{"id":"https://openalex.org/W2032054383","doi":"https://doi.org/10.1145/1005285.1005307","title":"Parametrized surfaces in huge P <sup>3</sup> of bidegree (1,2)","display_name":"Parametrized surfaces in huge P <sup>3</sup> of bidegree (1,2)","publication_year":2004,"publication_date":"2004-07-04","ids":{"openalex":"https://openalex.org/W2032054383","doi":"https://doi.org/10.1145/1005285.1005307","mag":"2032054383"},"language":"en","primary_location":{"id":"doi:10.1145/1005285.1005307","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1005285.1005307","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2004 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/A5019923233","display_name":"Mohamed Elkadi","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":"Mohamed Elkadi","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":"middle","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":false,"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/A5037352035","display_name":"Th\u1ecb H\u00e0 L\u00ea","orcid":"https://orcid.org/0000-0003-4684-3866"},"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":"Thi Ha L\u00ea","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":3,"corresponding_author_ids":["https://openalex.org/A5019923233"],"corresponding_institution_ids":["https://openalex.org/I201841394"],"apc_list":null,"apc_paid":null,"fwci":2.1903,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.85963321,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"141","last_page":"148"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9998000264167786,"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":0.9998000264167786,"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":0.996999979019165,"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":0.9958999752998352,"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/interpretation","display_name":"Interpretation (philosophy)","score":0.5651196837425232},{"id":"https://openalex.org/keywords/geometric-design","display_name":"Geometric design","score":0.4858939051628113},{"id":"https://openalex.org/keywords/modulus","display_name":"Modulus","score":0.4702391028404236},{"id":"https://openalex.org/keywords/locus","display_name":"Locus (genetics)","score":0.4435604214668274},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.440311074256897},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.39202311635017395},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.35834383964538574},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3538495898246765},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3507435917854309},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3319956064224243}],"concepts":[{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.5651196837425232},{"id":"https://openalex.org/C40319758","wikidata":"https://www.wikidata.org/wiki/Q5535477","display_name":"Geometric design","level":2,"score":0.4858939051628113},{"id":"https://openalex.org/C193867417","wikidata":"https://www.wikidata.org/wiki/Q6889814","display_name":"Modulus","level":2,"score":0.4702391028404236},{"id":"https://openalex.org/C84597430","wikidata":"https://www.wikidata.org/wiki/Q106227","display_name":"Locus (genetics)","level":3,"score":0.4435604214668274},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.440311074256897},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.39202311635017395},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.35834383964538574},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3538495898246765},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3507435917854309},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3319956064224243},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1005285.1005307","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1005285.1005307","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2004 international symposium on Symbolic and algebraic computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.5400000214576721}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1481918316","https://openalex.org/W1551207461","https://openalex.org/W1828839365","https://openalex.org/W1970549336","https://openalex.org/W1981948059","https://openalex.org/W1991466097","https://openalex.org/W2006512450","https://openalex.org/W2034966370","https://openalex.org/W2037188318","https://openalex.org/W2091084189","https://openalex.org/W4248269519"],"related_works":["https://openalex.org/W4313320911","https://openalex.org/W4327743144","https://openalex.org/W4245077728","https://openalex.org/W2607424049","https://openalex.org/W4390922876","https://openalex.org/W3183204001","https://openalex.org/W4206302830","https://openalex.org/W2185941092","https://openalex.org/W4386782890","https://openalex.org/W3210948575"],"abstract_inverted_index":{"Parametrized":[0],"surfaces":[1,33,75],"of":[2,22,34,45],"low":[3],"degrees":[4],"are":[5,48],"very":[6],"useful":[7],"in":[8,11,28],"applications,":[9],"specially":[10],"Computer":[12],"Aided":[13],"Geometric":[14,17],"Design":[15],"and":[16,76],"Modeling.":[18],"The":[19],"precise":[20],"description":[21,60],"their":[23,78],"geometry":[24],"is":[25],"not":[26],"easy":[27],"general.":[29],"Here":[30],"we":[31],"study":[32],"bidegree":[35],"(1,2).":[36],"We":[37,55,68],"show":[38],"that,":[39],"generically":[40],"up":[41],"to":[42],"linear":[43],"changes":[44],"coordinates,":[46],"they":[47],"classified":[49],"by":[50],"two":[51],"continuous":[52],"parameters":[53],"(modulus).":[54],"present":[56],"an":[57],"elegant":[58],"combinatorial":[59],"where":[61],"these":[62,74],"modulus":[63],"appear":[64],"as":[65],"cross":[66],"ratios.":[67],"provide":[69],"compact":[70],"implicit":[71],"equations":[72],"for":[73,77],"singular":[79],"locus":[80],"together":[81],"with":[82],"a":[83],"geometric":[84],"interpretation.":[85]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
