{"id":"https://openalex.org/W1999404149","doi":"https://doi.org/10.1145/1277500.1277515","title":"Real implicitization of curves and geometric extraneous components","display_name":"Real implicitization of curves and geometric extraneous components","publication_year":2007,"publication_date":"2007-07-25","ids":{"openalex":"https://openalex.org/W1999404149","doi":"https://doi.org/10.1145/1277500.1277515","mag":"1999404149"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1145/1277500.1277515","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"proceedings-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/A5053553622","display_name":"Mario Fioravanti","orcid":"https://orcid.org/0000-0002-9749-9084"},"institutions":[{"id":"https://openalex.org/I13134134","display_name":"Universidad de Cantabria","ror":"https://ror.org/046ffzj20","country_code":"ES","type":"education","lineage":["https://openalex.org/I13134134"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Mario Fioravanti","raw_affiliation_strings":["Universidad de Cantabria, Santander (Spain)"],"affiliations":[{"raw_affiliation_string":"Universidad de Cantabria, Santander (Spain)","institution_ids":["https://openalex.org/I13134134"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041501036","display_name":"Laureano Gonz\u00e1lez-Vega","orcid":"https://orcid.org/0000-0002-3934-3890"},"institutions":[{"id":"https://openalex.org/I13134134","display_name":"Universidad de Cantabria","ror":"https://ror.org/046ffzj20","country_code":"ES","type":"education","lineage":["https://openalex.org/I13134134"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Laureano Gonzalez-Vega","raw_affiliation_strings":["Universidad de Cantabria, Santander (Spain)"],"affiliations":[{"raw_affiliation_string":"Universidad de Cantabria, Santander (Spain)","institution_ids":["https://openalex.org/I13134134"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065334266","display_name":"Andreas Seidl","orcid":null},"institutions":[{"id":"https://openalex.org/I186354981","display_name":"University of Passau","ror":"https://ror.org/05ydjnb78","country_code":"DE","type":"education","lineage":["https://openalex.org/I186354981"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Andreas Seidl","raw_affiliation_strings":["Universitat Passau, Passau, Germany#TAB#"],"affiliations":[{"raw_affiliation_string":"Universitat Passau, Passau, Germany#TAB#","institution_ids":["https://openalex.org/I186354981"]}]}],"institution_assertions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":0,"max":63},"biblio":{"volume":null,"issue":null,"first_page":"87","last_page":"96"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9999,"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":0.9999,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9856,"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/T11159","display_name":"Manufacturing Process and Optimization","score":0.9746,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"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/parametric-equation","display_name":"Parametric equation","score":0.7023307},{"id":"https://openalex.org/keywords/quantifier-elimination","display_name":"Quantifier elimination","score":0.68389916},{"id":"https://openalex.org/keywords/geometric-design","display_name":"Geometric design","score":0.448076},{"id":"https://openalex.org/keywords/geometric-modeling","display_name":"Geometric Modeling","score":0.42454085}],"concepts":[{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.72635967},{"id":"https://openalex.org/C99636146","wikidata":"https://www.wikidata.org/wiki/Q35889","display_name":"Parametric equation","level":2,"score":0.7023307},{"id":"https://openalex.org/C32278780","wikidata":"https://www.wikidata.org/wiki/Q1849020","display_name":"Quantifier elimination","level":2,"score":0.68389916},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5806112},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5254449},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4684159},{"id":"https://openalex.org/C40319758","wikidata":"https://www.wikidata.org/wiki/Q5535477","display_name":"Geometric design","level":2,"score":0.448076},{"id":"https://openalex.org/C104065381","wikidata":"https://www.wikidata.org/wiki/Q1002535","display_name":"Geometric modeling","level":2,"score":0.42454085},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4191561},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3463878},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32957333},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.32642156},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.247172},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.18073943},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16813344},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08314943}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1145/1277500.1277515","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":53,"referenced_works":["https://openalex.org/W1504797307","https://openalex.org/W1539076476","https://openalex.org/W1539838732","https://openalex.org/W1553142094","https://openalex.org/W1560057946","https://openalex.org/W1570787829","https://openalex.org/W1576347883","https://openalex.org/W189523104","https://openalex.org/W1939145901","https://openalex.org/W1967590260","https://openalex.org/W1969130880","https://openalex.org/W1971343670","https://openalex.org/W1984258784","https://openalex.org/W1984435191","https://openalex.org/W2001921649","https://openalex.org/W2001976071","https://openalex.org/W2002352305","https://openalex.org/W2006512450","https://openalex.org/W2009011215","https://openalex.org/W2020298878","https://openalex.org/W2022637219","https://openalex.org/W2026722217","https://openalex.org/W2031337781","https://openalex.org/W2039758732","https://openalex.org/W2039791875","https://openalex.org/W2041942111","https://openalex.org/W2042712358","https://openalex.org/W2045697474","https://openalex.org/W2055431849","https://openalex.org/W2059860265","https://openalex.org/W2064044318","https://openalex.org/W2071113133","https://openalex.org/W2071390560","https://openalex.org/W2077186096","https://openalex.org/W2079278461","https://openalex.org/W2089372543","https://openalex.org/W2101561222","https://openalex.org/W2121296219","https://openalex.org/W2133261933","https://openalex.org/W2139009791","https://openalex.org/W2172187032","https://openalex.org/W2232657515","https://openalex.org/W2289808822","https://openalex.org/W2320437408","https://openalex.org/W2490484610","https://openalex.org/W2500071694","https://openalex.org/W2612686320","https://openalex.org/W4234682643","https://openalex.org/W4244681853","https://openalex.org/W4285719527","https://openalex.org/W4299599836","https://openalex.org/W4301491118","https://openalex.org/W4320800818"],"related_works":["https://openalex.org/W610482509","https://openalex.org/W4255956924","https://openalex.org/W4220701978","https://openalex.org/W3113701594","https://openalex.org/W3092209326","https://openalex.org/W3012372210","https://openalex.org/W2098679894","https://openalex.org/W2071113133","https://openalex.org/W1985426375","https://openalex.org/W1593530080"],"abstract_inverted_index":{"Real":[0],"implicitization":[1],"of":[2,14,34,49],"parametric":[3,15],"curves":[4,16],"has":[5],"important":[6],"applications":[7],"in":[8,76],"computer":[9],"aided":[10],"geometric":[11,41],"design.":[12],"Implicitization":[13],"by":[17,55],"resultant":[18],"computations":[19],"may":[20],"lead":[21],"to":[22,64,68],"super":[23],"uous":[24],"isolated":[25],"points.":[26],"Hence,":[27],"an":[28,71],"exact":[29,72],"implicit":[30,47],"description":[31,48],"should":[32],"consist":[33],"equations":[35],"and":[36,81],"further":[37],"conditions":[38,67],"excluding":[39],"these":[40],"extraneous":[42],"components.":[43],"Although":[44],"a":[45,61,77],"real":[46,56],"this":[50],"kind":[51],"can":[52],"be":[53],"obtained":[54],"quantifier":[57],"elimination,":[58],"we":[59],"give":[60],"direct":[62],"way":[63],"find":[65],"the":[66],"add":[69],"for":[70],"description.":[73],"This":[74],"results":[75],"more":[78],"effective":[79],"algorithm":[80],"nicer":[82],"formulas.":[83]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W1999404149","counts_by_year":[],"updated_date":"2024-12-08T05:04:16.630605","created_date":"2016-06-24"}