{"id":"https://openalex.org/W2302474486","doi":"https://doi.org/10.3390/sym8030013","title":"B\u00e9zier Triangles with G2 Continuity across Boundaries","display_name":"B\u00e9zier Triangles with G2 Continuity across Boundaries","publication_year":2016,"publication_date":"2016-03-15","ids":{"openalex":"https://openalex.org/W2302474486","doi":"https://doi.org/10.3390/sym8030013","mag":"2302474486"},"language":"en","primary_location":{"id":"doi:10.3390/sym8030013","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym8030013","pdf_url":"https://www.mdpi.com/2073-8994/8/3/13/pdf?version=1458029012","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/8/3/13/pdf?version=1458029012","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073790847","display_name":"Changki Lee","orcid":"https://orcid.org/0000-0001-8373-1500"},"institutions":[{"id":"https://openalex.org/I205490536","display_name":"Dongguk University","ror":"https://ror.org/057q6n778","country_code":"KR","type":"education","lineage":["https://openalex.org/I205490536"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Chang-Ki Lee","raw_affiliation_strings":["Department of Multimedia Engineering, Dongguk University"],"affiliations":[{"raw_affiliation_string":"Department of Multimedia Engineering, Dongguk University","institution_ids":["https://openalex.org/I205490536"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052444733","display_name":"Hae-Do Hwang","orcid":"https://orcid.org/0000-0003-2677-7806"},"institutions":[{"id":"https://openalex.org/I205490536","display_name":"Dongguk University","ror":"https://ror.org/057q6n778","country_code":"KR","type":"education","lineage":["https://openalex.org/I205490536"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Hae-Do Hwang","raw_affiliation_strings":["Department of Multimedia Engineering, Dongguk University"],"affiliations":[{"raw_affiliation_string":"Department of Multimedia Engineering, Dongguk University","institution_ids":["https://openalex.org/I205490536"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068996961","display_name":"Seung\u2010Hyun Yoon","orcid":"https://orcid.org/0000-0002-0015-8305"},"institutions":[{"id":"https://openalex.org/I205490536","display_name":"Dongguk University","ror":"https://ror.org/057q6n778","country_code":"KR","type":"education","lineage":["https://openalex.org/I205490536"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Seung-Hyun Yoon","raw_affiliation_strings":["Department of Multimedia Engineering, Dongguk University"],"affiliations":[{"raw_affiliation_string":"Department of Multimedia Engineering, Dongguk University","institution_ids":["https://openalex.org/I205490536"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5068996961"],"corresponding_institution_ids":["https://openalex.org/I205490536"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.3115,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.58803326,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"8","issue":"3","first_page":"13","last_page":"13"},"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9975000023841858,"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":0.9966999888420105,"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/barycentric-coordinate-system","display_name":"Barycentric coordinate system","score":0.5861809849739075},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5660361051559448},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5588969588279724},{"id":"https://openalex.org/keywords/triangle-mesh","display_name":"Triangle mesh","score":0.5070104598999023},{"id":"https://openalex.org/keywords/b\u00e9zier-curve","display_name":"B\u00e9zier curve","score":0.48817139863967896},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.4864387512207031},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.4762052297592163},{"id":"https://openalex.org/keywords/univariate","display_name":"Univariate","score":0.4713313579559326},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4636105000972748},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4312145709991455},{"id":"https://openalex.org/keywords/b\u00e9zier-surface","display_name":"B\u00e9zier surface","score":0.4132426679134369},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3780210614204407},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.32599353790283203},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.1518132984638214}],"concepts":[{"id":"https://openalex.org/C128356825","wikidata":"https://www.wikidata.org/wiki/Q738422","display_name":"Barycentric coordinate system","level":2,"score":0.5861809849739075},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5660361051559448},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5588969588279724},{"id":"https://openalex.org/C194401833","wikidata":"https://www.wikidata.org/wiki/Q3456889","display_name":"Triangle mesh","level":3,"score":0.5070104598999023},{"id":"https://openalex.org/C206423108","wikidata":"https://www.wikidata.org/wiki/Q214728","display_name":"B\u00e9zier curve","level":2,"score":0.48817139863967896},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.4864387512207031},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.4762052297592163},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.4713313579559326},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4636105000972748},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4312145709991455},{"id":"https://openalex.org/C100374796","wikidata":"https://www.wikidata.org/wiki/Q926066","display_name":"B\u00e9zier surface","level":3,"score":0.4132426679134369},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3780210614204407},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.32599353790283203},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.1518132984638214},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym8030013","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym8030013","pdf_url":"https://www.mdpi.com/2073-8994/8/3/13/pdf?version=1458029012","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:680773a36c934f42a3d91b2c150e51dc","is_oa":true,"landing_page_url":"https://doaj.org/article/680773a36c934f42a3d91b2c150e51dc","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 8, Iss 3, p 13 (2016)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/8/3/13/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym8030013","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry; Volume 8; Issue 3; Pages: 13","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym8030013","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym8030013","pdf_url":"https://www.mdpi.com/2073-8994/8/3/13/pdf?version=1458029012","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.5099999904632568}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2302474486.pdf","grobid_xml":"https://content.openalex.org/works/W2302474486.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1662763234","https://openalex.org/W1792437020","https://openalex.org/W1964484981","https://openalex.org/W1980382628","https://openalex.org/W1984026287","https://openalex.org/W1990323259","https://openalex.org/W1994372415","https://openalex.org/W1997368532","https://openalex.org/W2030677490","https://openalex.org/W2038373439","https://openalex.org/W2068499242","https://openalex.org/W2079256987","https://openalex.org/W2098788066","https://openalex.org/W2137124808"],"related_works":["https://openalex.org/W2359486342","https://openalex.org/W2360889479","https://openalex.org/W2896395566","https://openalex.org/W2091436390","https://openalex.org/W2357871848","https://openalex.org/W2388746963","https://openalex.org/W2381642105","https://openalex.org/W2952214742","https://openalex.org/W3085166426","https://openalex.org/W2361999794"],"abstract_inverted_index":{"PN":[0],"(point-normal)":[1],"triangles":[2,6,43],"are":[3],"cubic":[4],"B\u00e9zier":[5,42],"which":[7],"meet":[8],"at":[9,65],"their":[10],"edges":[11,30],"to":[12],"surface":[13],"a":[14,45],"triangular":[15,36],"mesh,":[16],"but":[17],"this":[18],"only":[19],"achieves":[20],"G0":[21],"continuity.":[22],"We":[23,84],"define":[24],"blending":[25,47,82],"regions":[26],"that":[27],"span":[28],"the":[29,40,70,78,86],"shared":[31],"by":[32,76,91],"adjacent":[33],"pairs":[34],"of":[35,52,69,80,88],"domains":[37],"and":[38],"blend":[39],"corresponding":[41],"using":[44],"univariate":[46],"function":[48],"formulated":[49],"in":[50],"terms":[51],"barycentric":[53],"coordinates.":[54],"This":[55],"produces":[56],"G2":[57],"continuity":[58,64],"across":[59],"boundaries":[60],"while":[61],"preserving":[62],"G1":[63],"vertices.":[66],"The":[67],"sharpness":[68],"blends":[71],"can":[72],"be":[73],"controlled":[74],"locally":[75],"varying":[77],"extent":[79],"these":[81],"regions.":[83],"demonstrate":[85],"effectiveness":[87],"our":[89],"technique":[90],"showing":[92],"several":[93],"modeling":[94],"examples.":[95]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}