{"id":"https://openalex.org/W2079465197","doi":"https://doi.org/10.1111/1467-8659.1150285","title":"Representing Conics using NURBS of Degree Two*","display_name":"Representing Conics using NURBS of Degree Two*","publication_year":1992,"publication_date":"1992-10-01","ids":{"openalex":"https://openalex.org/W2079465197","doi":"https://doi.org/10.1111/1467-8659.1150285","mag":"2079465197"},"language":"en","primary_location":{"id":"doi:10.1111/1467-8659.1150285","is_oa":false,"landing_page_url":"https://doi.org/10.1111/1467-8659.1150285","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/A5023893248","display_name":"Kaihuai Qin","orcid":"https://orcid.org/0000-0001-8902-142X"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kaihuai Qin","raw_affiliation_strings":["Department of Computer Science and Technology, Tsinghua University, Beijing, 100084, P.R. China","Department of Computer Science and Technology, Tsinghua University Beijing 100084, P.R. China#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Technology, Tsinghua University, Beijing, 100084, P.R. China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Department of Computer Science and Technology, Tsinghua University Beijing 100084, P.R. China#TAB#","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100429010","display_name":"Jiaguang Sun","orcid":"https://orcid.org/0000-0002-5884-7939"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiaguang Sun","raw_affiliation_strings":["Department of Computer Science and Technology, Tsinghua University, Beijing, 100084, P.R. China","Department of Computer Science and Technology, Tsinghua University Beijing 100084, P.R. China#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Technology, Tsinghua University, Beijing, 100084, P.R. China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Department of Computer Science and Technology, Tsinghua University Beijing 100084, P.R. China#TAB#","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055419823","display_name":"Xuefu Wang","orcid":"https://orcid.org/0000-0001-7212-7156"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xuefu Wang","raw_affiliation_strings":["Department of Computer Science and Technology, Tsinghua University, Beijing, 100084, P.R. China","Department of Computer Science and Technology, Tsinghua University Beijing 100084, P.R. China#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Technology, Tsinghua University, Beijing, 100084, P.R. China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Department of Computer Science and Technology, Tsinghua University Beijing 100084, P.R. China#TAB#","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I99065089"],"apc_list":{"value":3710,"currency":"USD","value_usd":3710},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.22089845,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"11","issue":"5","first_page":"285","last_page":"291"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9994000196456909,"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":0.9994000196456909,"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/T10996","display_name":"Computational Geometry and Mesh Generation","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"}},{"id":"https://openalex.org/T11159","display_name":"Manufacturing Process and Optimization","score":0.9866999983787537,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/conic-section","display_name":"Conic section","score":0.9611958265304565},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6155365705490112},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6042119264602661},{"id":"https://openalex.org/keywords/knot","display_name":"Knot (papermaking)","score":0.5514979958534241},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5382177233695984},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5297856330871582},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.5247191190719604},{"id":"https://openalex.org/keywords/arc-length","display_name":"Arc length","score":0.48349669575691223},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34367531538009644},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2792515754699707},{"id":"https://openalex.org/keywords/arc","display_name":"Arc (geometry)","score":0.27702105045318604},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2201395034790039},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.07734256982803345}],"concepts":[{"id":"https://openalex.org/C108598597","wikidata":"https://www.wikidata.org/wiki/Q124255","display_name":"Conic section","level":2,"score":0.9611958265304565},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6155365705490112},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6042119264602661},{"id":"https://openalex.org/C2779863119","wikidata":"https://www.wikidata.org/wiki/Q6423048","display_name":"Knot (papermaking)","level":2,"score":0.5514979958534241},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5382177233695984},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5297856330871582},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.5247191190719604},{"id":"https://openalex.org/C22251595","wikidata":"https://www.wikidata.org/wiki/Q670036","display_name":"Arc length","level":3,"score":0.48349669575691223},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34367531538009644},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2792515754699707},{"id":"https://openalex.org/C83415579","wikidata":"https://www.wikidata.org/wiki/Q161973","display_name":"Arc (geometry)","level":2,"score":0.27702105045318604},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2201395034790039},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.07734256982803345},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C42360764","wikidata":"https://www.wikidata.org/wiki/Q83588","display_name":"Chemical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1111/1467-8659.1150285","is_oa":false,"landing_page_url":"https://doi.org/10.1111/1467-8659.1150285","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4300566153","https://openalex.org/W2795378890","https://openalex.org/W2804689728","https://openalex.org/W2946724620","https://openalex.org/W2012685253","https://openalex.org/W2037437483","https://openalex.org/W3100053256","https://openalex.org/W2373292822","https://openalex.org/W2503332571","https://openalex.org/W2324703843"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper,":[3],"a":[4,27,59,78,91],"new":[5,60],"method":[6,19],"is":[7,37],"presented":[8],"for":[9,62,75],"representing":[10],"conics":[11,66],"precisely":[12,67],"using":[13,30,47],"NURBS":[14,63,93],"of":[15,77,90],"degree":[16],"two.":[17],"The":[18,55],"requires":[20],"only":[21],"four":[22],"control":[23,50],"vertices":[24],"to":[25,64],"represent":[26,65],"full":[28,32],"circle":[29],"the":[31,40,44,48,70,83,86],"circumscribing":[33],"square\u2010based":[34],"representation,":[35],"which":[36],"less":[38],"than":[39],"number":[41],"required":[42],"with":[43],"other":[45],"methods":[46],"square":[49],"vertex":[51],"configuration.9,":[52],"10,":[53],"13":[54],"paper":[56],"also":[57],"derives":[58],"condition":[61],"and":[68,72,81,85],"shows":[69],"sufficient":[71],"necessary":[73],"conditions":[74],"representation":[76],"circular":[79],"arc,":[80],"gives":[82],"definition":[84],"knot":[87],"vector":[88],"formulae":[89],"periodic":[92],"curve.":[94]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}