{"id":"https://openalex.org/W1987568398","doi":"https://doi.org/10.1142/s0218195991000281","title":"DEFORMATION OF N-DIMENSIONAL OBJECTS","display_name":"DEFORMATION OF N-DIMENSIONAL OBJECTS","publication_year":1991,"publication_date":"1991-12-01","ids":{"openalex":"https://openalex.org/W1987568398","doi":"https://doi.org/10.1142/s0218195991000281","mag":"1987568398"},"language":"en","primary_location":{"id":"doi:10.1142/s0218195991000281","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195991000281","pdf_url":null,"source":{"id":"https://openalex.org/S25827807","display_name":"International Journal of Computational Geometry & Applications","issn_l":"0218-1959","issn":["0218-1959","1793-6357"],"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 Computational Geometry &amp; Applications","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/A5052954875","display_name":"Paul Borrel","orcid":null},"institutions":[{"id":"https://openalex.org/I4210114115","display_name":"IBM Research - Thomas J. Watson Research Center","ror":"https://ror.org/0265w5591","country_code":"US","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210114115"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"PAUL BORREL","raw_affiliation_strings":["Interactive Geometric Modeling, IBM Research Division, Thomas J. Watson Research Center, P.O. Box 704, Yorktown Heights, NY 10598, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Interactive Geometric Modeling, IBM Research Division, Thomas J. Watson Research Center, P.O. Box 704, Yorktown Heights, NY 10598, USA","institution_ids":["https://openalex.org/I4210114115"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036652880","display_name":"Dominique Bechmann","orcid":null},"institutions":[{"id":"https://openalex.org/I4210161954","display_name":"D\u00e9partement d'Informatique","ror":"https://ror.org/05y6rqs46","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I2746051580","https://openalex.org/I29607241","https://openalex.org/I4210159245","https://openalex.org/I4210161954"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"DOMINIQUE BECHMANN","raw_affiliation_strings":["D\u00e9partement d'lnformatique, Universit\u00e9 Louis Pasteur, 7. rue Ren\u00e9 Descartes, 67084 Strasbourg cedex, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"D\u00e9partement d'lnformatique, Universit\u00e9 Louis Pasteur, 7. rue Ren\u00e9 Descartes, 67084 Strasbourg cedex, France","institution_ids":["https://openalex.org/I4210161954"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1193,"has_fulltext":false,"cited_by_count":46,"citation_normalized_percentile":{"value":0.77844511,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"01","issue":"04","first_page":"427","last_page":"453"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11159","display_name":"Manufacturing Process and Optimization","score":0.9830999970436096,"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":0.9830999970436096,"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":0.9764000177383423,"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/T13267","display_name":"Advanced Theoretical and Applied Studies in Material Sciences and Geometry","score":0.9459999799728394,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/mathematics","display_name":"Mathematics","score":0.7029948234558105},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.6782869696617126},{"id":"https://openalex.org/keywords/deformation","display_name":"Deformation (meteorology)","score":0.6337753534317017},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5729577541351318},{"id":"https://openalex.org/keywords/degrees-of-freedom","display_name":"Degrees of freedom (physics and chemistry)","score":0.5343014597892761},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5024926662445068},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.48727309703826904},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.48711252212524414},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.48115289211273193},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.476694792509079},{"id":"https://openalex.org/keywords/free-form-deformation","display_name":"Free-form deformation","score":0.4536624550819397},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4513853192329407},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.31995871663093567},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.31094977259635925},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.283833384513855},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27698782086372375}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7029948234558105},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.6782869696617126},{"id":"https://openalex.org/C204366326","wikidata":"https://www.wikidata.org/wiki/Q3027650","display_name":"Deformation (meteorology)","level":2,"score":0.6337753534317017},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5729577541351318},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.5343014597892761},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5024926662445068},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.48727309703826904},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.48711252212524414},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.48115289211273193},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.476694792509079},{"id":"https://openalex.org/C2780391921","wikidata":"https://www.wikidata.org/wiki/Q1454193","display_name":"Free-form deformation","level":3,"score":0.4536624550819397},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4513853192329407},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.31995871663093567},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.31094977259635925},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.283833384513855},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27698782086372375},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218195991000281","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195991000281","pdf_url":null,"source":{"id":"https://openalex.org/S25827807","display_name":"International Journal of Computational Geometry & Applications","issn_l":"0218-1959","issn":["0218-1959","1793-6357"],"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 Computational Geometry &amp; Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.699999988079071}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2356364244","https://openalex.org/W2298446516","https://openalex.org/W1970601671","https://openalex.org/W4242766352","https://openalex.org/W2329424818","https://openalex.org/W2313042761","https://openalex.org/W2157646637","https://openalex.org/W1539672458","https://openalex.org/W2001919142","https://openalex.org/W2072034972"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"a":[3,12,35,43,50,67],"new":[4],"technique":[5,101],"for":[6],"computing":[7],"space":[8],"deformations":[9],"that":[10],"interpolate":[11],"set":[13],"of":[14,24,34,39,75,99,106,112],"user-defined":[15],"constraints.":[16],"Constraints":[17],"are":[18],"specified":[19],"by":[20,85],"indicating":[21],"the":[22,32,73,97,103],"images":[23],"selected":[25],"points.":[26,89],"The":[27,61],"deformation":[28,113],"is":[29,64,93],"formulated":[30],"as":[31],"product":[33],"polynomial":[36],"function":[37],"f":[38],"\u211d":[40,46,54,58],"n":[41,59],"into":[42],"higher-dimensional":[44],"space,":[45],"m":[47,55],",":[48],"with":[49],"linear":[51],"projection":[52,62],"from":[53],"back":[56],"to":[57,80,102],".":[60],"matrix":[63],"computed":[65],"using":[66],"pseudo-inverse":[68],"technique.":[69],"For":[70],"sufficient":[71],"m,":[72],"degrees":[74],"freedom":[76],"may":[77],"be":[78],"used":[79],"optimize":[81],"potential":[82],"functions":[83],"controlled":[84],"attracting":[86],"and":[87,111],"repulsing":[88],"A":[90],"prototype":[91],"implementation":[92],"presented,":[94],"which":[95],"demonstrates":[96],"application":[98],"this":[100],"interactive":[104],"design":[105],"free-form":[107],"shapes":[108],"(when":[109,118],"n=3)":[110],"processes":[114],"in":[115],"space-time":[116],"domain":[117],"n=4).":[119]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
