{"id":"https://openalex.org/W2154510795","doi":"https://doi.org/10.1109/sibgra.2002.1167139","title":"Approximating parametric curves with strip trees using affine arithmetic","display_name":"Approximating parametric curves with strip trees using affine arithmetic","publication_year":2003,"publication_date":"2003-06-26","ids":{"openalex":"https://openalex.org/W2154510795","doi":"https://doi.org/10.1109/sibgra.2002.1167139","mag":"2154510795"},"language":"en","primary_location":{"id":"doi:10.1109/sibgra.2002.1167139","is_oa":false,"landing_page_url":"https://doi.org/10.1109/sibgra.2002.1167139","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings. XV Brazilian Symposium on Computer Graphics and Image Processing","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/A5005149231","display_name":"Luiz Henrique de Figueiredo","orcid":"https://orcid.org/0000-0001-5683-693X"},"institutions":[{"id":"https://openalex.org/I141883831","display_name":"Instituto Nacional de Matem\u00e1tica Pura e Aplicada","ror":"https://ror.org/028caqe42","country_code":"BR","type":"facility","lineage":["https://openalex.org/I141883831","https://openalex.org/I4210151455"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"L.H. De Figueiredo","raw_affiliation_strings":["IMPA-Instituto de Matem\u00e1tica Pura e Aplicada, Rio de Janeiro, Brazil"],"affiliations":[{"raw_affiliation_string":"IMPA-Instituto de Matem\u00e1tica Pura e Aplicada, Rio de Janeiro, Brazil","institution_ids":["https://openalex.org/I141883831"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001511641","display_name":"Jorge Stolfi","orcid":"https://orcid.org/0000-0002-3159-4839"},"institutions":[{"id":"https://openalex.org/I181391015","display_name":"Universidade Estadual de Campinas (UNICAMP)","ror":"https://ror.org/04wffgt70","country_code":"BR","type":"education","lineage":["https://openalex.org/I181391015"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"J. Stolfi","raw_affiliation_strings":["Instituo de Computa\u00e7\u00e3o, Universidade Estadual de Campinas (UNICAMP), Sao Paulo, Brazil"],"affiliations":[{"raw_affiliation_string":"Instituo de Computa\u00e7\u00e3o, Universidade Estadual de Campinas (UNICAMP), Sao Paulo, Brazil","institution_ids":["https://openalex.org/I181391015"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015241528","display_name":"Luiz Velho","orcid":"https://orcid.org/0000-0001-5489-4909"},"institutions":[{"id":"https://openalex.org/I141883831","display_name":"Instituto Nacional de Matem\u00e1tica Pura e Aplicada","ror":"https://ror.org/028caqe42","country_code":"BR","type":"facility","lineage":["https://openalex.org/I141883831","https://openalex.org/I4210151455"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"L. Velho","raw_affiliation_strings":["IMPA-Instituto de Matem\u00e1tica Pura e Aplicada, Rio de Janeiro, Brazil"],"affiliations":[{"raw_affiliation_string":"IMPA-Instituto de Matem\u00e1tica Pura e Aplicada, Rio de Janeiro, Brazil","institution_ids":["https://openalex.org/I141883831"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5005149231"],"corresponding_institution_ids":["https://openalex.org/I141883831"],"apc_list":null,"apc_paid":null,"fwci":0.9135,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.77006818,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"163","last_page":"170"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9997000098228455,"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":0.9997000098228455,"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/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9995999932289124,"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9961000084877014,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/affine-arithmetic","display_name":"Affine arithmetic","score":0.9180499911308289},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.8372063040733337},{"id":"https://openalex.org/keywords/bounding-overwatch","display_name":"Bounding overwatch","score":0.7539524435997009},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.7231428027153015},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6039391160011292},{"id":"https://openalex.org/keywords/parametric-equation","display_name":"Parametric equation","score":0.5998148322105408},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4145648181438446},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3597620725631714},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3312310576438904},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32359570264816284},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15964722633361816},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1407049596309662},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.14044511318206787}],"concepts":[{"id":"https://openalex.org/C167315692","wikidata":"https://www.wikidata.org/wiki/Q3622729","display_name":"Affine arithmetic","level":3,"score":0.9180499911308289},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.8372063040733337},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.7539524435997009},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.7231428027153015},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6039391160011292},{"id":"https://openalex.org/C99636146","wikidata":"https://www.wikidata.org/wiki/Q35889","display_name":"Parametric equation","level":2,"score":0.5998148322105408},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4145648181438446},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3597620725631714},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3312310576438904},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32359570264816284},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15964722633361816},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1407049596309662},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.14044511318206787}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/sibgra.2002.1167139","is_oa":false,"landing_page_url":"https://doi.org/10.1109/sibgra.2002.1167139","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings. XV Brazilian Symposium on Computer Graphics and Image Processing","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322749","display_name":"Funda\u00e7\u00e3o Carlos Chagas Filho de Amparo \u00e0 Pesquisa do Estado do Rio de Janeiro","ror":"https://ror.org/03kk0s825"},{"id":"https://openalex.org/F4320322904","display_name":"Financiadora de Estudos e Projetos","ror":"https://ror.org/030w99567"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W115562957","https://openalex.org/W179323378","https://openalex.org/W207485495","https://openalex.org/W1489091441","https://openalex.org/W1523163839","https://openalex.org/W1579640453","https://openalex.org/W1597196612","https://openalex.org/W1966495409","https://openalex.org/W1981404401","https://openalex.org/W2020655744","https://openalex.org/W2029331355","https://openalex.org/W2053913299","https://openalex.org/W2055754120","https://openalex.org/W2055945485","https://openalex.org/W2069323107","https://openalex.org/W2074429597","https://openalex.org/W2076005991","https://openalex.org/W2104103251","https://openalex.org/W2129251118","https://openalex.org/W2134029906","https://openalex.org/W2138126554","https://openalex.org/W2153962084","https://openalex.org/W2155166664","https://openalex.org/W2237767100","https://openalex.org/W2273879208","https://openalex.org/W4206570602","https://openalex.org/W4238692231","https://openalex.org/W4242724835","https://openalex.org/W6607236968","https://openalex.org/W6608340826","https://openalex.org/W6629196680"],"related_works":["https://openalex.org/W1970147231","https://openalex.org/W3129089851","https://openalex.org/W2147412345","https://openalex.org/W952765504","https://openalex.org/W1531645310","https://openalex.org/W2181927644","https://openalex.org/W3174895231","https://openalex.org/W2756505297","https://openalex.org/W3186580698","https://openalex.org/W2187273623"],"abstract_inverted_index":{"We":[0],"show":[1,41],"how":[2,42],"to":[3,7,43],"use":[4],"affine":[5,35],"arithmetic":[6],"represent":[8],"a":[9,13],"parametric":[10,49],"curve":[11,24],"with":[12],"strip":[14],"tree.":[15],"The":[16],"required":[17],"bounding":[18],"rectangles":[19],"for":[20,48],"pieces":[21],"of":[22],"the":[23,29],"are":[25],"computed":[26],"by":[27,34],"exploiting":[28],"linear":[30],"correlation":[31],"information":[32],"given":[33],"arithmetic.":[36],"As":[37],"an":[38],"application,":[39],"we":[40],"compute":[44],"approximate":[45],"distance":[46],"fields":[47],"curves.":[50]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}