{"id":"https://openalex.org/W1981341716","doi":"https://doi.org/10.1142/s0218654398000040","title":"NUMERICAL AND GEOMETRIC PROPERTIES OF INTERVAL B-SPLINES","display_name":"NUMERICAL AND GEOMETRIC PROPERTIES OF INTERVAL B-SPLINES","publication_year":1998,"publication_date":"1998-03-01","ids":{"openalex":"https://openalex.org/W1981341716","doi":"https://doi.org/10.1142/s0218654398000040","mag":"1981341716"},"language":"en","primary_location":{"id":"doi:10.1142/s0218654398000040","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218654398000040","pdf_url":null,"source":{"id":"https://openalex.org/S68340538","display_name":"International Journal of Shape Modeling","issn_l":"0218-6543","issn":["0218-6543","1793-639X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Shape Modeling","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/A5101496691","display_name":"Guoling Shen","orcid":"https://orcid.org/0000-0002-6876-4504"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"GUOLING SHEN","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5112381010","display_name":"Nicholas M. Patrikalakis","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"NICHOLAS M. PATRIKALAKIS","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.6651,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.8806075,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"04","issue":"01n02","first_page":"35","last_page":"62"},"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9599999785423279,"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/T11159","display_name":"Manufacturing Process and Optimization","score":0.9526000022888184,"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/interval","display_name":"Interval (graph theory)","score":0.681727409362793},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5863121151924133},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.19959577918052673}],"concepts":[{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.681727409362793},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5863121151924133},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.19959577918052673}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218654398000040","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218654398000040","pdf_url":null,"source":{"id":"https://openalex.org/S68340538","display_name":"International Journal of Shape Modeling","issn_l":"0218-6543","issn":["0218-6543","1793-639X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Shape Modeling","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.5299999713897705}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1541570725","https://openalex.org/W1972976946","https://openalex.org/W1984063983","https://openalex.org/W2000038876","https://openalex.org/W2005836823","https://openalex.org/W2018364992","https://openalex.org/W2020492229","https://openalex.org/W2041180141","https://openalex.org/W2044454977","https://openalex.org/W2045807661","https://openalex.org/W2066211930","https://openalex.org/W2066253548","https://openalex.org/W2066745438","https://openalex.org/W2072210914","https://openalex.org/W2074893347","https://openalex.org/W2076231474","https://openalex.org/W2077080517","https://openalex.org/W2389064487","https://openalex.org/W4206360718","https://openalex.org/W4243672067","https://openalex.org/W4249516290"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2142036596"],"abstract_inverted_index":{"This":[0],"paper":[1,52],"studies":[2],"the":[3,57],"numerical":[4],"and":[5,24,35,99],"geometric":[6,14],"properties":[7,40,48],"of":[8,59,68,76,80,89],"interval":[9,65,70,77,82,91,103],"B-splines,":[10,78],"a":[11],"newly":[12],"developed":[13],"representation":[15,27],"introduced":[16],"for":[17,25,102],"increased":[18],"robustness":[19],"in":[20,28,50,56],"solid":[21],"modeling":[22],"systems":[23],"uncertainty":[26],"data":[29],"fitting":[30],"problems.":[31],"Interval":[32],"B-spline":[33,60,71,83,92],"curves":[34,86],"surfaces":[36,88],"have":[37],"some":[38],"unique":[39],"that":[41],"are":[42],"different":[43],"from":[44],"classical":[45],"B-splines.":[46,104],"The":[47],"discussed":[49],"this":[51],"include":[53],"error":[54],"propagation":[55],"evaluation":[58],"basis":[61],"functions":[62],"using":[63],"rounded":[64],"arithmetic,":[66],"width":[67],"an":[69,81,90],"curve":[72,93],"or":[73,87,94],"surface,":[74,95],"transformation":[75],"hodograph":[79],"curve,":[84],"enveloping":[85],"variation":[96],"diminishing":[97],"property,":[98],"knot":[100],"insertion":[101]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
