{"id":"https://openalex.org/W3006019036","doi":"https://doi.org/10.1109/tvcg.2020.2972877","title":"RIAS: Repeated Invertible Averaging for Surface Multiresolution of Arbitrary Degree","display_name":"RIAS: Repeated Invertible Averaging for Surface Multiresolution of Arbitrary Degree","publication_year":2020,"publication_date":"2020-02-11","ids":{"openalex":"https://openalex.org/W3006019036","doi":"https://doi.org/10.1109/tvcg.2020.2972877","mag":"3006019036","pmid":"https://pubmed.ncbi.nlm.nih.gov/32070958"},"language":"en","primary_location":{"id":"doi:10.1109/tvcg.2020.2972877","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvcg.2020.2972877","pdf_url":null,"source":{"id":"https://openalex.org/S84775595","display_name":"IEEE Transactions on Visualization and Computer Graphics","issn_l":"1077-2626","issn":["1077-2626","1941-0506","2160-9306"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Visualization and Computer Graphics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5074704357","display_name":"Troy Alderson","orcid":"https://orcid.org/0000-0001-5528-8652"},"institutions":[{"id":"https://openalex.org/I168635309","display_name":"University of Calgary","ror":"https://ror.org/03yjb2x39","country_code":"CA","type":"education","lineage":["https://openalex.org/I168635309"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Troy Alderson","raw_affiliation_strings":["University of Calgary in Calgary, Calgary, AB, Canada"],"affiliations":[{"raw_affiliation_string":"University of Calgary in Calgary, Calgary, AB, Canada","institution_ids":["https://openalex.org/I168635309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021862056","display_name":"Ali Mahdavi\u2010Amiri","orcid":"https://orcid.org/0000-0002-4693-3565"},"institutions":[{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Ali Mahdavi-Amiri","raw_affiliation_strings":["Simon Fraser University in Burnaby, Burnaby, BC, Canada"],"affiliations":[{"raw_affiliation_string":"Simon Fraser University in Burnaby, Burnaby, BC, Canada","institution_ids":["https://openalex.org/I18014758"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074643777","display_name":"Faramarz Samavati","orcid":"https://orcid.org/0000-0001-9440-7562"},"institutions":[{"id":"https://openalex.org/I168635309","display_name":"University of Calgary","ror":"https://ror.org/03yjb2x39","country_code":"CA","type":"education","lineage":["https://openalex.org/I168635309"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Faramarz Samavati","raw_affiliation_strings":["University of Calgary in Calgary, Calgary, AB, Canada"],"affiliations":[{"raw_affiliation_string":"University of Calgary in Calgary, Calgary, AB, Canada","institution_ids":["https://openalex.org/I168635309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5074704357"],"corresponding_institution_ids":["https://openalex.org/I168635309"],"apc_list":null,"apc_paid":null,"fwci":0.3588,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.52750565,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"27","issue":"8","first_page":"3546","last_page":"3557"},"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":0.9621999859809875,"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/subdivision","display_name":"Subdivision","score":0.9044673442840576},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5775228142738342},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5660691261291504},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.5473185181617737},{"id":"https://openalex.org/keywords/subdivision-surface","display_name":"Subdivision surface","score":0.5306880474090576},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.47958555817604065},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4283078908920288},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41017335653305054},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.38750290870666504},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.357275128364563},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3454759120941162},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3278656303882599},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3107350468635559},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.20586267113685608},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10225623846054077}],"concepts":[{"id":"https://openalex.org/C143392562","wikidata":"https://www.wikidata.org/wiki/Q449111","display_name":"Subdivision","level":2,"score":0.9044673442840576},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5775228142738342},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5660691261291504},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.5473185181617737},{"id":"https://openalex.org/C199686383","wikidata":"https://www.wikidata.org/wiki/Q1529124","display_name":"Subdivision surface","level":3,"score":0.5306880474090576},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.47958555817604065},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4283078908920288},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41017335653305054},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38750290870666504},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.357275128364563},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3454759120941162},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3278656303882599},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3107350468635559},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20586267113685608},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10225623846054077},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"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":4,"locations":[{"id":"doi:10.1109/tvcg.2020.2972877","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvcg.2020.2972877","pdf_url":null,"source":{"id":"https://openalex.org/S84775595","display_name":"IEEE Transactions on Visualization and Computer Graphics","issn_l":"1077-2626","issn":["1077-2626","1941-0506","2160-9306"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Visualization and Computer Graphics","raw_type":"journal-article"},{"id":"pmid:32070958","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/32070958","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on visualization and computer graphics","raw_type":null},{"id":"pmh:doi:10.11575/prism/46107","is_oa":false,"landing_page_url":"http://doi.org/10.1109/TVCG.2020.2972877","pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"journal article"},{"id":"pmh:oai:prism.ucalgary.ca:1880/112705","is_oa":false,"landing_page_url":"http://hdl.handle.net/1880/112705","pdf_url":null,"source":{"id":"https://openalex.org/S4306402212","display_name":"PRISM (University of Calgary)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I168635309","host_organization_name":"University of Calgary","host_organization_lineage":["https://openalex.org/I168635309"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","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":31,"referenced_works":["https://openalex.org/W126840538","https://openalex.org/W129480699","https://openalex.org/W1494985239","https://openalex.org/W1528814089","https://openalex.org/W1541168874","https://openalex.org/W1985812168","https://openalex.org/W2001562259","https://openalex.org/W2003173111","https://openalex.org/W2017068862","https://openalex.org/W2019453016","https://openalex.org/W2030232224","https://openalex.org/W2032325716","https://openalex.org/W2039153495","https://openalex.org/W2062848417","https://openalex.org/W2077991339","https://openalex.org/W2091620062","https://openalex.org/W2125481678","https://openalex.org/W2127372291","https://openalex.org/W2127492694","https://openalex.org/W2138483787","https://openalex.org/W2154004471","https://openalex.org/W2165152889","https://openalex.org/W2336991609","https://openalex.org/W2808621144","https://openalex.org/W2948909614","https://openalex.org/W3002473372","https://openalex.org/W4250285865","https://openalex.org/W6605203544","https://openalex.org/W6605292075","https://openalex.org/W6682434965","https://openalex.org/W6773171097"],"related_works":["https://openalex.org/W2387884585","https://openalex.org/W2365894372","https://openalex.org/W646807382","https://openalex.org/W2078248985","https://openalex.org/W2377450293","https://openalex.org/W2370429828","https://openalex.org/W2415051010","https://openalex.org/W3083116488","https://openalex.org/W2143665433","https://openalex.org/W2296482608"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"we":[3],"introduce":[4],"two":[5],"local":[6,11],"surface":[7,21],"averaging":[8,45],"operators":[9,46],"with":[10],"inverses":[12],"and":[13,24,37,54,84,95],"use":[14],"them":[15],"to":[16,31,58,62,72,86],"devise":[17],"a":[18,52],"method":[19],"for":[20],"multiresolution":[22,61],"(subdivision":[23],"reverse":[25,94],"subdivision)":[26],"of":[27,51,82],"arbitrary":[28,63,80],"degree.":[29],"Similar":[30],"previous":[32],"works":[33],"by":[34],"Stam,":[35],"Zorin,":[36],"Schr\u00f6der":[38],"that":[39],"achieved":[40],"forward":[41],"subdivision":[42,67],"only,":[43],"our":[44],"involve":[47],"only":[48],"direct":[49],"neighbours":[50],"vertex,":[53],"can":[55],"be":[56],"configured":[57],"generalize":[59],"B-Spline":[60],"topology":[64],"surfaces.":[65],"Our":[66],"surfaces":[68],"are":[69,98],"hence":[70],"able":[71],"exhibit":[73,87],"C<sup>d</sup>":[74],"continuity":[75,89],"at":[76,90],"regular":[77],"vertices":[78],"(for":[79],"values":[81],"d)":[83],"appear":[85],"C<sup>1</sup>":[88],"extraordinary":[91],"vertices.":[92],"Smooth":[93],"non-uniform":[96],"subdivisions":[97],"additionally":[99],"supported.":[100]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-03-24T08:02:53.985720","created_date":"2025-10-10T00:00:00"}
