{"id":"https://openalex.org/W2029119997","doi":"https://doi.org/10.1016/0167-8396(90)90028-p","title":"Necessary and sufficient conditions for tangent plane continuity of B\u00e9zier surfaces","display_name":"Necessary and sufficient conditions for tangent plane continuity of B\u00e9zier surfaces","publication_year":1990,"publication_date":"1990-06-01","ids":{"openalex":"https://openalex.org/W2029119997","doi":"https://doi.org/10.1016/0167-8396(90)90028-p","mag":"2029119997"},"language":"en","primary_location":{"id":"doi:10.1016/0167-8396(90)90028-p","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0167-8396(90)90028-p","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/A5030916311","display_name":"Tony DeRose","orcid":null},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Tony D. DeRose","raw_affiliation_strings":["Department of Computer Science and Engineering, FR-35, University of Washington, Seattle, WA 98125, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, FR-35, University of Washington, Seattle, WA 98125, USA","institution_ids":["https://openalex.org/I201448701"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5030916311"],"corresponding_institution_ids":["https://openalex.org/I201448701"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":5.5988,"has_fulltext":false,"cited_by_count":71,"citation_normalized_percentile":{"value":0.96195486,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"7","issue":"1-4","first_page":"165","last_page":"179"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9995999932289124,"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":0.9995999932289124,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9508000016212463,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10531","display_name":"Advanced Vision and Imaging","score":0.9483000040054321,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/mathematics","display_name":"Mathematics","score":0.8624604344367981},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.7305946350097656},{"id":"https://openalex.org/keywords/tangent-space","display_name":"Tangent space","score":0.5957348942756653},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5620710849761963},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.5556116104125977},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5323747992515564},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.4800475835800171},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4364132881164551},{"id":"https://openalex.org/keywords/b\u00e9zier-curve","display_name":"B\u00e9zier curve","score":0.4327487349510193},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.390034019947052}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8624604344367981},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.7305946350097656},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.5957348942756653},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5620710849761963},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5556116104125977},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5323747992515564},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.4800475835800171},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4364132881164551},{"id":"https://openalex.org/C206423108","wikidata":"https://www.wikidata.org/wiki/Q214728","display_name":"B\u00e9zier curve","level":2,"score":0.4327487349510193},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.390034019947052}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/0167-8396(90)90028-p","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0167-8396(90)90028-p","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W575078097","https://openalex.org/W1591228564","https://openalex.org/W1996850393","https://openalex.org/W2077553158","https://openalex.org/W2138517065"],"related_works":["https://openalex.org/W2361271799","https://openalex.org/W2577818139","https://openalex.org/W47544861","https://openalex.org/W123898865","https://openalex.org/W2912635026","https://openalex.org/W4249328994","https://openalex.org/W2391887161","https://openalex.org/W2358302317","https://openalex.org/W2098859420","https://openalex.org/W4302552130"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
