{"id":"https://openalex.org/W2075656565","doi":"https://doi.org/10.1145/1037957.1037959","title":"On <i>C</i> <sup>2</sup> triangle/quad subdivision","display_name":"On <i>C</i> <sup>2</sup> triangle/quad subdivision","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2075656565","doi":"https://doi.org/10.1145/1037957.1037959","mag":"2075656565"},"language":"en","primary_location":{"id":"doi:10.1145/1037957.1037959","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1037957.1037959","pdf_url":null,"source":{"id":"https://openalex.org/S185367456","display_name":"ACM Transactions on Graphics","issn_l":"0730-0301","issn":["0730-0301","1557-7368"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Graphics","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/A5037680267","display_name":"Scott Schaefer","orcid":"https://orcid.org/0000-0002-0988-1452"},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Scott Schaefer","raw_affiliation_strings":["Rice University, Houston, TX","Rice University (Houston, TX)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Rice University, Houston, TX","institution_ids":["https://openalex.org/I74775410"]},{"raw_affiliation_string":"Rice University (Houston, TX)","institution_ids":["https://openalex.org/I74775410"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113597103","display_name":"Joe Warren","orcid":null},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Joe Warren","raw_affiliation_strings":["Rice University, Houston, TX","Rice University (Houston, TX)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Rice University, Houston, TX","institution_ids":["https://openalex.org/I74775410"]},{"raw_affiliation_string":"Rice University (Houston, TX)","institution_ids":["https://openalex.org/I74775410"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.9487,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.96357358,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"24","issue":"1","first_page":"28","last_page":"36"},"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":0.991100013256073,"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":0.9819999933242798,"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/combinatorics","display_name":"Combinatorics","score":0.5750203728675842},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.5457600355148315},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5001811981201172},{"id":"https://openalex.org/keywords/subdivision","display_name":"Subdivision","score":0.48358529806137085},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.4248999059200287},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4160909354686737},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.33560872077941895},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3201639950275421},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15290546417236328}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5750203728675842},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.5457600355148315},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5001811981201172},{"id":"https://openalex.org/C143392562","wikidata":"https://www.wikidata.org/wiki/Q449111","display_name":"Subdivision","level":2,"score":0.48358529806137085},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.4248999059200287},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4160909354686737},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.33560872077941895},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3201639950275421},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15290546417236328},{"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:10.1145/1037957.1037959","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1037957.1037959","pdf_url":null,"source":{"id":"https://openalex.org/S185367456","display_name":"ACM Transactions on Graphics","issn_l":"0730-0301","issn":["0730-0301","1557-7368"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Graphics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W126840538","https://openalex.org/W1528814089","https://openalex.org/W2001562259","https://openalex.org/W2017068862","https://openalex.org/W2018713086","https://openalex.org/W2032325716","https://openalex.org/W2118640547","https://openalex.org/W2152484195","https://openalex.org/W2155457888","https://openalex.org/W2223141336","https://openalex.org/W6682346696"],"related_works":["https://openalex.org/W2380333825","https://openalex.org/W2363537559","https://openalex.org/W2766590513","https://openalex.org/W2161069075","https://openalex.org/W2365894372","https://openalex.org/W2625321122","https://openalex.org/W2227899268","https://openalex.org/W2154004471","https://openalex.org/W2140517303","https://openalex.org/W3190988189"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"we":[3,24,37,70],"present":[4],"a":[5,62,73],"subdivision":[6],"scheme":[7,33,63,88],"for":[8,17],"mixed":[9],"triangle/quad":[10,54,94],"meshes":[11],"that":[12,23,36],"is":[13,89],"&lt;i&gt;C&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt;":[14,91],"everywhere":[15],"except":[16,35],"isolated,":[18],"extraordinary":[19],"points.":[20],"The":[21],"rules":[22],"describe":[25],"are":[26],"the":[27,49,52,93],"same":[28],"as":[29],"Stam":[30],"and":[31,60,78],"Loop's":[32],"[2003]":[34,80],"perform":[38],"an":[39],"unzipping":[40],"pass":[41],"prior":[42],"to":[43,58,85],"subdivision.":[44],"This":[45],"simple":[46],"modification":[47],"improves":[48],"smoothness":[50],"along":[51,92],"ordinary":[53],"boundary":[55],"from":[56],"&lt;i&gt;C&lt;/i&gt;&lt;sup&gt;1&lt;/sup&gt;":[57],"&lt;i&gt;C&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt;,":[59],"creates":[61],"capable":[64],"of":[65],"subdividing":[66],"arbitrary":[67],"meshes.":[68],"Finally,":[69],"end":[71],"with":[72],"proof":[74],"based":[75],"on":[76],"Levin":[77],"Levin's":[79],"joint":[81],"spectral":[82],"radius":[83],"calculation":[84],"show":[86],"our":[87],"indeed":[90],"boundary.":[95]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}