{"id":"https://openalex.org/W2087534346","doi":"https://doi.org/10.1145/1577190.1577205","title":"Curve/surface intersection problem by means of matrix representations","display_name":"Curve/surface intersection problem by means of matrix representations","publication_year":2009,"publication_date":"2009-08-03","ids":{"openalex":"https://openalex.org/W2087534346","doi":"https://doi.org/10.1145/1577190.1577205","mag":"2087534346"},"language":"en","primary_location":{"id":"doi:10.1145/1577190.1577205","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1577190.1577205","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2009 conference on Symbolic numeric computation","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://inria.hal.science/inria-00418403","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Luu Ba Thang","orcid":null},"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/I201841394","display_name":"Universit\u00e9 C\u00f4te d'Azur","ror":"https://ror.org/019tgvf94","country_code":"FR","type":"education","lineage":["https://openalex.org/I201841394"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Luu Ba Thang","raw_affiliation_strings":["University of Nice and INRIA Sophia Antipolis, Nice, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Nice and INRIA Sophia Antipolis, Nice, France","institution_ids":["https://openalex.org/I201841394","https://openalex.org/I1326498283"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088510335","display_name":"Laurent Bus\u00e9","orcid":"https://orcid.org/0009-0005-6528-7027"},"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":"Laurent Bus\u00e9","raw_affiliation_strings":["INRIA Sophia Antipolis, Sophia Antipolis, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"INRIA Sophia Antipolis, Sophia Antipolis, France","institution_ids":["https://openalex.org/I1326498283"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003683965","display_name":"Bernard Mourrain","orcid":"https://orcid.org/0000-0002-8813-1368"},"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":"Bernard Mourrain","raw_affiliation_strings":["INRIA Sophia Antipolis, Sophia Antipolis, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"INRIA Sophia Antipolis, Sophia Antipolis, France","institution_ids":["https://openalex.org/I1326498283"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"71","last_page":"78"},"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9932000041007996,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9886999726295471,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.69710373878479},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5975092649459839},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.5782316327095032},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5713936686515808},{"id":"https://openalex.org/keywords/linear-algebra","display_name":"Linear algebra","score":0.5465755462646484},{"id":"https://openalex.org/keywords/novelty","display_name":"Novelty","score":0.5264657139778137},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.463532954454422},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.4455450773239136},{"id":"https://openalex.org/keywords/matrix-algebra","display_name":"Matrix algebra","score":0.43758291006088257},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39723947644233704},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.20611914992332458},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18793517351150513},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.0775672197341919}],"concepts":[{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.69710373878479},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5975092649459839},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.5782316327095032},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5713936686515808},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.5465755462646484},{"id":"https://openalex.org/C2778738651","wikidata":"https://www.wikidata.org/wiki/Q16546687","display_name":"Novelty","level":2,"score":0.5264657139778137},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.463532954454422},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4455450773239136},{"id":"https://openalex.org/C2988995629","wikidata":"https://www.wikidata.org/wiki/Q2915729","display_name":"Matrix algebra","level":3,"score":0.43758291006088257},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39723947644233704},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20611914992332458},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18793517351150513},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0775672197341919},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C27206212","wikidata":"https://www.wikidata.org/wiki/Q34178","display_name":"Theology","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/1577190.1577205","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1577190.1577205","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2009 conference on Symbolic numeric computation","raw_type":"proceedings-article"},{"id":"pmh:oai:HAL:inria-00418403v1","is_oa":true,"landing_page_url":"https://inria.hal.science/inria-00418403","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SNC, Aug 2009, Kyoto, Japan. pp.71-78, ⟨10.1145/1577190.1577205⟩","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":{"id":"pmh:oai:HAL:inria-00418403v1","is_oa":true,"landing_page_url":"https://inria.hal.science/inria-00418403","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SNC, Aug 2009, Kyoto, Japan. pp.71-78, ⟨10.1145/1577190.1577205⟩","raw_type":"info:eu-repo/semantics/conferenceObject"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W625593473","https://openalex.org/W1579224486","https://openalex.org/W1983016830","https://openalex.org/W1984435191","https://openalex.org/W1984452258","https://openalex.org/W1990198686","https://openalex.org/W2013899348","https://openalex.org/W2015821533","https://openalex.org/W2034857732","https://openalex.org/W2048961297","https://openalex.org/W2049645908","https://openalex.org/W2059906458","https://openalex.org/W2075181487","https://openalex.org/W2079600081","https://openalex.org/W2087794615","https://openalex.org/W2124986435","https://openalex.org/W2232657515","https://openalex.org/W2798909945","https://openalex.org/W2951671279","https://openalex.org/W3101084619","https://openalex.org/W6620086211","https://openalex.org/W6750968397"],"related_works":["https://openalex.org/W2050090934","https://openalex.org/W2041511182","https://openalex.org/W622366405","https://openalex.org/W1784494460","https://openalex.org/W2029268228","https://openalex.org/W2099828814","https://openalex.org/W252631351","https://openalex.org/W1526519642","https://openalex.org/W4207050455","https://openalex.org/W2039747689"],"abstract_inverted_index":{"In":[0],"this":[1,48],"paper,":[2],"we":[3],"introduce":[4],"matrix":[5,22],"representations":[6,23,56],"of":[7,20,31,70],"algebraic":[8],"curves":[9],"and":[10],"surfaces":[11],"for":[12],"Computer":[13],"Aided":[14],"Geometric":[15],"Design":[16],"(CAGD).":[17],"The":[18,29],"idea":[19],"using":[21],"in":[24,47],"CAGD":[25],"is":[26,34,42],"quite":[27],"old.":[28],"novelty":[30],"our":[32],"contribution":[33],"to":[35,53,62],"enable":[36],"non":[37],"square":[38],"matrices,":[39],"extension":[40],"which":[41],"motivated":[43],"by":[44,57,68],"recent":[45],"research":[46],"topic.":[49],"We":[50],"show":[51],"how":[52],"manipulate":[54],"these":[55],"proposing":[58],"a":[59],"dedicated":[60],"algorithm":[61],"address":[63],"the":[64],"curve/surface":[65],"intersection":[66],"problem":[67],"means":[69],"numerical":[71],"linear":[72],"algebra":[73],"techniques.":[74]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}