{"id":"https://openalex.org/W1968884202","doi":"https://doi.org/10.1145/1236246.1236291","title":"Approximate continuity for parametric B\u00e9zier patches","display_name":"Approximate continuity for parametric B\u00e9zier patches","publication_year":2007,"publication_date":"2007-06-04","ids":{"openalex":"https://openalex.org/W1968884202","doi":"https://doi.org/10.1145/1236246.1236291","mag":"1968884202"},"language":"en","primary_location":{"id":"doi:10.1145/1236246.1236291","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1236246.1236291","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2007 ACM symposium on Solid and physical modeling","raw_type":"proceedings-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/A5100711279","display_name":"Yingbin Liu","orcid":"https://orcid.org/0000-0002-4795-4173"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Yingbin Liu","raw_affiliation_strings":["University of Waterloo","(University of Waterloo)"],"affiliations":[{"raw_affiliation_string":"University of Waterloo","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"(University of Waterloo)","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063572090","display_name":"Stephen Mann","orcid":"https://orcid.org/0000-0001-8528-2921"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Stephen Mann","raw_affiliation_strings":["University of Waterloo","(University of Waterloo)"],"affiliations":[{"raw_affiliation_string":"University of Waterloo","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"(University of Waterloo)","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100711279"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":null,"apc_paid":null,"fwci":2.0883,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.8477732,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"315","last_page":"321"},"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/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.991599977016449,"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":0.9810000061988831,"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/piecewise","display_name":"Piecewise","score":0.6784222722053528},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.64996337890625},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6178590059280396},{"id":"https://openalex.org/keywords/discontinuity","display_name":"Discontinuity (linguistics)","score":0.5878268480300903},{"id":"https://openalex.org/keywords/quartic-function","display_name":"Quartic function","score":0.579052209854126},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.5547043681144714},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.4807872176170349},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.4785324037075043},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.4775467813014984},{"id":"https://openalex.org/keywords/parametrization","display_name":"Parametrization (atmospheric modeling)","score":0.45314866304397583},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4360602796077728},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.42685744166374207},{"id":"https://openalex.org/keywords/parametric-surface","display_name":"Parametric surface","score":0.4195745587348938},{"id":"https://openalex.org/keywords/classification-of-discontinuities","display_name":"Classification of discontinuities","score":0.41449400782585144},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.237912118434906},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.20233911275863647},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09618744254112244},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.09269887208938599},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07853430509567261}],"concepts":[{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6784222722053528},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.64996337890625},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6178590059280396},{"id":"https://openalex.org/C2777042112","wikidata":"https://www.wikidata.org/wiki/Q5281658","display_name":"Discontinuity (linguistics)","level":2,"score":0.5878268480300903},{"id":"https://openalex.org/C130432447","wikidata":"https://www.wikidata.org/wiki/Q11420049","display_name":"Quartic function","level":2,"score":0.579052209854126},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5547043681144714},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.4807872176170349},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.4785324037075043},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.4775467813014984},{"id":"https://openalex.org/C202887219","wikidata":"https://www.wikidata.org/wiki/Q3895221","display_name":"Parametrization (atmospheric modeling)","level":3,"score":0.45314866304397583},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4360602796077728},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.42685744166374207},{"id":"https://openalex.org/C2187777","wikidata":"https://www.wikidata.org/wiki/Q1071743","display_name":"Parametric surface","level":3,"score":0.4195745587348938},{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.41449400782585144},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.237912118434906},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20233911275863647},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09618744254112244},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.09269887208938599},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07853430509567261},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C74902906","wikidata":"https://www.wikidata.org/wiki/Q1190858","display_name":"Radiative transfer","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1236246.1236291","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1236246.1236291","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2007 ACM symposium on Solid and physical modeling","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.7699999809265137,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1515759668","https://openalex.org/W1587477963","https://openalex.org/W1968884202","https://openalex.org/W1973905141","https://openalex.org/W2060126595","https://openalex.org/W2091775660","https://openalex.org/W2092153773","https://openalex.org/W2120984155","https://openalex.org/W2138517065"],"related_works":["https://openalex.org/W2323190011","https://openalex.org/W162062087","https://openalex.org/W3039499377","https://openalex.org/W4241629433","https://openalex.org/W2085032340","https://openalex.org/W2026226327","https://openalex.org/W1989965977","https://openalex.org/W1756153455","https://openalex.org/W2056095867","https://openalex.org/W2232767080"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,25,38,47],"present":[4],"a":[5,17,32],"piecewise":[6],"cubic,":[7],"parametric":[8],"surface":[9],"scheme":[10,97,116],"to":[11,42,69,85,103],"interpolate":[12,70],"positions":[13],"and":[14,73,108],"normals":[15,74,88],"on":[16,61,92,117],"triangulated":[18],"data":[19,23],"set.":[20],"For":[21],"each":[22,44],"triangle,":[24],"fit":[26],"three":[27],"triangular":[28],"cubic":[29,115],"patches":[30,66,99],"in":[31],"Clough-Tocher":[33],"like":[34],"arrangement.":[35],"However,":[36],"while":[37],"construct":[39],"the":[40,58,62,71,76,93,104],"micro-patches":[41],"meet":[43],"other":[45],"C1,":[46],"only":[48],"require":[49],"approximate":[50],"G1":[51,114],"continuity":[52],"across":[53],"macro-patches":[54],"boundaries.":[55],"To":[56],"control":[57],"normal":[59],"discontinuity":[60],"macro-patch":[63],"boundaries,":[64],"neighbouring":[65],"are":[67],"constructed":[68],"position":[72],"at":[75,89],"ends":[77],"of":[78],"their":[79],"common":[80],"boundary,":[81],"as":[82,84],"well":[83],"have":[86],"equal":[87],"additional":[90],"points":[91],"boundary.":[94],"The":[95],"resulting":[96],"constructs":[98],"with":[100],"similar":[101],"shape":[102,111],"quartic":[105],"Shirman-S\u00e9quin":[106],"construction,":[107],"has":[109],"better":[110],"than":[112],"Peters'":[113],"near":[118],"singular":[119],"data.":[120]},"counts_by_year":[{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}