{"id":"https://openalex.org/W2088259864","doi":"https://doi.org/10.1145/1073884.1073906","title":"Selfintersections of a b\u00e9zier bicubic surface","display_name":"Selfintersections of a b\u00e9zier bicubic surface","publication_year":2005,"publication_date":"2005-07-24","ids":{"openalex":"https://openalex.org/W2088259864","doi":"https://doi.org/10.1145/1073884.1073906","mag":"2088259864"},"language":"en","primary_location":{"id":"doi:10.1145/1073884.1073906","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1073884.1073906","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2005 international symposium on Symbolic and algebraic computation","raw_type":"proceedings-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/A5111902088","display_name":"Andr\u00e9 Galligo","orcid":null},"institutions":[{"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":true,"raw_author_name":"Andr\u00e9 Galligo","raw_affiliation_strings":["Universit\u00e9 de Nice Sophia-Antipolis, Nice Cedex, France"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Nice Sophia-Antipolis, Nice Cedex, France","institution_ids":["https://openalex.org/I201841394"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042169041","display_name":"Jean Pascal Pavone","orcid":null},"institutions":[{"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":"Jean Pascal Pavone","raw_affiliation_strings":["Universit\u00e9 de Nice Sophia-Antipolis, Nice Cedex, France"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Nice Sophia-Antipolis, Nice Cedex, France","institution_ids":["https://openalex.org/I201841394"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5111902088"],"corresponding_institution_ids":["https://openalex.org/I201841394"],"apc_list":null,"apc_paid":null,"fwci":0.8251,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.74582938,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"148","last_page":"155"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":1.0,"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":1.0,"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":0.9994999766349792,"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":0.9864000082015991,"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/bicubic-interpolation","display_name":"Bicubic interpolation","score":0.830898642539978},{"id":"https://openalex.org/keywords/b\u00e9zier-curve","display_name":"B\u00e9zier curve","score":0.8298885822296143},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.7749361991882324},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6030767560005188},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5742805004119873},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.5389332175254822},{"id":"https://openalex.org/keywords/b\u00e9zier-surface","display_name":"B\u00e9zier surface","score":0.4997525215148926},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.49063554406166077},{"id":"https://openalex.org/keywords/bivariate-analysis","display_name":"Bivariate analysis","score":0.4855801463127136},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.48335570096969604},{"id":"https://openalex.org/keywords/computer-aided-design","display_name":"Computer Aided Design","score":0.4678631126880646},{"id":"https://openalex.org/keywords/geometric-modeling","display_name":"Geometric modeling","score":0.45360100269317627},{"id":"https://openalex.org/keywords/cad","display_name":"CAD","score":0.4508677124977112},{"id":"https://openalex.org/keywords/geometric-design","display_name":"Geometric design","score":0.44877398014068604},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41016367077827454},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4028029441833496},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.38560667634010315},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36390799283981323},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3626784086227417},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.267204225063324},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.2252872884273529},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.18981704115867615},{"id":"https://openalex.org/keywords/engineering-drawing","display_name":"Engineering drawing","score":0.14339712262153625},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.1210949718952179},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11694461107254028},{"id":"https://openalex.org/keywords/multivariate-interpolation","display_name":"Multivariate interpolation","score":0.10671067237854004}],"concepts":[{"id":"https://openalex.org/C49608258","wikidata":"https://www.wikidata.org/wiki/Q611705","display_name":"Bicubic interpolation","level":4,"score":0.830898642539978},{"id":"https://openalex.org/C206423108","wikidata":"https://www.wikidata.org/wiki/Q214728","display_name":"B\u00e9zier curve","level":2,"score":0.8298885822296143},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.7749361991882324},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6030767560005188},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5742805004119873},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.5389332175254822},{"id":"https://openalex.org/C100374796","wikidata":"https://www.wikidata.org/wiki/Q926066","display_name":"B\u00e9zier surface","level":3,"score":0.4997525215148926},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.49063554406166077},{"id":"https://openalex.org/C64341305","wikidata":"https://www.wikidata.org/wiki/Q4919225","display_name":"Bivariate analysis","level":2,"score":0.4855801463127136},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.48335570096969604},{"id":"https://openalex.org/C119823426","wikidata":"https://www.wikidata.org/wiki/Q184793","display_name":"Computer Aided Design","level":2,"score":0.4678631126880646},{"id":"https://openalex.org/C104065381","wikidata":"https://www.wikidata.org/wiki/Q1002535","display_name":"Geometric modeling","level":2,"score":0.45360100269317627},{"id":"https://openalex.org/C194789388","wikidata":"https://www.wikidata.org/wiki/Q17855283","display_name":"CAD","level":2,"score":0.4508677124977112},{"id":"https://openalex.org/C40319758","wikidata":"https://www.wikidata.org/wiki/Q5535477","display_name":"Geometric design","level":2,"score":0.44877398014068604},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41016367077827454},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4028029441833496},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.38560667634010315},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36390799283981323},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3626784086227417},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.267204225063324},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.2252872884273529},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18981704115867615},{"id":"https://openalex.org/C199639397","wikidata":"https://www.wikidata.org/wiki/Q1788588","display_name":"Engineering drawing","level":1,"score":0.14339712262153625},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.1210949718952179},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11694461107254028},{"id":"https://openalex.org/C203332170","wikidata":"https://www.wikidata.org/wiki/Q6334079","display_name":"Multivariate interpolation","level":3,"score":0.10671067237854004},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1073884.1073906","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1073884.1073906","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2005 international symposium on Symbolic and algebraic computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W117048182","https://openalex.org/W120458350","https://openalex.org/W1481918316","https://openalex.org/W1483218536","https://openalex.org/W1496785083","https://openalex.org/W1503037433","https://openalex.org/W1517290374","https://openalex.org/W1551207461","https://openalex.org/W1561343803","https://openalex.org/W1578157337","https://openalex.org/W1581825425","https://openalex.org/W1589121839","https://openalex.org/W1623168034","https://openalex.org/W1828839365","https://openalex.org/W1968297701","https://openalex.org/W1977415556","https://openalex.org/W1984063983","https://openalex.org/W1984926837","https://openalex.org/W2006512450","https://openalex.org/W2034966370","https://openalex.org/W2043775053","https://openalex.org/W2048329955","https://openalex.org/W2052181099","https://openalex.org/W2096797656","https://openalex.org/W2116319659","https://openalex.org/W2147817337","https://openalex.org/W4232459207","https://openalex.org/W4234587084","https://openalex.org/W4248269519","https://openalex.org/W6605307435","https://openalex.org/W6639911218"],"related_works":["https://openalex.org/W2359526277","https://openalex.org/W1488847936","https://openalex.org/W2088259864","https://openalex.org/W2094455962","https://openalex.org/W2585339137","https://openalex.org/W4399304147","https://openalex.org/W2355871967","https://openalex.org/W2329209542","https://openalex.org/W3205931107","https://openalex.org/W2081089060"],"abstract_inverted_index":{"We":[0],"present":[1],"the":[2,48],"computation":[3],"of":[4,23,63],"selfintersections":[5],"as":[6],"a":[7,41,53],"major":[8],"problem":[9],"in":[10],"Computer":[11,37],"Aided":[12],"Geometric":[13,17],"Design":[14],"(CAD)":[15],"and":[16,19,70],"Modeling,":[18],"particularly":[20],"for":[21],"patches":[22],"parametrized":[24],"bicubic":[25],"surfaces.":[26],"Then":[27],"we":[28],"expose":[29],"two":[30],"complementary":[31],"contributions":[32],"on":[33],"that":[34],"subject":[35],"with":[36,60,65],"Algebra":[38],"tools:":[39],"First,":[40],"specific":[42],"sparse":[43],"bivariate":[44],"resultant":[45],"adapted":[46],"to":[47,58],"corresponding":[49],"elimination":[50],"problem,":[51],"second":[52],"semi-numeric":[54],"polynomial":[55],"solver":[56],"able":[57],"deal":[59],"large":[61],"system":[62],"equations":[64],"floating":[66],"point":[67],"coefficients.":[68],"Examples":[69],"timings":[71],"are":[72],"provided.":[73]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}