{"id":"https://openalex.org/W2090774435","doi":"https://doi.org/10.1111/1467-8659.1330055","title":"Solid Modeling Based on a New Paradigm","display_name":"Solid Modeling Based on a New Paradigm","publication_year":1994,"publication_date":"1994-08-01","ids":{"openalex":"https://openalex.org/W2090774435","doi":"https://doi.org/10.1111/1467-8659.1330055","mag":"2090774435"},"language":"en","primary_location":{"id":"doi:10.1111/1467-8659.1330055","is_oa":false,"landing_page_url":"https://doi.org/10.1111/1467-8659.1330055","pdf_url":null,"source":{"id":"https://openalex.org/S67831204","display_name":"Computer Graphics Forum","issn_l":"0167-7055","issn":["0167-7055","1467-8659"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer Graphics Forum","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/A5011292913","display_name":"Norimasa Yoshida","orcid":"https://orcid.org/0000-0001-8889-0949"},"institutions":[{"id":"https://openalex.org/I150744194","display_name":"Waseda University","ror":"https://ror.org/00ntfnx83","country_code":"JP","type":"education","lineage":["https://openalex.org/I150744194"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Norimasa Yoshida","raw_affiliation_strings":["Department of Mechanical Engineering, School of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169 JAPAN, Tel.+","Department of Mechanical Engineering, School of Science and Engineering, Waseda University, 3\u20104\u20101 Okubo, Shinjuku\u2010ku, Tokyo, 169 JAPAN, Tel.+Fax: +81\u20103\u20103207\u20103167"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, School of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169 JAPAN, Tel.+","institution_ids":["https://openalex.org/I150744194"]},{"raw_affiliation_string":"Department of Mechanical Engineering, School of Science and Engineering, Waseda University, 3\u20104\u20101 Okubo, Shinjuku\u2010ku, Tokyo, 169 JAPAN, Tel.+Fax: +81\u20103\u20103207\u20103167","institution_ids":["https://openalex.org/I150744194"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103460109","display_name":"Masato Shiokawa","orcid":null},"institutions":[{"id":"https://openalex.org/I150744194","display_name":"Waseda University","ror":"https://ror.org/00ntfnx83","country_code":"JP","type":"education","lineage":["https://openalex.org/I150744194"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Masato Shiokawa","raw_affiliation_strings":["Department of Mechanical Engineering, School of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169 JAPAN, Tel.+","Department of Mechanical Engineering, School of Science and Engineering, Waseda University, 3\u20104\u20101 Okubo, Shinjuku\u2010ku, Tokyo, 169 JAPAN, Tel.+Fax: +81\u20103\u20103207\u20103167"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, School of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169 JAPAN, Tel.+","institution_ids":["https://openalex.org/I150744194"]},{"raw_affiliation_string":"Department of Mechanical Engineering, School of Science and Engineering, Waseda University, 3\u20104\u20101 Okubo, Shinjuku\u2010ku, Tokyo, 169 JAPAN, Tel.+Fax: +81\u20103\u20103207\u20103167","institution_ids":["https://openalex.org/I150744194"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035911512","display_name":"Fujio Yamaguchi","orcid":null},"institutions":[{"id":"https://openalex.org/I150744194","display_name":"Waseda University","ror":"https://ror.org/00ntfnx83","country_code":"JP","type":"education","lineage":["https://openalex.org/I150744194"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Fujio Yamaguchi","raw_affiliation_strings":["Department of Mechanical Engineering, School of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169 JAPAN, Tel.+","Department of Mechanical Engineering, School of Science and Engineering, Waseda University, 3\u20104\u20101 Okubo, Shinjuku\u2010ku, Tokyo, 169 JAPAN, Tel.+Fax: +81\u20103\u20103207\u20103167"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, School of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169 JAPAN, Tel.+","institution_ids":["https://openalex.org/I150744194"]},{"raw_affiliation_string":"Department of Mechanical Engineering, School of Science and Engineering, Waseda University, 3\u20104\u20101 Okubo, Shinjuku\u2010ku, Tokyo, 169 JAPAN, Tel.+Fax: +81\u20103\u20103207\u20103167","institution_ids":["https://openalex.org/I150744194"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5011292913"],"corresponding_institution_ids":["https://openalex.org/I150744194"],"apc_list":{"value":3710,"currency":"USD","value_usd":3710},"apc_paid":null,"fwci":2.2469,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.87955025,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":"3","first_page":"55","last_page":"64"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11159","display_name":"Manufacturing Process and Optimization","score":0.9986000061035156,"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":0.9986000061035156,"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/T10783","display_name":"Additive Manufacturing and 3D Printing Technologies","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/2203","display_name":"Automotive 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":0.9929999709129333,"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/computation","display_name":"Computation","score":0.6447669863700867},{"id":"https://openalex.org/keywords/geometric-design","display_name":"Geometric design","score":0.6440825462341309},{"id":"https://openalex.org/keywords/geometric-modeling","display_name":"Geometric modeling","score":0.596170961856842},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5958495140075684},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5856902003288269},{"id":"https://openalex.org/keywords/boundary-representation","display_name":"Boundary representation","score":0.5176068544387817},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5066981911659241},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.47914308309555054},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.473347932100296},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.47089532017707825},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4701685309410095},{"id":"https://openalex.org/keywords/division","display_name":"Division (mathematics)","score":0.4638853669166565},{"id":"https://openalex.org/keywords/boolean-data-type","display_name":"Boolean data type","score":0.4426574409008026},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4314206838607788},{"id":"https://openalex.org/keywords/boolean-algebra","display_name":"Boolean algebra","score":0.4117191731929779},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.3933229148387909},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3452904522418976},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.20962324738502502},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1304706335067749},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12108230590820312}],"concepts":[{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6447669863700867},{"id":"https://openalex.org/C40319758","wikidata":"https://www.wikidata.org/wiki/Q5535477","display_name":"Geometric design","level":2,"score":0.6440825462341309},{"id":"https://openalex.org/C104065381","wikidata":"https://www.wikidata.org/wiki/Q1002535","display_name":"Geometric modeling","level":2,"score":0.596170961856842},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5958495140075684},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5856902003288269},{"id":"https://openalex.org/C117258860","wikidata":"https://www.wikidata.org/wiki/Q895153","display_name":"Boundary representation","level":3,"score":0.5176068544387817},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5066981911659241},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.47914308309555054},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.473347932100296},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47089532017707825},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4701685309410095},{"id":"https://openalex.org/C60798267","wikidata":"https://www.wikidata.org/wiki/Q1226939","display_name":"Division (mathematics)","level":2,"score":0.4638853669166565},{"id":"https://openalex.org/C7342684","wikidata":"https://www.wikidata.org/wiki/Q520777","display_name":"Boolean data type","level":2,"score":0.4426574409008026},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4314206838607788},{"id":"https://openalex.org/C39685927","wikidata":"https://www.wikidata.org/wiki/Q173183","display_name":"Boolean algebra","level":2,"score":0.4117191731929779},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.3933229148387909},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3452904522418976},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.20962324738502502},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1304706335067749},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12108230590820312},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1111/1467-8659.1330055","is_oa":false,"landing_page_url":"https://doi.org/10.1111/1467-8659.1330055","pdf_url":null,"source":{"id":"https://openalex.org/S67831204","display_name":"Computer Graphics Forum","issn_l":"0167-7055","issn":["0167-7055","1467-8659"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer Graphics Forum","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2060411699","https://openalex.org/W3113701594","https://openalex.org/W4255956924","https://openalex.org/W101255224","https://openalex.org/W4220701978","https://openalex.org/W1593530080","https://openalex.org/W583949386","https://openalex.org/W1985426375","https://openalex.org/W583396443","https://openalex.org/W2090774435"],"abstract_inverted_index":{"Abstract":[0],"The":[1,64],"technique":[2],"of":[3,23,31,33,36,54,66],"solid":[4,46],"modeling":[5,47,77],"is":[6,12,58,142],"essential":[7],"in":[8,25,73,98,135],"CAD/CAM":[9],"applications,":[10],"and":[11,28,57,76,126,128,139,147],"currently":[13],"well":[14],"established.":[15],"However,":[16],"problems":[17],"remain,":[18],"such":[19],"as":[20],"the":[21,29,67,70,85,92,103,116,122,136,140],"lack":[22,30],"uniformity":[24],"geometric":[26,80,111,123],"computations":[27,81,112],"stability":[32],"Boolean":[34,74,145],"operations":[35,146],"two":[37],"solids.":[38],"In":[39],"this":[40],"paper,":[41],"we":[42],"introduce":[43],"a":[44,61],"theoretical":[45],"system":[48,68,104],"that":[49],"operates":[50],"on":[51,60],"boundary":[52],"representations":[53],"polyhedral":[55],"objects":[56],"based":[59],"new":[62],"paradigm.":[63],"characteristics":[65],"are":[69,82,113,132],"following:":[71],"(I)":[72],"Operations":[75],"transformations,":[78],"all":[79,110],"performed":[83,114],"by":[84,115],"4":[86,88,93,95],"\u00d7":[87,94],"determinant":[89],"method":[90,97],"or":[91],"matrix":[96],"homogeneous":[99],"space,":[100],"which":[101,120],"allows":[102],"to":[105],"avoid":[106],"division":[107],"operations,":[108],"(2)":[109],"exact":[117],"integer":[118,137],"arithmetic,":[119],"makes":[121],"algorithms":[124],"stable":[125],"simple,":[127],"(3)":[129],"primitive":[130],"solids":[131],"constructed":[133],"consistently":[134],"domain,":[138],"consistency":[141],"assured":[143],"throughout":[144],"transformations.":[148]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}