{"id":"https://openalex.org/W3176503512","doi":"https://doi.org/10.1142/s0218196721500284","title":"Exact and approximate similarities of non-necessarily rational planar, parametrized curves, using centers of gravity and inertia tensors","display_name":"Exact and approximate similarities of non-necessarily rational planar, parametrized curves, using centers of gravity and inertia tensors","publication_year":2021,"publication_date":"2021-04-21","ids":{"openalex":"https://openalex.org/W3176503512","doi":"https://doi.org/10.1142/s0218196721500284","mag":"3176503512"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196721500284","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196721500284","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","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/A5041883278","display_name":"Juan Gerardo Alc\u00e1zar","orcid":"https://orcid.org/0000-0002-1665-9710"},"institutions":[{"id":"https://openalex.org/I189268942","display_name":"Universidad de Alcal\u00e1","ror":"https://ror.org/04pmn0e78","country_code":"ES","type":"education","lineage":["https://openalex.org/I189268942"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Juan Gerardo Alc\u00e1zar","raw_affiliation_strings":["Departamento de F\u00edsica y Matem\u00e1ticas, Universidad de Alcal\u00e1, E-28871 Madrid, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de F\u00edsica y Matem\u00e1ticas, Universidad de Alcal\u00e1, E-28871 Madrid, Spain","institution_ids":["https://openalex.org/I189268942"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073647033","display_name":"Emily Quintero","orcid":null},"institutions":[{"id":"https://openalex.org/I189268942","display_name":"Universidad de Alcal\u00e1","ror":"https://ror.org/04pmn0e78","country_code":"ES","type":"education","lineage":["https://openalex.org/I189268942"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Emily Quintero","raw_affiliation_strings":["Departamento de F\u00edsica y Matem\u00e1ticas, Universidad de Alcal\u00e1, E-28871 Madrid, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de F\u00edsica y Matem\u00e1ticas, Universidad de Alcal\u00e1, E-28871 Madrid, Spain","institution_ids":["https://openalex.org/I189268942"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5041883278"],"corresponding_institution_ids":["https://openalex.org/I189268942"],"apc_list":null,"apc_paid":null,"fwci":0.178,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.45676035,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"31","issue":"04","first_page":"581","last_page":"603"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9998000264167786,"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":0.9998000264167786,"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.996399998664856,"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":0.989799976348877,"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/mathematics","display_name":"Mathematics","score":0.8319203853607178},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6347861289978027},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.5956393480300903},{"id":"https://openalex.org/keywords/similarity","display_name":"Similarity (geometry)","score":0.5740622878074646},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.528876781463623},{"id":"https://openalex.org/keywords/inertia","display_name":"Inertia","score":0.5277058482170105},{"id":"https://openalex.org/keywords/congruence","display_name":"Congruence (geometry)","score":0.5261282920837402},{"id":"https://openalex.org/keywords/matrix-similarity","display_name":"Matrix similarity","score":0.46232178807258606},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4411448836326599},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4255746901035309},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3703848719596863},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.26859620213508606},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.16124644875526428},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.0836043655872345}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8319203853607178},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6347861289978027},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.5956393480300903},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.5740622878074646},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.528876781463623},{"id":"https://openalex.org/C110407247","wikidata":"https://www.wikidata.org/wiki/Q122508","display_name":"Inertia","level":2,"score":0.5277058482170105},{"id":"https://openalex.org/C132074034","wikidata":"https://www.wikidata.org/wiki/Q154210","display_name":"Congruence (geometry)","level":2,"score":0.5261282920837402},{"id":"https://openalex.org/C39739852","wikidata":"https://www.wikidata.org/wiki/Q254491","display_name":"Matrix similarity","level":3,"score":0.46232178807258606},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4411448836326599},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4255746901035309},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3703848719596863},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.26859620213508606},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.16124644875526428},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0836043655872345},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.0},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196721500284","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196721500284","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W28996014","https://openalex.org/W1532721371","https://openalex.org/W1572189095","https://openalex.org/W1638384496","https://openalex.org/W1835536927","https://openalex.org/W1965692635","https://openalex.org/W1970850580","https://openalex.org/W2011703168","https://openalex.org/W2039073905","https://openalex.org/W2055755574","https://openalex.org/W2068937275","https://openalex.org/W2146838377","https://openalex.org/W2163112186","https://openalex.org/W2163808362","https://openalex.org/W2592206328","https://openalex.org/W2621117423","https://openalex.org/W2797819118","https://openalex.org/W2810171306","https://openalex.org/W2962127608","https://openalex.org/W2963653844","https://openalex.org/W2973118323","https://openalex.org/W2987507782","https://openalex.org/W3016246872","https://openalex.org/W3080151684","https://openalex.org/W3135092828","https://openalex.org/W4240715508"],"related_works":["https://openalex.org/W2388471861","https://openalex.org/W2354789018","https://openalex.org/W2391316944","https://openalex.org/W4380684998","https://openalex.org/W2787537126","https://openalex.org/W1979758163","https://openalex.org/W4226251895","https://openalex.org/W2000394358","https://openalex.org/W2022145663","https://openalex.org/W2067704152"],"abstract_inverted_index":{"We":[0],"provide":[1],"an":[2],"algorithm":[3,29,60],"to":[4,40],"detect":[5],"whether":[6,15],"two":[7],"bounded,":[8],"planar":[9,80],"parametrized":[10],"curves":[11,24,76],"are":[12,103,127,131,167],"similar,":[13],"i.e.":[14,174],"there":[16],"exists":[17],"a":[18,91,116,123],"similarity":[19,92,121],"transforming":[20],"one":[21],"of":[22,54,66,68,73,78,101,147,172],"the":[23,26,41,44,52,64,74,79,84,99,109,112,120,129,135,139,145,148,160,170],"onto":[25,105],"other.":[27],"The":[28,59],"is":[30,46,61,94,122,141],"valid":[31],"for":[32,156,169],"completely":[33],"general":[34,137],"parametrizations,":[35],"and":[36,70,108,133,154],"can":[37,162],"be":[38,163],"adapted":[39],"case":[42,138,171],"when":[43,90,119],"input":[45],"given":[47],"with":[48],"finite":[49],"precision,":[50],"using":[51],"notion":[53],"approximate":[55],"[Formula:":[56],"see":[57],"text].":[58],"based":[62],"on":[63],"computation":[65],"centers":[67,100],"gravity":[69,102],"inertia":[71,113],"tensors":[72,114],"considered":[75],"or":[77],"regions":[81],"enclosed":[82],"by":[83],"curves,":[85],"which":[86],"have":[87],"nice":[88],"properties":[89],"transformation":[93],"applied.":[95],"In":[96],"more":[97,136],"detail,":[98],"mapped":[104],"each":[106],"other,":[107],"matrices":[110,130],"representing":[111],"satisfy":[115],"simple":[117],"relationship:":[118],"congruence":[124],"(i.e.":[125],"distances":[126],"preserved)":[128],"congruent,":[132],"in":[134],"relationship":[140],"analogous,":[142],"but":[143],"involves":[144],"square":[146],"scaling":[149],"constant.":[150],"Using":[151],"both":[152],"properties,":[153],"except":[155],"certain":[157],"pathological":[158],"cases,":[159],"similarities":[161],"found.":[164],"Additional":[165],"ideas":[166],"presented":[168],"closed,":[173],"compact,":[175],"curves.":[176]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
