{"id":"https://openalex.org/W2017362127","doi":"https://doi.org/10.1137/110845860","title":"Conformal Mapping with as Uniform as Possible Conformal Factor","display_name":"Conformal Mapping with as Uniform as Possible Conformal Factor","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2017362127","doi":"https://doi.org/10.1137/110845860","mag":"2017362127"},"language":"en","primary_location":{"id":"doi:10.1137/110845860","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110845860","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"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 Imaging Sciences","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/A5029796008","display_name":"Yonathan Aflalo","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yonathan Aflalo","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091366774","display_name":"Ron Kimmel","orcid":"https://orcid.org/0000-0002-3180-7961"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ron Kimmel","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5032678480","display_name":"Michael Zibulevsky","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael Zibulevsky","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5029796008"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.171,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.90807164,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"6","issue":"1","first_page":"78","last_page":"101"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9995999932289124,"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":0.9995999932289124,"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9993000030517578,"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":0.9855999946594238,"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/conformal-map","display_name":"Conformal map","score":0.7986684441566467},{"id":"https://openalex.org/keywords/gaussian-curvature","display_name":"Gaussian curvature","score":0.6112868189811707},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6094290614128113},{"id":"https://openalex.org/keywords/conformal-geometry","display_name":"Conformal geometry","score":0.5551007986068726},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.5195969939231873},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4913302958011627},{"id":"https://openalex.org/keywords/constant-curvature","display_name":"Constant curvature","score":0.489555686712265},{"id":"https://openalex.org/keywords/eikonal-equation","display_name":"Eikonal equation","score":0.47002577781677246},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.46510180830955505},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.46258944272994995},{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.44797059893608093},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.4297429919242859},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.41498661041259766},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.368112176656723},{"id":"https://openalex.org/keywords/conformal-symmetry","display_name":"Conformal symmetry","score":0.2456437349319458}],"concepts":[{"id":"https://openalex.org/C98214594","wikidata":"https://www.wikidata.org/wiki/Q850275","display_name":"Conformal map","level":2,"score":0.7986684441566467},{"id":"https://openalex.org/C16140857","wikidata":"https://www.wikidata.org/wiki/Q945953","display_name":"Gaussian curvature","level":3,"score":0.6112868189811707},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6094290614128113},{"id":"https://openalex.org/C125669323","wikidata":"https://www.wikidata.org/wiki/Q513175","display_name":"Conformal geometry","level":4,"score":0.5551007986068726},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.5195969939231873},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4913302958011627},{"id":"https://openalex.org/C2779668893","wikidata":"https://www.wikidata.org/wiki/Q2250422","display_name":"Constant curvature","level":3,"score":0.489555686712265},{"id":"https://openalex.org/C40375134","wikidata":"https://www.wikidata.org/wiki/Q1303846","display_name":"Eikonal equation","level":2,"score":0.47002577781677246},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.46510180830955505},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.46258944272994995},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.44797059893608093},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.4297429919242859},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.41498661041259766},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.368112176656723},{"id":"https://openalex.org/C173848574","wikidata":"https://www.wikidata.org/wiki/Q3507963","display_name":"Conformal symmetry","level":3,"score":0.2456437349319458},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/110845860","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110845860","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"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 Imaging Sciences","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.278.5375","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.278.5375","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.technion.ac.il/%7Eron/PAPERS/Journal/AflaloKimmelZibulevskySIAM2013.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.303.6154","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.303.6154","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.technion.ac.il/%7Eron/PAPERS/Journal/AflKimZibSIAM2012.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.49000000953674316,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1501247794","https://openalex.org/W1535896976","https://openalex.org/W1590776313","https://openalex.org/W1969617809","https://openalex.org/W1984697939","https://openalex.org/W1996204208","https://openalex.org/W1998936196","https://openalex.org/W1999244633","https://openalex.org/W1999690352","https://openalex.org/W2001473319","https://openalex.org/W2012872284","https://openalex.org/W2054113582","https://openalex.org/W2057396117","https://openalex.org/W2074551095","https://openalex.org/W2105106232","https://openalex.org/W2115118342","https://openalex.org/W2117913575","https://openalex.org/W2127033124","https://openalex.org/W2141409037","https://openalex.org/W2161253909","https://openalex.org/W2537228944","https://openalex.org/W2561843528"],"related_works":["https://openalex.org/W4244326923","https://openalex.org/W3208990458","https://openalex.org/W4380136192","https://openalex.org/W4379089548","https://openalex.org/W4298148578","https://openalex.org/W2504596514","https://openalex.org/W207565189","https://openalex.org/W2964473916","https://openalex.org/W3100085997","https://openalex.org/W2017362127"],"abstract_inverted_index":{"According":[0],"to":[1,36,123,134],"the":[2,23,51,73,81,92,97,106,110,113,137,147,165,175,192,215],"uniformization":[3],"theorem,":[4],"any":[5],"surface":[6,59,114],"can":[7,60,84,116,210],"be":[8,34,61,86,117,211],"conformally":[9],"mapped":[10,62],"into":[11,63,220],"a":[12,15,29,41,57,69,180,187,195,204,207,221],"domain":[13,44,93,209],"of":[14,53,91,146],"constant":[16],"Gaussian":[17,47],"curvature.":[18,48],"The":[19,103],"conformal":[20,74,107,138,148],"factor":[21,108,139,149],"indicates":[22],"local":[24],"scaling":[25],"introduced":[26],"by":[27,72,88,190,213],"such":[28,163],"mapping.":[30],"This":[31],"process":[32],"could":[33],"used":[35],"compute":[37],"geometric":[38],"quantities":[39],"in":[40,68,121,174],"simplified":[42],"flat":[43,197,223],"with":[45,226],"zero":[46],"For":[49],"example,":[50,96],"computation":[52],"geodesic":[54,184],"distances":[55,185],"on":[56,80,109,186,194,206],"curved":[58,208],"solving":[64],"an":[65,77],"eikonal":[66,78],"equation":[67,79],"plane":[70,83,111],"weighted":[71,82,196,222],"factor.":[75],"Solving":[76],"then":[85],"done":[87],"regular":[89],"sampling":[90],"using,":[94],"for":[95,182,229],"celebrated":[98],"fast":[99],"marching":[100],"method":[101,181],"(FMM).":[102],"connection":[104],"between":[105],"and":[112,150],"geometry":[115],"justified":[118],"analytically.":[119],"Still,":[120],"order":[122],"construct":[124],"consistent":[125,230],"numerical":[126,166],"solvers":[127],"that":[128,136,154,161],"exploit":[129],"this":[130],"relation,":[131],"one":[132],"needs":[133],"prove":[135],"is":[140,159,200],"bounded.":[141],"We":[142],"provide":[143],"theoretical":[144],"bounds":[145],"introduce":[151,179],"optimization":[152],"formulations":[153],"control":[155],"its":[156],"behavior.":[157],"It":[158,199],"demonstrated":[160],"without":[162],"restrictions":[164],"results":[167],"are":[168],"unboundedly":[169],"inaccurate.":[170],"Putting":[171],"all":[172],"ingredients":[173],"right":[176],"order,":[177],"we":[178],"computing":[183],"two-dimensional":[188],"manifold":[189],"using":[191],"FMM":[193],"domain.":[198],"also":[201],"shown":[202],"how":[203],"metric":[205,217],"reconstructed":[212],"reformulating":[214],"nonflat":[216],"restoration":[218],"problem":[219],"domain,":[224],"again,":[225],"bounded":[227],"weights":[228],"results.":[231]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}