{"id":"https://openalex.org/W150433239","doi":"https://doi.org/10.1016/0167-8396(87)90007-0","title":"The octant of a sphere as a non-degenerate triangular B\u00e9zier patch","display_name":"The octant of a sphere as a non-degenerate triangular B\u00e9zier patch","publication_year":1987,"publication_date":"1987-12-01","ids":{"openalex":"https://openalex.org/W150433239","doi":"https://doi.org/10.1016/0167-8396(87)90007-0","mag":"150433239"},"language":"en","primary_location":{"id":"doi:10.1016/0167-8396(87)90007-0","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0167-8396(87)90007-0","pdf_url":null,"source":{"id":"https://openalex.org/S135221619","display_name":"Computer Aided Geometric Design","issn_l":"0167-8396","issn":["0167-8396","1879-2332"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer Aided Geometric Design","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/A5030194777","display_name":"Gerald Farin","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"G. Farin","raw_affiliation_strings":["Department of Computer Science, Arizona State University, Tempe, AZ 85287, U.S.A"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Arizona State University, Tempe, AZ 85287, U.S.A","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111868261","display_name":"Bruce Piper","orcid":null},"institutions":[{"id":"https://openalex.org/I165799507","display_name":"Rensselaer Polytechnic Institute","ror":"https://ror.org/01rtyzb94","country_code":"US","type":"education","lineage":["https://openalex.org/I165799507"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"B. Piper","raw_affiliation_strings":["Department of Mathematics, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, U.S.A","Department of Mathematics, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, U.S.A.#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, U.S.A","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, U.S.A.#TAB#","institution_ids":["https://openalex.org/I165799507"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002882410","display_name":"A.J. Worsey","orcid":null},"institutions":[{"id":"https://openalex.org/I153901656","display_name":"University of North Carolina Wilmington","ror":"https://ror.org/02t0qr014","country_code":"US","type":"education","lineage":["https://openalex.org/I153901656"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A.J. Worsey","raw_affiliation_strings":["Department of Mathematical Sciences, University of North Carolina at Wilmington, Wilmington, NC 28403, U.S.A","Department of Mathematical Sciences University of North Carolina at Wilmington, Wilmington, NC 28403, U.S.A.#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, University of North Carolina at Wilmington, Wilmington, NC 28403, U.S.A","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematical Sciences University of North Carolina at Wilmington, Wilmington, NC 28403, U.S.A.#TAB#","institution_ids":["https://openalex.org/I153901656"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5030194777"],"corresponding_institution_ids":[],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":2.686,"has_fulltext":false,"cited_by_count":50,"citation_normalized_percentile":{"value":0.88184367,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"4","issue":"4","first_page":"329","last_page":"332"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9977999925613403,"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":0.9977999925613403,"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/T13267","display_name":"Advanced Theoretical and Applied Studies in Material Sciences and Geometry","score":0.965399980545044,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9449999928474426,"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/octant","display_name":"Octant (instrument)","score":0.9897817969322205},{"id":"https://openalex.org/keywords/quartic-function","display_name":"Quartic function","score":0.8137936592102051},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7933300733566284},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.7162182331085205},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.473578542470932},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4352136254310608},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.42302340269088745},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4172782003879547},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33966952562332153},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1782536804676056},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.12214210629463196},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06773877143859863}],"concepts":[{"id":"https://openalex.org/C177994039","wikidata":"https://www.wikidata.org/wiki/Q427293","display_name":"Octant (instrument)","level":2,"score":0.9897817969322205},{"id":"https://openalex.org/C130432447","wikidata":"https://www.wikidata.org/wiki/Q11420049","display_name":"Quartic function","level":2,"score":0.8137936592102051},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7933300733566284},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.7162182331085205},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.473578542470932},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4352136254310608},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.42302340269088745},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4172782003879547},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33966952562332153},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1782536804676056},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.12214210629463196},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06773877143859863}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/0167-8396(87)90007-0","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0167-8396(87)90007-0","pdf_url":null,"source":{"id":"https://openalex.org/S135221619","display_name":"Computer Aided Geometric Design","issn_l":"0167-8396","issn":["0167-8396","1879-2332"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer Aided Geometric Design","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":6,"referenced_works":["https://openalex.org/W1974162841","https://openalex.org/W2010535246","https://openalex.org/W2041712145","https://openalex.org/W2042646934","https://openalex.org/W2138517065","https://openalex.org/W6653262809"],"related_works":["https://openalex.org/W2791665318","https://openalex.org/W4300615779","https://openalex.org/W3143729892","https://openalex.org/W2406295471","https://openalex.org/W2902492219","https://openalex.org/W1494854022","https://openalex.org/W2048208478","https://openalex.org/W2610034574","https://openalex.org/W2074263105","https://openalex.org/W2372265507"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
