{"id":"https://openalex.org/W2119782385","doi":"https://doi.org/10.1007/11802914_13","title":"Approximate \u03bc-Bases of Rational Curves and Surfaces","display_name":"Approximate \u03bc-Bases of Rational Curves and Surfaces","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2119782385","doi":"https://doi.org/10.1007/11802914_13","mag":"2119782385"},"language":"en","primary_location":{"id":"doi:10.1007/11802914_13","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11802914_13","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5026950579","display_name":"Li\u2010Yong Shen","orcid":null},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Liyong Shen","raw_affiliation_strings":["Department of Mathematics, University of Science and Technology of China, China","KLMM, Institute of Systems Science, AMSS, Chinese Academy of Sciences,"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Science and Technology of China, China","institution_ids":["https://openalex.org/I126520041"]},{"raw_affiliation_string":"KLMM, Institute of Systems Science, AMSS, Chinese Academy of Sciences,","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032285268","display_name":"Falai Chen","orcid":"https://orcid.org/0000-0002-9898-5922"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Falai Chen","raw_affiliation_strings":["Department of Mathematics, University of Science and Technology of China, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Science and Technology of China, China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045854462","display_name":"Bert J\u00fcttler","orcid":"https://orcid.org/0000-0002-5518-7795"},"institutions":[{"id":"https://openalex.org/I121883995","display_name":"Johannes Kepler University of Linz","ror":"https://ror.org/052r2xn60","country_code":"AT","type":"education","lineage":["https://openalex.org/I121883995"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Bert J\u00fcttler","raw_affiliation_strings":["Institute of Applied Geometry, Johannes Kepler University, Linz, Austria"],"affiliations":[{"raw_affiliation_string":"Institute of Applied Geometry, Johannes Kepler University, Linz, Austria","institution_ids":["https://openalex.org/I121883995"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100604592","display_name":"Jiansong Deng","orcid":"https://orcid.org/0000-0003-4093-373X"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiansong Deng","raw_affiliation_strings":["Department of Mathematics, University of Science and Technology of China, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Science and Technology of China, China","institution_ids":["https://openalex.org/I126520041"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5026950579"],"corresponding_institution_ids":["https://openalex.org/I126520041","https://openalex.org/I19820366","https://openalex.org/I4210120485"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.15296753,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"175","last_page":"188"},"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/T10571","display_name":"Robotic Mechanisms and Dynamics","score":0.9876999855041504,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T11159","display_name":"Manufacturing Process and Optimization","score":0.9782999753952026,"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/parametric-equation","display_name":"Parametric equation","score":0.6717902421951294},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6157302260398865},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5798546671867371},{"id":"https://openalex.org/keywords/parametric-surface","display_name":"Parametric surface","score":0.5404139757156372},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4944462776184082},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4752659201622009},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.47487661242485046},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4520735740661621},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.450501024723053},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4466087818145752},{"id":"https://openalex.org/keywords/rational-surface","display_name":"Rational surface","score":0.437975138425827},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4123753309249878},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3933199644088745},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3474305272102356},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1325748860836029}],"concepts":[{"id":"https://openalex.org/C99636146","wikidata":"https://www.wikidata.org/wiki/Q35889","display_name":"Parametric equation","level":2,"score":0.6717902421951294},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6157302260398865},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5798546671867371},{"id":"https://openalex.org/C2187777","wikidata":"https://www.wikidata.org/wiki/Q1071743","display_name":"Parametric surface","level":3,"score":0.5404139757156372},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4944462776184082},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4752659201622009},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.47487661242485046},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4520735740661621},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.450501024723053},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4466087818145752},{"id":"https://openalex.org/C2777979628","wikidata":"https://www.wikidata.org/wiki/Q208756","display_name":"Rational surface","level":3,"score":0.437975138425827},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4123753309249878},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3933199644088745},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3474305272102356},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1325748860836029},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C82706917","wikidata":"https://www.wikidata.org/wiki/Q10251","display_name":"Plasma","level":2,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/11802914_13","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11802914_13","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.95.1534","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.95.1534","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://staff.ustc.edu.cn/~dengjs/files/papers/36 appromu.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1546935257","https://openalex.org/W1976784541","https://openalex.org/W1978015690","https://openalex.org/W1980133112","https://openalex.org/W2019799078","https://openalex.org/W2039758732","https://openalex.org/W2055431849","https://openalex.org/W2059451733","https://openalex.org/W2059860265","https://openalex.org/W2076481648","https://openalex.org/W2101561222","https://openalex.org/W2117849070","https://openalex.org/W2133261933","https://openalex.org/W2232657515","https://openalex.org/W2247974340","https://openalex.org/W2377996140","https://openalex.org/W2798987218","https://openalex.org/W4248826752"],"related_works":["https://openalex.org/W1581927719","https://openalex.org/W2026959341","https://openalex.org/W2045615359","https://openalex.org/W2010636443","https://openalex.org/W2115463023","https://openalex.org/W2350142587","https://openalex.org/W2117849070","https://openalex.org/W2014666561","https://openalex.org/W1978015690","https://openalex.org/W2375011831"],"abstract_inverted_index":null,"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}