{"id":"https://openalex.org/W4241446338","doi":"https://doi.org/10.1145/1882261.1866168","title":"Consistent normal interpolation","display_name":"Consistent normal interpolation","publication_year":2010,"publication_date":"2010-12-01","ids":{"openalex":"https://openalex.org/W4241446338","doi":"https://doi.org/10.1145/1882261.1866168"},"language":"en","primary_location":{"id":"doi:10.1145/1882261.1866168","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1882261.1866168","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/A5053426992","display_name":"Alexander Reshetov","orcid":"https://orcid.org/0000-0003-1278-0414"},"institutions":[{"id":"https://openalex.org/I4210158342","display_name":"Intel (United Kingdom)","ror":"https://ror.org/058cxws58","country_code":"GB","type":"company","lineage":["https://openalex.org/I1343180700","https://openalex.org/I4210158342"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Alexander Reshetov","raw_affiliation_strings":["Intel"],"affiliations":[{"raw_affiliation_string":"Intel","institution_ids":["https://openalex.org/I4210158342"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050584442","display_name":"Alexei Soupikov","orcid":null},"institutions":[{"id":"https://openalex.org/I4210158342","display_name":"Intel (United Kingdom)","ror":"https://ror.org/058cxws58","country_code":"GB","type":"company","lineage":["https://openalex.org/I1343180700","https://openalex.org/I4210158342"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Alexei Soupikov","raw_affiliation_strings":["Intel"],"affiliations":[{"raw_affiliation_string":"Intel","institution_ids":["https://openalex.org/I4210158342"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109394409","display_name":"William R. Mark","orcid":null},"institutions":[{"id":"https://openalex.org/I4210158342","display_name":"Intel (United Kingdom)","ror":"https://ror.org/058cxws58","country_code":"GB","type":"company","lineage":["https://openalex.org/I1343180700","https://openalex.org/I4210158342"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"William R. Mark","raw_affiliation_strings":["Intel"],"affiliations":[{"raw_affiliation_string":"Intel","institution_ids":["https://openalex.org/I4210158342"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5053426992"],"corresponding_institution_ids":["https://openalex.org/I4210158342"],"apc_list":null,"apc_paid":null,"fwci":0.7243,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.83314654,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"29","issue":"6","first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9993000030517578,"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":0.9987000226974487,"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/classification-of-discontinuities","display_name":"Classification of discontinuities","score":0.7015247941017151},{"id":"https://openalex.org/keywords/rendering","display_name":"Rendering (computer graphics)","score":0.6956194043159485},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5645955801010132},{"id":"https://openalex.org/keywords/normal","display_name":"Normal","score":0.5421558022499084},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.517479658126831},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.4986000061035156},{"id":"https://openalex.org/keywords/simplicity","display_name":"Simplicity","score":0.4935842752456665},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.47226086258888245},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4457875192165375},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.41493311524391174},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.40122583508491516},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3781468868255615},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3739492893218994},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.28116557002067566},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20512479543685913},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.10049399733543396},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.09208035469055176},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0858689546585083}],"concepts":[{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.7015247941017151},{"id":"https://openalex.org/C205711294","wikidata":"https://www.wikidata.org/wiki/Q176953","display_name":"Rendering (computer graphics)","level":2,"score":0.6956194043159485},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5645955801010132},{"id":"https://openalex.org/C118732077","wikidata":"https://www.wikidata.org/wiki/Q273176","display_name":"Normal","level":3,"score":0.5421558022499084},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.517479658126831},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.4986000061035156},{"id":"https://openalex.org/C2776372474","wikidata":"https://www.wikidata.org/wiki/Q508291","display_name":"Simplicity","level":2,"score":0.4935842752456665},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.47226086258888245},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4457875192165375},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.41493311524391174},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.40122583508491516},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3781468868255615},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3739492893218994},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.28116557002067566},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20512479543685913},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.10049399733543396},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.09208035469055176},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0858689546585083},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1882261.1866168","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1882261.1866168","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W2012354353","https://openalex.org/W2052166673","https://openalex.org/W2103360877","https://openalex.org/W2112529694","https://openalex.org/W2122585444","https://openalex.org/W2141475216","https://openalex.org/W2149062555","https://openalex.org/W2161357479","https://openalex.org/W2161446118","https://openalex.org/W2162803433"],"related_works":["https://openalex.org/W2368019753","https://openalex.org/W2333930193","https://openalex.org/W2737356002","https://openalex.org/W2246241526","https://openalex.org/W4301122218","https://openalex.org/W4390844433","https://openalex.org/W1983403172","https://openalex.org/W2101902994","https://openalex.org/W1606959408","https://openalex.org/W2097163504"],"abstract_inverted_index":{"Rendering":[0],"a":[1,16,97,114],"polygonal":[2,28],"surface":[3,19,86],"with":[4],"Phong":[5,101,170],"normal":[6,102],"interpolation":[7,103],"allows":[8,105],"shading":[9,154],"to":[10,137],"appear":[11],"as":[12],"it":[13,136],"would":[14],"for":[15,38],"true":[17],"curved":[18],"while":[20,158],"maintaining":[21],"the":[22,85,91,125,153,162,168],"efficiency":[23],"and":[24,48,109,130,134,155,165],"simplicity":[25,166],"of":[26,52,100,113,161,167],"coarse":[27],"geometry.":[29],"However,":[30],"this":[31],"approximation":[32],"fails":[33],"in":[34,90],"certain":[35],"situations,":[36],"especially":[37],"grazing":[39],"viewing":[40],"directions.":[41],"Well-known":[42],"problems":[43],"include":[44],"physically":[45,106],"impossible":[46],"reflections":[47,108],"implausible":[49],"illumination.":[50],"Some":[51],"these":[53],"artifacts":[54,148],"can":[55],"be":[56],"mitigated":[57],"through":[58],"special-case":[59],"processing,":[60],"although":[61],"no":[62],"universal":[63],"or":[64],"generally":[65],"accepted":[66],"approaches":[67],"are":[68],"available.":[69],"In":[70],"particular,":[71],"all":[72],"known":[73],"solutions":[74],"that":[75,77,104,123],"guarantee":[76],"reflected":[78],"rays":[79],"will":[80],"always":[81],"point":[82],"outward":[83],"from":[84],"also":[87],"create":[88],"discontinuities":[89],"reflection":[92],"ray":[93],"direction.":[94],"We":[95,117],"present":[96],"simple":[98],"modification":[99],"plausible":[107],"creates":[110],"an":[111,119],"appearance":[112],"smooth":[115],"surface.":[116],"introduce":[118],"additional":[120],"scalar":[121],"parameter":[122],"characterizes":[124],"deviation":[126],"between":[127,152],"per-vertex":[128],"normals":[129,133,157],"per":[131],"face":[132],"use":[135],"adjust":[138],"linearly":[139],"interpolated":[140],"normals.":[141],"The":[142],"proposed":[143],"technique":[144],"eliminates":[145],"perceptually":[146],"objectionable":[147],"caused":[149],"by":[150],"inconsistencies":[151],"geometric":[156],"retaining":[159],"most":[160],"practical":[163],"advantages":[164],"original":[169],"formulation.":[171]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
