{"id":"https://openalex.org/W1888533516","doi":"https://doi.org/10.1109/robot.1987.1087940","title":"PAR: A representation scheme for rotational parts","display_name":"PAR: A representation scheme for rotational parts","publication_year":2005,"publication_date":"2005-03-23","ids":{"openalex":"https://openalex.org/W1888533516","doi":"https://doi.org/10.1109/robot.1987.1087940","mag":"1888533516"},"language":"en","primary_location":{"id":"doi:10.1109/robot.1987.1087940","is_oa":false,"landing_page_url":"https://doi.org/10.1109/robot.1987.1087940","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings. 1987 IEEE International Conference on Robotics and Automation","raw_type":"proceedings-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/A5086568865","display_name":"Yung-Chia Lee","orcid":null},"institutions":[{"id":"https://openalex.org/I4210116723","display_name":"Robotics Research (United States)","ror":"https://ror.org/020w2fr77","country_code":"US","type":"company","lineage":["https://openalex.org/I4210116723"]},{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Yung-Chia Lee","raw_affiliation_strings":["The Robotics Research Laboratory, Department of Electrical Engineering and Computer Science, The University of Michigan, Ann Arbor, MI"],"affiliations":[{"raw_affiliation_string":"The Robotics Research Laboratory, Department of Electrical Engineering and Computer Science, The University of Michigan, Ann Arbor, MI","institution_ids":["https://openalex.org/I4210116723","https://openalex.org/I27837315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112869787","display_name":"Kuen-Fang Jea","orcid":null},"institutions":[{"id":"https://openalex.org/I4210116723","display_name":"Robotics Research (United States)","ror":"https://ror.org/020w2fr77","country_code":"US","type":"company","lineage":["https://openalex.org/I4210116723"]},{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"K. Jea","raw_affiliation_strings":["The Robotics Research Laboratory, Department of Electrical Engineering and Computer Science, The University of Michigan, Ann Arbor, MI"],"affiliations":[{"raw_affiliation_string":"The Robotics Research Laboratory, Department of Electrical Engineering and Computer Science, The University of Michigan, Ann Arbor, MI","institution_ids":["https://openalex.org/I4210116723","https://openalex.org/I27837315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5086568865"],"corresponding_institution_ids":["https://openalex.org/I27837315","https://openalex.org/I4210116723"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.09387841,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"4","issue":null,"first_page":"973","last_page":"978"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9994999766349792,"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":0.9994999766349792,"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/T11159","display_name":"Manufacturing Process and Optimization","score":0.9987999796867371,"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/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"}}],"keywords":[{"id":"https://openalex.org/keywords/constructive-solid-geometry","display_name":"Constructive solid geometry","score":0.8183118104934692},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.7630284428596497},{"id":"https://openalex.org/keywords/boundary-representation","display_name":"Boundary representation","score":0.7189128398895264},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.6902689933776855},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.606765627861023},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5328735709190369},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.49819517135620117},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4942917823791504},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.470523476600647},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44818827509880066},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41814643144607544},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3553745746612549},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.23060384392738342},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2230902910232544},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1256927251815796}],"concepts":[{"id":"https://openalex.org/C188032258","wikidata":"https://www.wikidata.org/wiki/Q1128371","display_name":"Constructive solid geometry","level":2,"score":0.8183118104934692},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.7630284428596497},{"id":"https://openalex.org/C117258860","wikidata":"https://www.wikidata.org/wiki/Q895153","display_name":"Boundary representation","level":3,"score":0.7189128398895264},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.6902689933776855},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.606765627861023},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5328735709190369},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.49819517135620117},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4942917823791504},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.470523476600647},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44818827509880066},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41814643144607544},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3553745746612549},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.23060384392738342},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2230902910232544},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1256927251815796},{"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/robot.1987.1087940","is_oa":false,"landing_page_url":"https://doi.org/10.1109/robot.1987.1087940","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings. 1987 IEEE International Conference on Robotics and Automation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6000000238418579,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W162326662","https://openalex.org/W562745084","https://openalex.org/W1588365310","https://openalex.org/W1861436941","https://openalex.org/W1974733453","https://openalex.org/W2598508540","https://openalex.org/W6606594127"],"related_works":["https://openalex.org/W2245459674","https://openalex.org/W121240622","https://openalex.org/W3184883859","https://openalex.org/W4243120341","https://openalex.org/W1980637227","https://openalex.org/W2168491670","https://openalex.org/W1987651011","https://openalex.org/W2400708825","https://openalex.org/W4246315177","https://openalex.org/W4245143250"],"abstract_inverted_index":{"A":[0],"new":[1],"representation":[2,16,92],"scheme":[3,17,60],"PAR":[4,27,59,83,94],"(Principal":[5],"Axis":[6],"Representation)":[7],"for":[8,18],"rotational":[9],"parts":[10],"is":[11,28,61,78,95],"proposed":[12],"as":[13],"an":[14,32,86],"internal":[15],"Constructive":[19],"Solid":[20],"Geometry":[21],"(CSG).":[22],"The":[23],"main":[24],"idea":[25],"of":[26,41,48,69,81],"to":[29,72],"represent":[30],"uniquely":[31],"object":[33],"by":[34,66],"its":[35,70],"principal":[36],"axis":[37],"and":[38,64],"a":[39,67,90],"set":[40],"boundary":[42],"curves":[43],"so":[44],"that":[45,88],"geometrical":[46],"properties":[47],"the":[49,58,73,79,82],"part":[50],"can":[51],"be":[52],"easily":[53],"computed.":[54],"In":[55],"his":[56],"paper,":[57],"first":[62],"described":[63],"followed":[65],"proof":[68],"equivalence":[71],"CSG":[74],"scheme.":[75,84],"Also":[76],"proved":[77],"uniqueness":[80],"Finally,":[85],"algorithm":[87],"converts":[89],"CGS":[91],"into":[93],"briefly":[96],"discussed":[97],"along":[98],"with":[99],"examples.":[100]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}