{"id":"https://openalex.org/W1994445804","doi":"https://doi.org/10.1109/cadcg.2009.5246895","title":"A note to “Dimensions of spline spaces over unconstricted triangulations” [J. Comput. Appl. Math. 192: 320–327, 2006]","display_name":"A note to “Dimensions of spline spaces over unconstricted triangulations” [J. Comput. Appl. Math. 192: 320–327, 2006]","publication_year":2009,"publication_date":"2009-08-01","ids":{"openalex":"https://openalex.org/W1994445804","doi":"https://doi.org/10.1109/cadcg.2009.5246895","mag":"1994445804"},"language":"en","primary_location":{"id":"doi:10.1109/cadcg.2009.5246895","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cadcg.2009.5246895","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 11th IEEE International Conference on Computer-Aided Design and Computer Graphics","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/A5040125155","display_name":"Na Yi","orcid":null},"institutions":[{"id":"https://openalex.org/I167274908","display_name":"Guangxi University for Nationalities","ror":"https://ror.org/0495efn48","country_code":"CN","type":"education","lineage":["https://openalex.org/I167274908"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Na Yi","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning, Guangxi, China","Faculty of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning, 530006, China"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning, Guangxi, China","institution_ids":["https://openalex.org/I167274908"]},{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning, 530006, China","institution_ids":["https://openalex.org/I167274908"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034269062","display_name":"Huan\u2010Wen Liu","orcid":"https://orcid.org/0000-0001-9332-9021"},"institutions":[{"id":"https://openalex.org/I167274908","display_name":"Guangxi University for Nationalities","ror":"https://ror.org/0495efn48","country_code":"CN","type":"education","lineage":["https://openalex.org/I167274908"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huan-Wen Liu","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning, Guangxi, China","Faculty of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning, 530006, China"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning, Guangxi, China","institution_ids":["https://openalex.org/I167274908"]},{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning, 530006, China","institution_ids":["https://openalex.org/I167274908"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5040125155"],"corresponding_institution_ids":["https://openalex.org/I167274908"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10024104,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"18","issue":null,"first_page":"259","last_page":"262"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.989799976348877,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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":0.9785000085830688,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.6010215282440186},{"id":"https://openalex.org/keywords/triangulation","display_name":"Triangulation","score":0.5693801641464233},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.515968382358551},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43337929248809814},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3766244649887085},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13786956667900085},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.135804682970047}],"concepts":[{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.6010215282440186},{"id":"https://openalex.org/C135981907","wikidata":"https://www.wikidata.org/wiki/Q188056","display_name":"Triangulation","level":2,"score":0.5693801641464233},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.515968382358551},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43337929248809814},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3766244649887085},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13786956667900085},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.135804682970047},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cadcg.2009.5246895","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cadcg.2009.5246895","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 11th IEEE International Conference on Computer-Aided Design and Computer Graphics","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W350193506","https://openalex.org/W1982974812","https://openalex.org/W2021643006","https://openalex.org/W2138517065"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W4402427056","https://openalex.org/W238609530","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2734192830","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W3016395638"],"abstract_inverted_index":{"Let":[0],"Omega":[1,38],"be":[2,20],"a":[3,7,21,40,62,87],"regular":[4],"triangulation":[5],"of":[6,24,42,49,65],"two":[8],"dimensional":[9],"domain":[10],"and":[11,108,113],"S":[12,53],"n":[15,56],"r":[18,30,59],"(Omega)":[19,60],"vector":[22],"space":[23],"functions":[25],"in":[26,37,75,98,102],"C":[27],"whose":[31],"restriction":[32],"to":[33,92],"each":[34],"small":[35],"triangle":[36],"is":[39,90,105,116],"polynomial":[41],"total":[43],"degree":[44],"at":[45],"most":[46],"n.":[47],"Dimensions":[48],"bivariate":[50],"spline":[51],"spaces":[52],"over":[61],"special":[63],"kind":[64],"triangulation,":[66,70],"called":[67],"the":[68,76,95,99],"unconstricted":[69],"were":[71],"given":[72,91],"by":[73],"Farin":[74],"paper":[77,104],"[J.":[78],"Comput.":[79],"Appl.":[80],"Math.":[81],"192(2006),":[82],"320-327].":[83],"In":[84],"this":[85],"paper,":[86],"counter":[88],"example":[89],"show":[93],"that":[94],"condition":[96,115],"used":[97],"main":[100],"theorem":[101],"Farin's":[103],"not":[106],"correct,":[107],"then":[109],"an":[110],"improved":[111],"necessary":[112],"sufficient":[114],"presented.":[117]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}