.org/W6693397905","https://openalex.org/W6751716669"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2385282872"],"abstract_inverted_index":{"Additive":[0],"manufacturing":[1],"technologies":[2],"have":[3,176],"allowed":[4],"the":[5,22,45,63,71,96,142,153,162,166,170,185],"production":[6],"of":[7,21,85,134,155,165,188],"complex":[8],"geometries":[9],"that":[10,190],"are":[11,159],"typically":[12],"obtained":[13],"by":[14,74],"applying":[15],"topology":[16,75,99],"optimization":[17,23,100,110],"techniques.":[18],"The":[19,57,148],"outcome":[20],"process":[24],"is":[25,80,87,150],"a":[26,83,92,103,113,118,127,132,181,198],"tessellated":[27],"geometry,":[28],"which":[29,158],"has":[30],"reduced":[31],"aesthetic":[32],"quality":[33],"and":[34,37,51,82,140,195],"unwanted":[35],"spikes":[36],"cusps.":[38],"Filters":[39],"can":[40,54,191],"be":[41,55,193],"applied":[42],"to":[43,94,102,129],"improve":[44],"surface":[46,164],"quality,":[47],"but":[48],"volume":[49],"shrinking":[50],"geometry":[52],"modification":[53],"noticed.":[56],"design":[58,105],"practice":[59],"suggests":[60],"manually":[61],"re-designing":[62],"object":[64],"in":[65,197],"Computer-Aided":[66],"Design":[67],"(CAD)":[68],"software,":[69],"imitating":[70],"shape":[72],"suggested":[73],"optimization.":[76],"However,":[77],"this":[78],"operation":[79],"tedious":[81],"lot":[84],"time":[86],"wasted.":[88],"This":[89],"paper":[90],"proposes":[91],"methodology":[93,149],"automate":[95],"conversion":[97],"from":[98],"output":[101],"CAD-compatible":[104],"for":[106,122],"industrial":[107,146],"components.":[108,147,167],"Topology":[109],"usually":[111],"produces":[112],"dense":[114],"triangle":[115],"mesh":[116],"with":[117],"high":[119],"topological":[120],"genus":[121],"those":[123],"objects.":[124],"We":[125],"present":[126],"method":[128],"automatically":[130],"generate":[131],"collection":[133],"spline":[135],"(tensor-product)":[136],"patches":[137,157],"joined":[138],"watertight":[139],"test":[141],"approach":[143],"on":[144,152,161,169],"real-wise":[145],"based":[151],"use":[154],"quadrilateral":[156],"built":[160],"external":[163],"Based":[168],"tests":[171],"carried":[172],"out,":[173],"promising":[174],"results":[175],"been":[177],"obtained.":[178],"It":[179],"constitutes":[180],"first":[182],"step":[183],"towards":[184],"automatic":[186],"generation":[187],"shapes":[189],"readily":[192],"imported":[194],"edited":[196],"CAD":[199],"system.":[200]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}