{"id":"https://openalex.org/W2517636276","doi":"https://doi.org/10.1111/cgf.12962","title":"Complex Transfinite Barycentric Mappings with Similarity Kernels","display_name":"Complex Transfinite Barycentric Mappings with Similarity Kernels","publication_year":2016,"publication_date":"2016-08-01","ids":{"openalex":"https://openalex.org/W2517636276","doi":"https://doi.org/10.1111/cgf.12962","mag":"2517636276"},"language":"en","primary_location":{"id":"doi:10.1111/cgf.12962","is_oa":false,"landing_page_url":"https://doi.org/10.1111/cgf.12962","pdf_url":null,"source":{"id":"https://openalex.org/S67831204","display_name":"Computer Graphics Forum","issn_l":"0167-7055","issn":["0167-7055","1467-8659"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer Graphics Forum","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/A5100694759","display_name":"Renjie Chen","orcid":"https://orcid.org/0000-0002-4353-6134"},"institutions":[{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Renjie Chen","raw_affiliation_strings":["Max Planck Institute for Informatics Saarbr\u00fccken Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Max Planck Institute for Informatics Saarbr\u00fccken Germany","institution_ids":["https://openalex.org/I4210109712"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075360338","display_name":"Craig Gotsman","orcid":"https://orcid.org/0000-0001-8579-3588"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]},{"id":"https://openalex.org/I4210149000","display_name":"Jacobs Institute","ror":"https://ror.org/04c00sd86","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I4210149000"]},{"id":"https://openalex.org/I4405261073","display_name":"Cornell Tech","ror":"https://ror.org/04qscbg47","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295","https://openalex.org/I4405261073"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Craig Gotsman","raw_affiliation_strings":["Jacobs Technion\u2010Cornell Institute Cornell Tech New York USA","Jacobs Technion-Cornell Institute, Cornell Tech, New York, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Jacobs Technion\u2010Cornell Institute Cornell Tech New York USA","institution_ids":["https://openalex.org/I205783295","https://openalex.org/I4210149000","https://openalex.org/I4405261073"]},{"raw_affiliation_string":"Jacobs Technion-Cornell Institute, Cornell Tech, New York, USA","institution_ids":["https://openalex.org/I205783295","https://openalex.org/I4210149000","https://openalex.org/I4405261073"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3710,"currency":"USD","value_usd":3710},"apc_paid":null,"fwci":1.7707,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.87564767,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"35","issue":"5","first_page":"41","last_page":"53"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9998000264167786,"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":0.9990000128746033,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9987999796867371,"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/barycentric-coordinate-system","display_name":"Barycentric coordinate system","score":0.9732152223587036},{"id":"https://openalex.org/keywords/transfinite-number","display_name":"Transfinite number","score":0.8737375736236572},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6867209672927856},{"id":"https://openalex.org/keywords/similarity","display_name":"Similarity (geometry)","score":0.5320540070533752},{"id":"https://openalex.org/keywords/injective-function","display_name":"Injective function","score":0.4643341302871704},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.27162569761276245},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.22807154059410095},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20379462838172913},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15137359499931335},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.07210177183151245}],"concepts":[{"id":"https://openalex.org/C128356825","wikidata":"https://www.wikidata.org/wiki/Q738422","display_name":"Barycentric coordinate system","level":2,"score":0.9732152223587036},{"id":"https://openalex.org/C147358099","wikidata":"https://www.wikidata.org/wiki/Q1069891","display_name":"Transfinite number","level":2,"score":0.8737375736236572},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6867209672927856},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.5320540070533752},{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.4643341302871704},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.27162569761276245},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.22807154059410095},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20379462838172913},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15137359499931335},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.07210177183151245}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1111/cgf.12962","is_oa":false,"landing_page_url":"https://doi.org/10.1111/cgf.12962","pdf_url":null,"source":{"id":"https://openalex.org/S67831204","display_name":"Computer Graphics Forum","issn_l":"0167-7055","issn":["0167-7055","1467-8659"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer Graphics Forum","raw_type":"journal-article"},{"id":"pmh:oai:pure.mpg.de:item_2339858","is_oa":false,"landing_page_url":"http://hdl.handle.net/11858/00-001M-0000-002B-430B-5","pdf_url":null,"source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Computer Graphics Forum","raw_type":"info:eu-repo/semantics/article"}],"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/W280536263","https://openalex.org/W1558580869","https://openalex.org/W1965851707","https://openalex.org/W1974956622","https://openalex.org/W1977148430","https://openalex.org/W2009940960","https://openalex.org/W2021167140","https://openalex.org/W2031392866","https://openalex.org/W2039508899","https://openalex.org/W2079209697","https://openalex.org/W2119204856","https://openalex.org/W2123615816","https://openalex.org/W2129412583","https://openalex.org/W2135785391","https://openalex.org/W2137742453","https://openalex.org/W2138784103","https://openalex.org/W2293537096","https://openalex.org/W2328294984","https://openalex.org/W2346992053","https://openalex.org/W4233370650","https://openalex.org/W4298234423","https://openalex.org/W6696989663"],"related_works":["https://openalex.org/W2089968568","https://openalex.org/W2048273249","https://openalex.org/W2950239705","https://openalex.org/W2261099788","https://openalex.org/W2498880115","https://openalex.org/W4287864648","https://openalex.org/W3007397602","https://openalex.org/W2031392866","https://openalex.org/W1558580869","https://openalex.org/W2517636276"],"abstract_inverted_index":{"Abstract":[0],"Transfinite":[1],"barycentric":[2,10,85,107,132,151],"kernels":[3,39,124],"are":[4,13],"the":[5,27,32,51,62,83,89,100,104],"continuous":[6],"version":[7],"of":[8,18,34,50,61,103],"traditional":[9],"coordinates":[11,108],"and":[12,53,72,97,112],"used":[14,127],"to":[15,67,75,82,128],"define":[16,76],"interpolants":[17],"values":[19],"given":[20],"on":[21],"a":[22,35,79],"smooth":[23],"planar":[24,36,70,150],"contour.":[25],"When":[26],"data":[28],"is":[29,143],"two\u2010dimensional,":[30],"i.e.":[31],"boundary":[33],"map,":[37],"these":[38,69],"may":[40,125],"be":[41,126],"conveniently":[42],"expressed":[43],"using":[44,134],"complex":[45],"number":[46],"algebra,":[47],"simplifying":[48],"much":[49],"notation":[52],"results.":[54],"In":[55],"this":[56],"paper":[57],"we":[58],"develop":[59,88],"some":[60],"basic":[63],"complex\u2010valued":[64],"algebra":[65],"needed":[66],"describe":[68],"maps,":[71],"use":[73],"it":[74],"similarity":[77,92,117,123],"kernels,":[78,93],"natural":[80],"alternative":[81],"usual":[84],"kernels.":[86,118],"We":[87,119],"theory":[90],"behind":[91],"explore":[94],"their":[95],"properties,":[96],"show":[98,121],"that":[99],"transfinite":[101,131],"versions":[102],"popular":[105],"three\u2010point":[106],"(Laplace,":[109],"mean":[110],"value":[111],"Wachspress)":[113],"have":[114],"surprisingly":[115],"simple":[116],"furthermore":[120],"how":[122],"invert":[129],"injective":[130],"mappings":[133],"an":[135],"iterative":[136],"algorithm":[137],"which":[138],"converges":[139],"quite":[140],"rapidly.":[141],"This":[142],"useful":[144],"for":[145],"rendering":[146],"images":[147],"deformed":[148],"by":[149],"mappings.":[152]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
