{"id":"https://openalex.org/W4249169491","doi":"https://doi.org/10.1109/gmap.2004.1290031","title":"Rational quadratic approximation to real plane algebraic curves","display_name":"Rational quadratic approximation to real plane algebraic curves","publication_year":2004,"publication_date":"2004-06-10","ids":{"openalex":"https://openalex.org/W4249169491","doi":"https://doi.org/10.1109/gmap.2004.1290031"},"language":"en","primary_location":{"id":"doi:10.1109/gmap.2004.1290031","is_oa":false,"landing_page_url":"https://doi.org/10.1109/gmap.2004.1290031","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Geometric Modeling and Processing, 2004. Proceedings","raw_type":"proceedings-article"},"type":"conference-paper","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/A5017479931","display_name":"Xiao-Shan Gao","orcid":"https://orcid.org/0000-0003-2021-9395"},"institutions":[{"id":"https://openalex.org/I4210129227","display_name":"Chinese Academy of Agricultural Mechanization Sciences","ror":"https://ror.org/03792qf33","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210129227"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiao-Shan Gao","raw_affiliation_strings":["Key Lab of Mathematics Mechanization Institute of Systems Science, AMSS, Academia Sinica, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Lab of Mathematics Mechanization Institute of Systems Science, AMSS, Academia Sinica, Beijing, China","institution_ids":["https://openalex.org/I4210129227"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100351409","display_name":"Ming Li","orcid":"https://orcid.org/0000-0002-2725-353X"},"institutions":[{"id":"https://openalex.org/I4210129227","display_name":"Chinese Academy of Agricultural Mechanization Sciences","ror":"https://ror.org/03792qf33","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210129227"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ming Li","raw_affiliation_strings":["Key Lab of Mathematics Mechanization Institute of Systems Science, AMSS, Academia Sinica, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Lab of Mathematics Mechanization Institute of Systems Science, AMSS, Academia Sinica, Beijing, China","institution_ids":["https://openalex.org/I4210129227"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210129227"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.50697757,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"21","issue":null,"first_page":"93","last_page":"102"},"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":0.9886000156402588,"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":0.9793999791145325,"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/b\u00e9zier-curve","display_name":"B\u00e9zier curve","score":0.7306205034255981},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.673101007938385},{"id":"https://openalex.org/keywords/algebraic-curve","display_name":"Algebraic curve","score":0.6082334518432617},{"id":"https://openalex.org/keywords/stable-curve","display_name":"Stable curve","score":0.5979928970336914},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5616598129272461},{"id":"https://openalex.org/keywords/osculating-circle","display_name":"Osculating circle","score":0.555227518081665},{"id":"https://openalex.org/keywords/plane-curve","display_name":"Plane curve","score":0.5519348382949829},{"id":"https://openalex.org/keywords/convex-curve","display_name":"Convex curve","score":0.5301129817962646},{"id":"https://openalex.org/keywords/curve-fitting","display_name":"Curve fitting","score":0.5030130743980408},{"id":"https://openalex.org/keywords/quartic-plane-curve","display_name":"Quartic plane curve","score":0.4393289387226105},{"id":"https://openalex.org/keywords/family-of-curves","display_name":"Family of curves","score":0.43918681144714355},{"id":"https://openalex.org/keywords/tripling-oriented-doche\u2013icart\u2013kohel-curve","display_name":"Tripling-oriented Doche\u2013Icart\u2013Kohel curve","score":0.4150044322013855},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4097551107406616},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3537030816078186},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.33425748348236084},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.33261245489120483},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.27871763706207275},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.23849424719810486},{"id":"https://openalex.org/keywords/real-algebraic-geometry","display_name":"Real algebraic geometry","score":0.1896241009235382},{"id":"https://openalex.org/keywords/convex-combination","display_name":"Convex combination","score":0.1842154860496521},{"id":"https://openalex.org/keywords/schoofs-algorithm","display_name":"Schoof's algorithm","score":0.17446741461753845},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.15326526761054993}],"concepts":[{"id":"https://openalex.org/C206423108","wikidata":"https://www.wikidata.org/wiki/Q214728","display_name":"B\u00e9zier curve","level":2,"score":0.7306205034255981},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.673101007938385},{"id":"https://openalex.org/C207043602","wikidata":"https://www.wikidata.org/wiki/Q266237","display_name":"Algebraic curve","level":2,"score":0.6082334518432617},{"id":"https://openalex.org/C184363387","wikidata":"https://www.wikidata.org/wiki/Q3001219","display_name":"Stable curve","level":4,"score":0.5979928970336914},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5616598129272461},{"id":"https://openalex.org/C40890689","wikidata":"https://www.wikidata.org/wiki/Q2166240","display_name":"Osculating circle","level":2,"score":0.555227518081665},{"id":"https://openalex.org/C43809302","wikidata":"https://www.wikidata.org/wiki/Q1060874","display_name":"Plane curve","level":2,"score":0.5519348382949829},{"id":"https://openalex.org/C128618672","wikidata":"https://www.wikidata.org/wiki/Q3001187","display_name":"Convex curve","level":5,"score":0.5301129817962646},{"id":"https://openalex.org/C184389593","wikidata":"https://www.wikidata.org/wiki/Q603159","display_name":"Curve fitting","level":2,"score":0.5030130743980408},{"id":"https://openalex.org/C84181032","wikidata":"https://www.wikidata.org/wiki/Q1857574","display_name":"Quartic plane curve","level":3,"score":0.4393289387226105},{"id":"https://openalex.org/C53622353","wikidata":"https://www.wikidata.org/wiki/Q1518913","display_name":"Family of curves","level":2,"score":0.43918681144714355},{"id":"https://openalex.org/C37055786","wikidata":"https://www.wikidata.org/wiki/Q7843607","display_name":"Tripling-oriented Doche\u2013Icart\u2013Kohel curve","level":5,"score":0.4150044322013855},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4097551107406616},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3537030816078186},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.33425748348236084},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.33261245489120483},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.27871763706207275},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.23849424719810486},{"id":"https://openalex.org/C2731732","wikidata":"https://www.wikidata.org/wiki/Q7301119","display_name":"Real algebraic geometry","level":3,"score":0.1896241009235382},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.1842154860496521},{"id":"https://openalex.org/C121444067","wikidata":"https://www.wikidata.org/wiki/Q2835817","display_name":"Schoof's algorithm","level":4,"score":0.17446741461753845},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.15326526761054993},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C197875053","wikidata":"https://www.wikidata.org/wiki/Q7269266","display_name":"Quarter period","level":3,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/gmap.2004.1290031","is_oa":false,"landing_page_url":"https://doi.org/10.1109/gmap.2004.1290031","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Geometric Modeling and Processing, 2004. Proceedings","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.89.2607","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.89.2607","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mmrc.iss.ac.cn/pub/mm22.pdf/7.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W116910719","https://openalex.org/W1484040084","https://openalex.org/W1541607068","https://openalex.org/W1560057946","https://openalex.org/W1966047467","https://openalex.org/W1983469327","https://openalex.org/W1986353267","https://openalex.org/W2012447921","https://openalex.org/W2017794685","https://openalex.org/W2026082049","https://openalex.org/W2053314097","https://openalex.org/W2055481061","https://openalex.org/W2061817964","https://openalex.org/W2076336573","https://openalex.org/W2090513675","https://openalex.org/W2115760608","https://openalex.org/W2139415633","https://openalex.org/W2146926081","https://openalex.org/W2148605194","https://openalex.org/W2165088725","https://openalex.org/W2323642229","https://openalex.org/W4241628619","https://openalex.org/W4249870635","https://openalex.org/W6684197042"],"related_works":["https://openalex.org/W2443880266","https://openalex.org/W1967787874","https://openalex.org/W4321319478","https://openalex.org/W4297423194","https://openalex.org/W2271098465","https://openalex.org/W2963248375","https://openalex.org/W2377223625","https://openalex.org/W2626888491","https://openalex.org/W2544988382","https://openalex.org/W4249169491"],"abstract_inverted_index":{"An":[0],"algorithm":[1,21],"is":[2,35,46,68],"proposed":[3],"to":[4,9,86],"give":[5],"a":[6,71,76,99,120],"global":[7,79],"approximation":[8,29,94,107],"an":[10],"implicit":[11],"real":[12],"plane":[13],"algebraic":[14],"curve":[15,26,31,34,57,73,83],"with":[16,48,98],"rational":[17,50],"quadratic":[18,51,103,110],"B-splines.":[19],"The":[20,33,105],"consists":[22],"of":[23,93,102,124],"three":[24],"steps:":[25],"segmentation,":[27],"segment":[28,45],"and":[30,65,118],"tracing.":[32],"first":[36],"divided":[37],"into":[38,61],"so-called":[39],"triangle":[40],"convex":[41],"segments.":[42,104],"Then":[43],"each":[44,66],"approximated":[47],"several":[49,62],"Bezier":[52],"curves.":[53],"At":[54],"last,":[55],"the":[56,82,87,125],"segments":[58],"are":[59],"connected":[60],"maximal":[63],"branches":[64],"branch":[67],"represented":[69],"by":[70],"B-spline":[72],"resulting":[74],"in":[75],"C/sup":[77],"1/":[78],"parameterization":[80],"for":[81],"branch.":[84],"Due":[85],"detailed":[88],"geometric":[89,116],"analysis,":[90],"high":[91],"accuracy":[92],"may":[95],"be":[96],"achieved":[97],"small":[100],"number":[101],"final":[106],"based":[108],"on":[109],"spline":[111],"curves":[112],"keeps":[113],"many":[114],"important":[115],"features":[117],"gives":[119],"refined":[121],"topological":[122],"structure":[123],"original":[126],"curve.":[127]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
