{"id":"https://openalex.org/W2952560824","doi":"https://doi.org/10.1016/j.cagx.2019.100006","title":"Representation of NURBS surfaces by Controlled Iterated Functions System automata","display_name":"Representation of NURBS surfaces by Controlled Iterated Functions System automata","publication_year":2019,"publication_date":"2019-06-07","ids":{"openalex":"https://openalex.org/W2952560824","doi":"https://doi.org/10.1016/j.cagx.2019.100006","mag":"2952560824"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.cagx.2019.100006","pdf_url":null,"source":{"id":"https://openalex.org/S4210216932","display_name":"Computers & Graphics X","issn_l":"2590-1486","issn":["2590-1486"],"is_oa":true,"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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true},"type":"article","type_crossref":"journal-article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1016/j.cagx.2019.100006","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083239356","display_name":"Lucas Morlet","orcid":null},"institutions":[{"id":"https://openalex.org/I4387155724","display_name":"Laboratoire d'Informatique de Bourgogne","ror":"https://ror.org/038kqx890","country_code":null,"type":"facility","lineage":["https://openalex.org/I177064439","https://openalex.org/I4387155724"]}],"countries":[],"is_corresponding":false,"raw_author_name":"Lucas Morlet","raw_affiliation_strings":["LIB - Laboratoire d'Informatique de Bourgogne [Dijon] (UFR Sciences et Techniques\r\n9 Avenue Alain Savary\r\nBP 47870\r\n21078 DIJON CEDEX - France)"],"affiliations":[{"raw_affiliation_string":"LIB - Laboratoire d'Informatique de Bourgogne [Dijon] (UFR Sciences et Techniques\r\n9 Avenue Alain Savary\r\nBP 47870\r\n21078 DIJON CEDEX - France)","institution_ids":["https://openalex.org/I4387155724"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065925135","display_name":"Christian Gentil","orcid":null},"institutions":[{"id":"https://openalex.org/I4387155724","display_name":"Laboratoire d'Informatique de Bourgogne","ror":"https://ror.org/038kqx890","country_code":null,"type":"facility","lineage":["https://openalex.org/I177064439","https://openalex.org/I4387155724"]}],"countries":[],"is_corresponding":false,"raw_author_name":"Christian Gentil","raw_affiliation_strings":["LIB - Laboratoire d'Informatique de Bourgogne [Dijon] (UFR Sciences et Techniques\r\n9 Avenue Alain Savary\r\nBP 47870\r\n21078 DIJON CEDEX - France)"],"affiliations":[{"raw_affiliation_string":"LIB - Laboratoire d'Informatique de Bourgogne [Dijon] (UFR Sciences et Techniques\r\n9 Avenue Alain Savary\r\nBP 47870\r\n21078 DIJON CEDEX - France)","institution_ids":["https://openalex.org/I4387155724"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008133097","display_name":"Sandrine Lanquetin","orcid":null},"institutions":[{"id":"https://openalex.org/I4387155724","display_name":"Laboratoire d'Informatique de Bourgogne","ror":"https://ror.org/038kqx890","country_code":null,"type":"facility","lineage":["https://openalex.org/I177064439","https://openalex.org/I4387155724"]}],"countries":[],"is_corresponding":false,"raw_author_name":"Sandrine Lanquetin","raw_affiliation_strings":["LIB - Laboratoire d'Informatique de Bourgogne [Dijon] (UFR Sciences et Techniques\r\n9 Avenue Alain Savary\r\nBP 47870\r\n21078 DIJON CEDEX - France)"],"affiliations":[{"raw_affiliation_string":"LIB - Laboratoire d'Informatique de Bourgogne [Dijon] (UFR Sciences et Techniques\r\n9 Avenue Alain Savary\r\nBP 47870\r\n21078 DIJON CEDEX - France)","institution_ids":["https://openalex.org/I4387155724"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113694702","display_name":"Marc Neveu","orcid":null},"institutions":[{"id":"https://openalex.org/I4387155724","display_name":"Laboratoire d'Informatique de Bourgogne","ror":"https://ror.org/038kqx890","country_code":null,"type":"facility","lineage":["https://openalex.org/I177064439","https://openalex.org/I4387155724"]}],"countries":[],"is_corresponding":false,"raw_author_name":"Marc Neveu","raw_affiliation_strings":["LIB - Laboratoire d'Informatique de Bourgogne [Dijon] (UFR Sciences et Techniques\r\n9 Avenue Alain Savary\r\nBP 47870\r\n21078 DIJON CEDEX - France)"],"affiliations":[{"raw_affiliation_string":"LIB - Laboratoire d'Informatique de Bourgogne [Dijon] (UFR Sciences et Techniques\r\n9 Avenue Alain Savary\r\nBP 47870\r\n21078 DIJON CEDEX - France)","institution_ids":["https://openalex.org/I4387155724"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022445136","display_name":"Jean-Luc Baril","orcid":"https://orcid.org/0000-0002-9811-8028"},"institutions":[{"id":"https://openalex.org/I4387155724","display_name":"Laboratoire d'Informatique de Bourgogne","ror":"https://ror.org/038kqx890","country_code":null,"type":"facility","lineage":["https://openalex.org/I177064439","https://openalex.org/I4387155724"]}],"countries":[],"is_corresponding":false,"raw_author_name":"Jean-Luc Baril","raw_affiliation_strings":["LIB - Laboratoire d'Informatique de Bourgogne [Dijon] (UFR Sciences et Techniques\r\n9 Avenue Alain Savary\r\nBP 47870\r\n21078 DIJON CEDEX - France)"],"affiliations":[{"raw_affiliation_string":"LIB - Laboratoire d'Informatique de Bourgogne [Dijon] (UFR Sciences et Techniques\r\n9 Avenue Alain Savary\r\nBP 47870\r\n21078 DIJON CEDEX - France)","institution_ids":["https://openalex.org/I4387155724"]}]}],"institution_assertions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2400,"currency":"USD","value_usd":2400,"provenance":"doaj"},"apc_paid":{"value":2400,"currency":"USD","value_usd":2400,"provenance":"doaj"},"fwci":0.533,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":3,"citation_normalized_percentile":{"value":0.619833,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":74,"max":77},"biblio":{"volume":"2","issue":null,"first_page":"100006","last_page":"100006"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9998,"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":0.9998,"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/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9935,"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"}},{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9825,"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/iterated-function-system","display_name":"Iterated function system","score":0.8172525},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.5996548},{"id":"https://openalex.org/keywords/subdivision-surface","display_name":"Subdivision surface","score":0.5123049},{"id":"https://openalex.org/keywords/formalism","display_name":"Formalism (music)","score":0.435573}],"concepts":[{"id":"https://openalex.org/C168460219","wikidata":"https://www.wikidata.org/wiki/Q1502167","display_name":"Iterated function system","level":3,"score":0.8172525},{"id":"https://openalex.org/C143392562","wikidata":"https://www.wikidata.org/wiki/Q449111","display_name":"Subdivision","level":2,"score":0.6284254},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.5996548},{"id":"https://openalex.org/C35527583","wikidata":"https://www.wikidata.org/wiki/Q189156","display_name":"Cellular automaton","level":2,"score":0.59881955},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.5762956},{"id":"https://openalex.org/C199686383","wikidata":"https://www.wikidata.org/wiki/Q1529124","display_name":"Subdivision surface","level":3,"score":0.5123049},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.490371},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.4873894},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.43970084},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.43791366},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.435573},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42696944},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3698348},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2936276},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17837533},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.111145705},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C558565934","wikidata":"https://www.wikidata.org/wiki/Q2743","display_name":"Musical","level":2,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0},{"id":"https://openalex.org/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","level":1,"score":0.0},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.0},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.cagx.2019.100006","pdf_url":null,"source":{"id":"https://openalex.org/S4210216932","display_name":"Computers & Graphics X","issn_l":"2590-1486","issn":["2590-1486"],"is_oa":true,"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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true},{"is_oa":false,"landing_page_url":"https://doaj.org/article/02a86417780642c78ec0256756a83ba5","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":true,"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":null,"is_accepted":false,"is_published":false},{"is_oa":false,"landing_page_url":"https://hal.archives-ouvertes.fr/hal-03064531","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":["Centre National de la Recherche Scientifique"],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},{"is_oa":false,"landing_page_url":"https://hal-univ-bourgogne.archives-ouvertes.fr/hal-02413476","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":["Centre National de la Recherche Scientifique"],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},{"is_oa":false,"landing_page_url":"https://u-bourgogne.hal.science/hal-02413476","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":["Centre National de la Recherche Scientifique"],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},{"is_oa":false,"landing_page_url":"https://hal.science/hal-03064531","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":["Centre National de la Recherche Scientifique"],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.cagx.2019.100006","pdf_url":null,"source":{"id":"https://openalex.org/S4210216932","display_name":"Computers & Graphics X","issn_l":"2590-1486","issn":["2590-1486"],"is_oa":true,"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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":22,"referenced_works":["https://openalex.org/W1985231079","https://openalex.org/W2000690667","https://openalex.org/W2002598109","https://openalex.org/W2041180141","https://openalex.org/W2055270817","https://openalex.org/W2056816721","https://openalex.org/W2060894163","https://openalex.org/W2083574922","https://openalex.org/W2095069333","https://openalex.org/W2110610472","https://openalex.org/W2116334708","https://openalex.org/W2132624520","https://openalex.org/W2145646280","https://openalex.org/W2149938550","https://openalex.org/W2168619051","https://openalex.org/W2210456747","https://openalex.org/W225579838","https://openalex.org/W2339378878","https://openalex.org/W2912736831","https://openalex.org/W3146588356","https://openalex.org/W4243945279","https://openalex.org/W4249775755"],"related_works":["https://openalex.org/W646807382","https://openalex.org/W3083116488","https://openalex.org/W2415051010","https://openalex.org/W2393550435","https://openalex.org/W2387884585","https://openalex.org/W2377450293","https://openalex.org/W2370429828","https://openalex.org/W2365894372","https://openalex.org/W2143665433","https://openalex.org/W2078248985"],"abstract_inverted_index":{"Iterated":[0,34],"Function":[1,35],"Systems":[2,36],"(IFS)":[3],"are":[4,38,47,111,157,164,190],"a":[5,13,78,102,145,148,167,176,193,207],"standard":[6,22],"tool":[7],"to":[8,88,178,205],"generate":[9],"fractal":[10],"shapes.":[11,63],"In":[12],"more":[14],"general":[15],"way,":[16],"they":[17,51],"can":[18,52,58,67,141],"represent":[19],"most":[20],"of":[21,41,85,95,105,116,127,134,169,185,195,201],"surfaces":[23,28,70,117,213],"like":[24],"B\u00e9zier":[25],"or":[26],"B-Spline":[27],"known":[29],"as":[30,144,166],"self-similar":[31,62],"surfaces.":[32,222],"Controlled":[33],"(CIFS)":[37],"an":[39],"extension":[40],"IFS":[42,55,75],"based":[43],"on":[44,101],"automata.":[45,197],"CIFS":[46,66,80,103,181,217],"basically":[48],"multi-states":[49],"IFS,":[50],"handle":[53],"all":[54],"shapes":[56],"but":[57],"also":[59],"manage":[60,89],"multi":[61],"For":[64],"example":[65],"describe":[68],"subdivision":[69,221],"around":[71],"extraordinary":[72],"vertices":[73],"whereas":[74],"cannot.":[76],"Having":[77],"common":[79],"formalism":[81],"facilitates":[82],"the":[83,112,123,132,154,170,180],"development":[84],"generic":[86],"methods":[87],"interactions":[90],"(junctions,":[91],"differences...)":[92],"between":[93,209],"objects":[94],"different":[96],"natures.":[97],"This":[98,137,198],"work":[99],"focuses":[100],"approach":[104],"Non-Uniform":[106],"Rational":[107],"B-Splines":[108],"(NURBS)":[109],"which":[110],"main":[113],"used":[114],"representation":[115,200],"in":[118,153,216],"CAGD":[119],"systems.":[120],"By":[121],"analyzing":[122],"recursive":[124],"generating":[125,155],"process":[126,156],"basis":[128],"functions,":[129],"we":[130],"prove":[131],"stationarity":[133],"NURBS":[135,140,184,196,202],"computation.":[136],"implies":[138],"that":[139],"be":[142],"represented":[143,215],"finite":[146],"automaton:":[147],"CIFS.":[149],"Subdivision":[150],"transformations":[151],"implied":[152],"directly":[158],"deduced":[159,191],"from":[160],"blossoming":[161],"formulation":[162],"and":[163,211,220],"expressed":[165],"function":[168],"initial":[171],"nodal":[172],"vector.":[173],"We":[174],"provide":[175],"method":[177],"construct":[179],"automata":[182,189],"for":[183],"any-degree.":[186],"Then":[187],"NURBS-surfaces":[188],"using":[192],"\"tensor-product\"":[194],"new":[199],"allows":[203],"us":[204],"build":[206],"bridge":[208],"them":[210],"other":[212],"already":[214],"formalism:":[218],"fractals":[219]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2952560824","counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2024-12-15T00:26:06.168830","created_date":"2019-06-27"}