{"id":"https://openalex.org/W2069106519","doi":"https://doi.org/10.1137/s0036142999363863","title":"Geometric Computation of Curvature Driven Plane Curve Evolutions","display_name":"Geometric Computation of Curvature Driven Plane Curve Evolutions","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2069106519","doi":"https://doi.org/10.1137/s0036142999363863","mag":"2069106519"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142999363863","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142999363863","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-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/A5061972665","display_name":"Feifan Cao","orcid":"https://orcid.org/0009-0002-4806-5236"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Fr\u00e9d\u00e9ric Cao","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5090845509","display_name":"Lionel Moisan","orcid":"https://orcid.org/0000-0001-6019-2698"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lionel Moisan","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5061972665"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5921,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.69712526,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"39","issue":"2","first_page":"624","last_page":"646"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.14560000598430634,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.14560000598430634,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.13920000195503235,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.07129999995231628,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8752784729003906},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.8004591464996338},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.6627178192138672},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.6264962553977966},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5428057909011841},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.48558276891708374},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4766426980495453},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4721873998641968},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.458121657371521},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.443676233291626},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.32256555557250977},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1450413167476654}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8752784729003906},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.8004591464996338},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.6627178192138672},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6264962553977966},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5428057909011841},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.48558276891708374},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4766426980495453},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4721873998641968},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.458121657371521},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.443676233291626},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.32256555557250977},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1450413167476654},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s0036142999363863","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142999363863","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.27.6985","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.27.6985","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cmla.ens-cachan.fr/Utilisateurs/cao/./curves.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.28.810","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.28.810","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cmla.ens-cachan.fr/Cmla/Publications/1999/CMLA9929.ps.gz","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1498500832","https://openalex.org/W1553761880","https://openalex.org/W1638384496","https://openalex.org/W1973134742","https://openalex.org/W1973369053","https://openalex.org/W1978539725","https://openalex.org/W1983633249","https://openalex.org/W1991113069","https://openalex.org/W2005100432","https://openalex.org/W2031772988","https://openalex.org/W2032316144","https://openalex.org/W2054967428","https://openalex.org/W2062791543","https://openalex.org/W2063703787","https://openalex.org/W2065164181","https://openalex.org/W2072084230","https://openalex.org/W2073632408","https://openalex.org/W2082052570","https://openalex.org/W2109973988","https://openalex.org/W2147963686","https://openalex.org/W2163844249","https://openalex.org/W4246410024"],"related_works":["https://openalex.org/W3185235544","https://openalex.org/W2911623553","https://openalex.org/W4297791327","https://openalex.org/W2897842840","https://openalex.org/W2397777611","https://openalex.org/W1502031429","https://openalex.org/W2417585376","https://openalex.org/W1994157709","https://openalex.org/W4294336468","https://openalex.org/W2010200921"],"abstract_inverted_index":{"We":[0,96],"present":[1],"a":[2,11,25,79,105],"new":[3],"numerical":[4,94,112],"scheme":[5,52,73,103],"for":[6,48],"planar":[7],"curve":[8,80],"evolution":[9],"with":[10,37],"normal":[12],"velocity":[13],"equal":[14,43],"to":[15,44],"$F(\\kappa)$,":[16],"where":[17],"$\\kappa$":[18],"is":[19,24,35,53,69,74],"the":[20,72],"curvature":[21],"and":[22,31,56,71,99,116],"F":[23],"nondecreasing":[26],"function":[27],"such":[28],"that":[29],"F(0)=0":[30],"either":[32],"$x\\mapsto":[33],"F(x^3)$":[34],"Lipschitz":[36,38],"constant":[39],"less":[40],"than":[41],"or":[42,46],"1":[45],"$F(x)=x^\\gamma$":[47],"$\\gamma\\geq":[49],"1/3$.":[50],"The":[51],"completely":[54],"geometrical":[55],"avoids":[57],"some":[58,111],"drawbacks":[59],"of":[60,101],"finite":[61],"difference":[62],"schemes.":[63],"In":[64],"particular,":[65],"no":[66],"special":[67],"parameterization":[68],"needed":[70],"monotone":[75],"(that":[76],"is,":[77],"if":[78],"initially":[81],"surrounds":[82],"another":[83],"one,":[84],"then":[85],"this":[86,102],"remains":[87],"true":[88],"during":[89],"their":[90],"evolution),":[91],"which":[92],"guarantees":[93],"stability.":[95],"prove":[97],"consistency":[98],"convergence":[100],"in":[104],"weak":[106],"sense.":[107],"Finally,":[108],"we":[109],"display":[110],"experiments":[113],"on":[114],"synthetic":[115],"real":[117],"data.":[118]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}