{"id":"https://openalex.org/W1986748775","doi":"https://doi.org/10.1145/1542362.1542423","title":"Adaptive isotopic approximation of nonsingular curves","display_name":"Adaptive isotopic approximation of nonsingular curves","publication_year":2009,"publication_date":"2009-06-08","ids":{"openalex":"https://openalex.org/W1986748775","doi":"https://doi.org/10.1145/1542362.1542423","mag":"1986748775"},"language":"en","primary_location":{"id":"doi:10.1145/1542362.1542423","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1542362.1542423","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-fifth annual symposium on Computational geometry","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/A5104361613","display_name":"Long Lin","orcid":null},"institutions":[{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Long Lin","raw_affiliation_strings":["Courant Institute, NYU, New York, NY, USA","Courant Institute, NYU, New York, NY, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Courant Institute, NYU, New York, NY, USA","institution_ids":["https://openalex.org/I36672615"]},{"raw_affiliation_string":"Courant Institute, NYU, New York, NY, USA#TAB#","institution_ids":["https://openalex.org/I36672615"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078989577","display_name":"Chee Yap","orcid":"https://orcid.org/0000-0003-2952-3545"},"institutions":[{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chee K. Yap","raw_affiliation_strings":["Courant Institute, NYU, New York, NY, USA","Courant Institute, NYU, New York, NY, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Courant Institute, NYU, New York, NY, USA","institution_ids":["https://openalex.org/I36672615"]},{"raw_affiliation_string":"Courant Institute, NYU, New York, NY, USA#TAB#","institution_ids":["https://openalex.org/I36672615"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5104361613"],"corresponding_institution_ids":["https://openalex.org/I36672615"],"apc_list":null,"apc_paid":null,"fwci":7.7043,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.98011449,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"351","last_page":"360"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9889000058174133,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.98089998960495,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/subdivision","display_name":"Subdivision","score":0.7234997153282166},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.7166975140571594},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.712713360786438},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.6791965961456299},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5501216650009155},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.5300759077072144},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5187302231788635},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.516709566116333},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42105263471603394},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2108248770236969},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09804853796958923}],"concepts":[{"id":"https://openalex.org/C143392562","wikidata":"https://www.wikidata.org/wiki/Q449111","display_name":"Subdivision","level":2,"score":0.7234997153282166},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7166975140571594},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.712713360786438},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.6791965961456299},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5501216650009155},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.5300759077072144},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5187302231788635},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.516709566116333},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42105263471603394},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2108248770236969},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09804853796958923},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1542362.1542423","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1542362.1542423","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-fifth annual symposium on Computational geometry","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":38,"referenced_works":["https://openalex.org/W38614314","https://openalex.org/W170497285","https://openalex.org/W203551860","https://openalex.org/W578994982","https://openalex.org/W1501243125","https://openalex.org/W1511166374","https://openalex.org/W1574151794","https://openalex.org/W1595559231","https://openalex.org/W1604917823","https://openalex.org/W1964839258","https://openalex.org/W1972064980","https://openalex.org/W1983469327","https://openalex.org/W2021369132","https://openalex.org/W2025941018","https://openalex.org/W2042650700","https://openalex.org/W2048184489","https://openalex.org/W2054255883","https://openalex.org/W2058634350","https://openalex.org/W2074068518","https://openalex.org/W2080681806","https://openalex.org/W2082910094","https://openalex.org/W2104167753","https://openalex.org/W2117337629","https://openalex.org/W2120694921","https://openalex.org/W2132710642","https://openalex.org/W2139230981","https://openalex.org/W2140258961","https://openalex.org/W2162082792","https://openalex.org/W2164167093","https://openalex.org/W2169964384","https://openalex.org/W2185434502","https://openalex.org/W2229412420","https://openalex.org/W2489873395","https://openalex.org/W2609774945","https://openalex.org/W3041834803","https://openalex.org/W4233857083","https://openalex.org/W4237889386","https://openalex.org/W4249516290"],"related_works":["https://openalex.org/W2384806462","https://openalex.org/W4389950792","https://openalex.org/W2375549870","https://openalex.org/W4376632515","https://openalex.org/W2140072033","https://openalex.org/W2163269603","https://openalex.org/W4205312897","https://openalex.org/W1106115901","https://openalex.org/W2921326696","https://openalex.org/W2964287305"],"abstract_inverted_index":{"We":[0,32,63,137],"consider":[1],"domain":[2],"subdivision":[3,77],"algorithms":[4,19,148],"for":[5,52],"computing":[6],"isotopic":[7],"approximations":[8],"of":[9,41,126],"nonsingular":[10],"curves":[11],"represented":[12],"implicitly":[13],"by":[14],"an":[15],"equation":[16],"f(X,Y)=0.":[17],"Two":[18],"in":[20,68,119],"this":[21],"area":[22],"are":[23],"from":[24],"Snyder":[25],"(1992)":[26],"and":[27,54,71,101,122,159],"Plantinga":[28,56,156],"&":[29,57,157],"Vegter":[30,58],"(2004).":[31],"introduce":[33],"a":[34],"new":[35],"algorithm":[36,67,109,130],"that":[37,146],"combines":[38],"the":[39,49,91,114,120,124],"advantages":[40],"these":[42],"two":[43,69],"algorithms:":[44],"like":[45,55],"Snyder,":[46],"we":[47,59,75,89],"use":[48],"parametrizability":[50],"criterion":[51],"subdivision,":[53],"exploit":[60],"non-local":[61],"isotopy.":[62],"further":[64],"extend":[65,90],"our":[66,147],"important":[70],"practical":[72],"directions:":[73],"first,":[74],"allow":[76],"cells":[78],"to":[79,94,134],"be":[80,95,105,150],"rectangles":[81],"with":[82,98],"arbitrary":[83,99],"but":[84],"bounded":[85],"aspect":[86],"ratios.":[87],"Second,":[88],"input":[92],"domains":[93],"regions":[96],"R0":[97,127],"geometry":[100],"which":[102],"might":[103],"not":[104],"simply":[106],"connected.":[107],"Our":[108,129],"halts":[110],"as":[111,113],"long":[112],"curve":[115],"has":[116],"no":[117],"singularities":[118],"region,":[121],"intersects":[123],"boundary":[125],"transversally.":[128],"is":[131],"also":[132],"easy":[133],"implement":[135],"exactly.":[136],"report":[138],"on":[139],"very":[140],"encouraging":[141],"preliminary":[142],"experimental":[143],"results,":[144],"showing":[145],"can":[149],"much":[151],"more":[152],"efficient":[153],"than":[154],"both":[155],"Vegter's":[158],"Snyder's":[160],"algorithms.":[161]},"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":10}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}