{"id":"https://openalex.org/W1998526928","doi":"https://doi.org/10.1007/s00454-006-1278-3","title":"Lines Tangent to Four Triangles in Three-Dimensional Space","display_name":"Lines Tangent to Four Triangles in Three-Dimensional Space","publication_year":2007,"publication_date":"2007-03-01","ids":{"openalex":"https://openalex.org/W1998526928","doi":"https://doi.org/10.1007/s00454-006-1278-3","mag":"1998526928"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-006-1278-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-006-1278-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-006-1278-3.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-006-1278-3.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091742760","display_name":"Herv\u00e9 Br\u00f6nnimann","orcid":null},"institutions":[{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"H. Bronnimann","raw_affiliation_strings":["Department of Computer and Information Science, Polytechnic University, Brooklyn, NY 11201, USA","Department of Computer and Information Science, Polytechnic University, Brooklyn, NY 11201, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer and Information Science, Polytechnic University, Brooklyn, NY 11201, USA","institution_ids":[]},{"raw_affiliation_string":"Department of Computer and Information Science, Polytechnic University, Brooklyn, NY 11201, USA#TAB#","institution_ids":["https://openalex.org/I57206974"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043040182","display_name":"Olivier Devillers","orcid":"https://orcid.org/0000-0003-4275-5068"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"O. Devillers","raw_affiliation_strings":["INRIA Sophia-Antipolis, 2004 Rte des Lucioles, B.P. 93, 06902 Sophia-Antipolis Cedex, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"INRIA Sophia-Antipolis, 2004 Rte des Lucioles, B.P. 93, 06902 Sophia-Antipolis Cedex, France","institution_ids":["https://openalex.org/I1326498283"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041225170","display_name":"Sylvain Lazard","orcid":"https://orcid.org/0000-0002-6032-0802"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I4210121838","display_name":"Laboratoire Lorrain de Recherche en Informatique et ses Applications","ror":"https://ror.org/02vnf0c38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I277688954","https://openalex.org/I4210107720","https://openalex.org/I4210121838","https://openalex.org/I4210159245","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I4210127166","display_name":"Centre Inria de l'Universit\u00e9 de Lorraine","ror":"https://ror.org/03fcjvn64","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210127166"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"S. Lazard","raw_affiliation_strings":["INRIA Lorraine (LORIA), 615 Rue du Jardin Botanique, 54602 Villers-les-Nancy, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"INRIA Lorraine (LORIA), 615 Rue du Jardin Botanique, 54602 Villers-les-Nancy, France","institution_ids":["https://openalex.org/I4210127166","https://openalex.org/I1326498283","https://openalex.org/I4210121838"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078229263","display_name":"Frank Sottile","orcid":"https://orcid.org/0000-0003-0087-7120"},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"F. Sottile","raw_affiliation_strings":["Department of Mathematics, Texas A&M University, College Station, TX 77843, USA","Department of Mathematics,#N#Texas A&M University,#N#College Station, TX 77843, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Texas A&M University, College Station, TX 77843, USA","institution_ids":["https://openalex.org/I91045830"]},{"raw_affiliation_string":"Department of Mathematics,#N#Texas A&M University,#N#College Station, TX 77843, USA","institution_ids":["https://openalex.org/I91045830"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.5371,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.77236744,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"37","issue":"3","first_page":"369","last_page":"380"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9993000030517578,"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"}},{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.9945999979972839,"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/tangent","display_name":"Tangent","score":0.7913249731063843},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7166382670402527},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.6655445098876953},{"id":"https://openalex.org/keywords/general-position","display_name":"General position","score":0.6309858560562134},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5632165670394897},{"id":"https://openalex.org/keywords/tangent-cone","display_name":"Tangent cone","score":0.5561615824699402},{"id":"https://openalex.org/keywords/tangent-space","display_name":"Tangent space","score":0.5003824234008789},{"id":"https://openalex.org/keywords/tangent-vector","display_name":"Tangent vector","score":0.4949161410331726},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.4862336218357086},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.4703866243362427},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4398230016231537},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08905446529388428}],"concepts":[{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.7913249731063843},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7166382670402527},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.6655445098876953},{"id":"https://openalex.org/C150397156","wikidata":"https://www.wikidata.org/wiki/Q591310","display_name":"General position","level":2,"score":0.6309858560562134},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5632165670394897},{"id":"https://openalex.org/C149944404","wikidata":"https://www.wikidata.org/wiki/Q2392464","display_name":"Tangent cone","level":3,"score":0.5561615824699402},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.5003824234008789},{"id":"https://openalex.org/C47890412","wikidata":"https://www.wikidata.org/wiki/Q1179296","display_name":"Tangent vector","level":3,"score":0.4949161410331726},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.4862336218357086},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.4703866243362427},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4398230016231537},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08905446529388428},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00454-006-1278-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-006-1278-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-006-1278-3.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:HAL:inria-00000598v1","is_oa":false,"landing_page_url":"https://inria.hal.science/inria-00000598","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Discrete and Computational Geometry, 2007, 37 (3), pp.369-380. ⟨10.1007/s00454-006-1278-3⟩","raw_type":"Journal articles"},{"id":"pmh:oai:HAL:inria-00071223v1","is_oa":false,"landing_page_url":"https://inria.hal.science/inria-00071223","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"[Research Report] RR-5693, INRIA. 2005","raw_type":"Reports"}],"best_oa_location":{"id":"doi:10.1007/s00454-006-1278-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-006-1278-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-006-1278-3.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.5299999713897705}],"awards":[{"id":"https://openalex.org/G5412631906","display_name":"CAREER:   Computation, Combinatorics, and Reality in Algebraic Geometry, with Applications","funder_award_id":"0134860","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6911238460","display_name":"Generic Software Foundations for Geometric Computing","funder_award_id":"0133599","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320310638","display_name":"McGill University","ror":"https://ror.org/01pxwe438"},{"id":"https://openalex.org/F4320313934","display_name":"Institut national de recherche en informatique et en automatique (INRIA)","ror":"https://ror.org/02kvxyf05"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1998526928.pdf","grobid_xml":"https://content.openalex.org/works/W1998526928.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W92756310","https://openalex.org/W170832643","https://openalex.org/W1503537831","https://openalex.org/W1601864594","https://openalex.org/W1963803722","https://openalex.org/W1979877896","https://openalex.org/W1980261256","https://openalex.org/W1991640613","https://openalex.org/W2004979970","https://openalex.org/W2022266599","https://openalex.org/W2027982698","https://openalex.org/W2043913766","https://openalex.org/W2046148772","https://openalex.org/W2081622320","https://openalex.org/W2082015250","https://openalex.org/W2083046806","https://openalex.org/W2150192362","https://openalex.org/W2952389111","https://openalex.org/W4213028887","https://openalex.org/W4297776103","https://openalex.org/W4300640952","https://openalex.org/W6606918271","https://openalex.org/W6648095969","https://openalex.org/W7036533293"],"related_works":["https://openalex.org/W1969325112","https://openalex.org/W2361271799","https://openalex.org/W2484616478","https://openalex.org/W123898865","https://openalex.org/W4249328994","https://openalex.org/W2391887161","https://openalex.org/W2353074735","https://openalex.org/W2381565014","https://openalex.org/W2384343431","https://openalex.org/W1966593065"],"abstract_inverted_index":null,"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}