{"id":"https://openalex.org/W1984469426","doi":"https://doi.org/10.1177/027836499101000512","title":"Modeling Spaces for Toleranced Objects","display_name":"Modeling Spaces for Toleranced Objects","publication_year":1991,"publication_date":"1991-10-01","ids":{"openalex":"https://openalex.org/W1984469426","doi":"https://doi.org/10.1177/027836499101000512","mag":"1984469426"},"language":"en","primary_location":{"id":"doi:10.1177/027836499101000512","is_oa":false,"landing_page_url":"https://doi.org/10.1177/027836499101000512","pdf_url":null,"source":{"id":"https://openalex.org/S73484101","display_name":"The International Journal of Robotics Research","issn_l":"0278-3649","issn":["0278-3649","1741-3176"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320017","host_organization_name":"SAGE Publishing","host_organization_lineage":["https://openalex.org/P4310320017"],"host_organization_lineage_names":["SAGE Publishing"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The International Journal of Robotics Research","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/A5044014402","display_name":"M. Martin Boyer","orcid":"https://orcid.org/0000-0001-9849-1132"},"institutions":[{"id":"https://openalex.org/I70931966","display_name":"Universit\u00e9 de Montr\u00e9al","ror":"https://ror.org/0161xgx34","country_code":"CA","type":"education","lineage":["https://openalex.org/I70931966"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"M. Boyer","raw_affiliation_strings":["D\u00e9partement d'informatique et de recherche op\u00e9rationnelle Universit\u00e9 de Montr\u00e9al Montr\u00e9al, Qu\u00e9bec, Canada H3C 3J7"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"D\u00e9partement d'informatique et de recherche op\u00e9rationnelle Universit\u00e9 de Montr\u00e9al Montr\u00e9al, Qu\u00e9bec, Canada H3C 3J7","institution_ids":["https://openalex.org/I70931966"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103985974","display_name":"Nathaniel Stewart","orcid":null},"institutions":[{"id":"https://openalex.org/I70931966","display_name":"Universit\u00e9 de Montr\u00e9al","ror":"https://ror.org/0161xgx34","country_code":"CA","type":"education","lineage":["https://openalex.org/I70931966"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"N.F. Stewart","raw_affiliation_strings":["D\u00e9partement d'informatique et de recherche op\u00e9rationnelle Universit\u00e9 de Montr\u00e9al Montr\u00e9al, Qu\u00e9bec, Canada H3C 3J7"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"D\u00e9partement d'informatique et de recherche op\u00e9rationnelle Universit\u00e9 de Montr\u00e9al Montr\u00e9al, Qu\u00e9bec, Canada H3C 3J7","institution_ids":["https://openalex.org/I70931966"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5044014402"],"corresponding_institution_ids":["https://openalex.org/I70931966"],"apc_list":null,"apc_paid":null,"fwci":4.5796,"has_fulltext":false,"cited_by_count":60,"citation_normalized_percentile":{"value":0.94605678,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"10","issue":"5","first_page":"570","last_page":"582"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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":0.9883999824523926,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9803000092506409,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/hyperspace","display_name":"Hyperspace","score":0.8033682107925415},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6056655645370483},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5222995281219482},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.5193554162979126},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4930255115032196},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.48722901940345764},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44354087114334106},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4372006356716156},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4260319471359253},{"id":"https://openalex.org/keywords/ball","display_name":"Ball (mathematics)","score":0.42163020372390747},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4086885452270508},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3684820532798767},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.24998563528060913},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2215307056903839}],"concepts":[{"id":"https://openalex.org/C39368324","wikidata":"https://www.wikidata.org/wiki/Q5024959","display_name":"Hyperspace","level":2,"score":0.8033682107925415},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6056655645370483},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5222995281219482},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.5193554162979126},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4930255115032196},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.48722901940345764},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44354087114334106},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4372006356716156},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4260319471359253},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.42163020372390747},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4086885452270508},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3684820532798767},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.24998563528060913},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2215307056903839},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1177/027836499101000512","is_oa":false,"landing_page_url":"https://doi.org/10.1177/027836499101000512","pdf_url":null,"source":{"id":"https://openalex.org/S73484101","display_name":"The International Journal of Robotics Research","issn_l":"0278-3649","issn":["0278-3649","1741-3176"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320017","host_organization_name":"SAGE Publishing","host_organization_lineage":["https://openalex.org/P4310320017"],"host_organization_lineage_names":["SAGE Publishing"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The International Journal of Robotics Research","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.550000011920929,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"},{"score":0.47999998927116394,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1606010360","https://openalex.org/W1966699136","https://openalex.org/W2013517877","https://openalex.org/W2044285874","https://openalex.org/W2059029870","https://openalex.org/W2067634170","https://openalex.org/W2074954154","https://openalex.org/W4236339255","https://openalex.org/W4244064761"],"related_works":["https://openalex.org/W1855976979","https://openalex.org/W2268755818","https://openalex.org/W4298324453","https://openalex.org/W4294294347","https://openalex.org/W2145396827","https://openalex.org/W2279239548","https://openalex.org/W115379796","https://openalex.org/W63976795","https://openalex.org/W2404658402","https://openalex.org/W2610298398"],"abstract_inverted_index":{"In":[0,40],"this":[1],"article":[2],"we":[3,154],"propose":[4],"a":[5,58,82,90,97,102],"modeling":[6],"space":[7],"for":[8,81],"objects":[9],"defined":[10,61],"in":[11],"terms":[12],"of":[13,20,28,57,84,113,147],"tolerances":[14],"based":[15],"on":[16,121,125],"Requicha's":[17],"sug":[18],"gestion":[19],"using":[21],"variational":[22,92],"classes.":[23,127],"Variational":[24],"classes":[25,161],"are":[26,132,141],"subsets":[27],"the":[29,44,46,49,54,72,114,130,139,144,148,156,159,163],"hyperspace":[30],"2":[31],"En":[32],",":[33],"where":[34],"E":[35],"n":[36],"is":[37],"euclidean":[38],"n-space.":[39],"order":[41],"to":[42],"motivate":[43],"ideas,":[45],"discussion":[47],"involves":[48],"same":[50],"simple":[51],"example":[52],"throughout:":[53],"specifi":[55],"cation":[56],"ball":[59],"bearing":[60],"by":[62,70,169],"position,":[63],"size,":[64],"and":[65,78,162],"form":[66],"constraints.":[67],"We":[68,94,108],"begin":[69],"discussing":[71],"relationship":[73,157],"between":[74,158],"Reguicha's":[75],"original":[76],"proposal":[77,80],"our":[79],"definition":[83],"what":[85],"should":[86],"be":[87],"viewed":[88],"as":[89,129],"permissible":[91,98],"class.":[93],"call":[95],"such":[96],"class,":[99],"together":[100],"with":[101],"nominal":[103],"solid":[104],"S,":[105],"an":[106],"R-class.":[107],"then":[109],"introduce":[110],"generalized":[111,145],"versions":[112,146],"regularized":[115,135,149],"Boolean":[116,136,150],"operations,":[117,137],"which":[118],"operate":[119],"not":[120],"r-sets,":[122],"but":[123],"rather":[124],"R-":[126,160],"Just":[128],"r-sets":[131],"closed":[133,142],"under":[134,143],"so":[138],"R-classes":[140],"opera":[151],"tions.":[152],"Finally,":[153],"discuss":[155],"particular":[164],"feature":[165],"tolerancing":[166],"methods":[167],"proposed":[168],"Requicha.":[170]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}