{"id":"https://openalex.org/W2942139228","doi":"https://doi.org/10.1109/tvcg.2019.2913418","title":"Spectral Analysis of Quadrature Rules and Fourier Truncation-Based Methods Applied to Shading Integrals","display_name":"Spectral Analysis of Quadrature Rules and Fourier Truncation-Based Methods Applied to Shading Integrals","publication_year":2019,"publication_date":"2019-04-27","ids":{"openalex":"https://openalex.org/W2942139228","doi":"https://doi.org/10.1109/tvcg.2019.2913418","mag":"2942139228","pmid":"https://pubmed.ncbi.nlm.nih.gov/31034416"},"language":"en","primary_location":{"id":"doi:10.1109/tvcg.2019.2913418","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvcg.2019.2913418","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":true,"oa_status":"green","oa_url":"http://hdl.handle.net/10230/37154","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013739865","display_name":"Ricardo Marques","orcid":"https://orcid.org/0000-0001-8261-4409"},"institutions":[{"id":"https://openalex.org/I170486558","display_name":"Universitat Pompeu Fabra","ror":"https://ror.org/04n0g0b29","country_code":"ES","type":"education","lineage":["https://openalex.org/I170486558"]},{"id":"https://openalex.org/I4210089667","display_name":"TARH (Portugal)","ror":"https://ror.org/008yah456","country_code":"PT","type":"company","lineage":["https://openalex.org/I4210089667"]}],"countries":["ES","PT"],"is_corresponding":true,"raw_author_name":"Ricardo Marques","raw_affiliation_strings":["Grup de Recerca de Tecnologies Interactives, Universitat Pompeu Fabra, Barcelona, Spain","ITN - Instituto tecnologico e nuclear (EN10 2686-953 Sacavem - Portugal)"],"affiliations":[{"raw_affiliation_string":"Grup de Recerca de Tecnologies Interactives, Universitat Pompeu Fabra, Barcelona, Spain","institution_ids":["https://openalex.org/I170486558"]},{"raw_affiliation_string":"ITN - Instituto tecnologico e nuclear (EN10 2686-953 Sacavem - Portugal)","institution_ids":["https://openalex.org/I4210089667"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076531248","display_name":"Christian Bouville","orcid":"https://orcid.org/0000-0001-5884-9849"},"institutions":[{"id":"https://openalex.org/I2802519937","display_name":"Institut de Recherche en Informatique et Syst\u00e8mes Al\u00e9atoires","ror":"https://ror.org/00myn0z94","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I205703379","https://openalex.org/I2802204017","https://openalex.org/I2802519937","https://openalex.org/I28221208","https://openalex.org/I4210127572","https://openalex.org/I4210159245","https://openalex.org/I56067802"]},{"id":"https://openalex.org/I56067802","display_name":"Universit\u00e9 de Rennes","ror":"https://ror.org/015m7wh34","country_code":"FR","type":"education","lineage":["https://openalex.org/I56067802"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Christian Bouville","raw_affiliation_strings":["IRISA, University of Rennes, 1 Rennes, France","PERCEPT - Computational Visual Perception and Applications (IRISA\r\n263 Avenue du G\u00e9n\u00e9ral Leclerc \u2013 CS 74205\r\nCampus de Beaulieu \u2013 35042  Rennes C\u00e9dex - France)","IRISA-D6 - MEDIA ET INTERACTIONS (France)"],"affiliations":[{"raw_affiliation_string":"IRISA, University of Rennes, 1 Rennes, France","institution_ids":["https://openalex.org/I2802519937","https://openalex.org/I56067802"]},{"raw_affiliation_string":"PERCEPT - Computational Visual Perception and Applications (IRISA\r\n263 Avenue du G\u00e9n\u00e9ral Leclerc \u2013 CS 74205\r\nCampus de Beaulieu \u2013 35042  Rennes C\u00e9dex - France)","institution_ids":["https://openalex.org/I2802519937"]},{"raw_affiliation_string":"IRISA-D6 - MEDIA ET INTERACTIONS (France)","institution_ids":["https://openalex.org/I2802519937"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048208600","display_name":"Kadi Bouatouch","orcid":null},"institutions":[{"id":"https://openalex.org/I2802519937","display_name":"Institut de Recherche en Informatique et Syst\u00e8mes Al\u00e9atoires","ror":"https://ror.org/00myn0z94","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I205703379","https://openalex.org/I2802204017","https://openalex.org/I2802519937","https://openalex.org/I28221208","https://openalex.org/I4210127572","https://openalex.org/I4210159245","https://openalex.org/I56067802"]},{"id":"https://openalex.org/I56067802","display_name":"Universit\u00e9 de Rennes","ror":"https://ror.org/015m7wh34","country_code":"FR","type":"education","lineage":["https://openalex.org/I56067802"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Kadi Bouatouch","raw_affiliation_strings":["IRISA, University of Rennes, 1 Rennes, France","IRISA-D6 - MEDIA ET INTERACTIONS (France)","PERCEPT - Computational Visual Perception and Applications (IRISA\r\n263 Avenue du G\u00e9n\u00e9ral Leclerc \u2013 CS 74205\r\nCampus de Beaulieu \u2013 35042  Rennes C\u00e9dex - France)"],"affiliations":[{"raw_affiliation_string":"IRISA, University of Rennes, 1 Rennes, France","institution_ids":["https://openalex.org/I2802519937","https://openalex.org/I56067802"]},{"raw_affiliation_string":"IRISA-D6 - MEDIA ET INTERACTIONS (France)","institution_ids":["https://openalex.org/I2802519937"]},{"raw_affiliation_string":"PERCEPT - Computational Visual Perception and Applications (IRISA\r\n263 Avenue du G\u00e9n\u00e9ral Leclerc \u2013 CS 74205\r\nCampus de Beaulieu \u2013 35042  Rennes C\u00e9dex - France)","institution_ids":["https://openalex.org/I2802519937"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5013739865"],"corresponding_institution_ids":["https://openalex.org/I170486558","https://openalex.org/I4210089667"],"apc_list":null,"apc_paid":null,"fwci":0.3882,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.58341633,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"26","issue":"10","first_page":"3022","last_page":"3036"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12304","display_name":"Radiative Heat Transfer Studies","score":0.9962000250816345,"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/T12304","display_name":"Radiative Heat Transfer Studies","score":0.9962000250816345,"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":0.9961000084877014,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9943000078201294,"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/quadrature","display_name":"Quadrature (astronomy)","score":0.7086808085441589},{"id":"https://openalex.org/keywords/spherical-harmonics","display_name":"Spherical harmonics","score":0.6869342923164368},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.6651414632797241},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.503471314907074},{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.4917488396167755},{"id":"https://openalex.org/keywords/radiance","display_name":"Radiance","score":0.4837901294231415},{"id":"https://openalex.org/keywords/clenshaw\u2013curtis-quadrature","display_name":"Clenshaw\u2013Curtis quadrature","score":0.4645165503025055},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.459118515253067},{"id":"https://openalex.org/keywords/truncation-error","display_name":"Truncation error","score":0.4566291272640228},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44765836000442505},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.4405115842819214},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35398218035697937},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3169483244419098},{"id":"https://openalex.org/keywords/gaussian-quadrature","display_name":"Gaussian quadrature","score":0.29479753971099854},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.2935006022453308},{"id":"https://openalex.org/keywords/nystr\u00f6m-method","display_name":"Nystr\u00f6m method","score":0.2904941439628601},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.13745465874671936},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11646685004234314}],"concepts":[{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.7086808085441589},{"id":"https://openalex.org/C3768446","wikidata":"https://www.wikidata.org/wiki/Q877100","display_name":"Spherical harmonics","level":2,"score":0.6869342923164368},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.6651414632797241},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.503471314907074},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.4917488396167755},{"id":"https://openalex.org/C23690007","wikidata":"https://www.wikidata.org/wiki/Q1411145","display_name":"Radiance","level":2,"score":0.4837901294231415},{"id":"https://openalex.org/C172657837","wikidata":"https://www.wikidata.org/wiki/Q5131618","display_name":"Clenshaw\u2013Curtis quadrature","level":5,"score":0.4645165503025055},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.459118515253067},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.4566291272640228},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44765836000442505},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.4405115842819214},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35398218035697937},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3169483244419098},{"id":"https://openalex.org/C167196314","wikidata":"https://www.wikidata.org/wiki/Q767680","display_name":"Gaussian quadrature","level":4,"score":0.29479753971099854},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.2935006022453308},{"id":"https://openalex.org/C48265008","wikidata":"https://www.wikidata.org/wiki/Q7071295","display_name":"Nystr\u00f6m method","level":3,"score":0.2904941439628601},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.13745465874671936},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11646685004234314},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tvcg.2019.2913418","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvcg.2019.2913418","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:31034416","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/31034416","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:oai:recercat.cat:2072/355096","is_oa":true,"landing_page_url":"http://hdl.handle.net/10230/37154","pdf_url":null,"source":{"id":"https://openalex.org/S4306402147","display_name":"RECERCAT (Consorci de Serveis Universitaris de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210090028","host_organization_name":"Consorci de Serveis Universitaris de Catalunya","host_organization_lineage":["https://openalex.org/I4210090028"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:HAL:hal-02476478v1","is_oa":false,"landing_page_url":"https://inria.hal.science/hal-02476478","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Visualization and Computer Graphics, In press, pp.1-1. ⟨10.1109/TVCG.2019.2913418⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:recercat.cat:2072/355096","is_oa":true,"landing_page_url":"http://hdl.handle.net/10230/37154","pdf_url":null,"source":{"id":"https://openalex.org/S4306402147","display_name":"RECERCAT (Consorci de Serveis Universitaris de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210090028","host_organization_name":"Consorci de Serveis Universitaris de Catalunya","host_organization_lineage":["https://openalex.org/I4210090028"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W10473411","https://openalex.org/W1538225255","https://openalex.org/W1543326485","https://openalex.org/W1571295563","https://openalex.org/W1578723177","https://openalex.org/W1969253908","https://openalex.org/W1969679542","https://openalex.org/W1977659080","https://openalex.org/W1993553799","https://openalex.org/W1995741243","https://openalex.org/W1996598508","https://openalex.org/W2000834181","https://openalex.org/W2002337266","https://openalex.org/W2047342172","https://openalex.org/W2048959181","https://openalex.org/W2049153601","https://openalex.org/W2073446669","https://openalex.org/W2085452700","https://openalex.org/W2093529512","https://openalex.org/W2093625674","https://openalex.org/W2099478163","https://openalex.org/W2120062331","https://openalex.org/W2139046107","https://openalex.org/W2144337074","https://openalex.org/W2164369380","https://openalex.org/W2165916500","https://openalex.org/W2229024660","https://openalex.org/W2341112121","https://openalex.org/W2569481888","https://openalex.org/W2969071059","https://openalex.org/W2998555201","https://openalex.org/W4237938407","https://openalex.org/W4388321579","https://openalex.org/W6632360536","https://openalex.org/W6689614062"],"related_works":["https://openalex.org/W4237740072","https://openalex.org/W2040666836","https://openalex.org/W2238041693","https://openalex.org/W2112774109","https://openalex.org/W125347959","https://openalex.org/W4294281846","https://openalex.org/W4387847482","https://openalex.org/W1990789772","https://openalex.org/W4377005030","https://openalex.org/W138907054"],"abstract_inverted_index":{"We":[0,26,47,96],"propose":[1],"a":[2,15,86,126,156,184,196],"theoretical":[3,158,191],"framework,":[4],"based":[5],"on":[6,60,70],"the":[7,24,31,42,50,54,61,71,74,91,102,110,117,152,167,176],"theory":[8],"of":[9,18,33,44,53,81,89,104,198],"Sobolev":[10],"spaces,":[11],"that":[12,49,124],"allows":[13,84],"for":[14,21,85,172],"comprehensive":[16],"analysis":[17,80,100],"quadrature":[19,45,55,82],"rules":[20],"integration":[22,128,186],"over":[23],"sphere.":[25],"apply":[27],"this":[28],"framework":[29,150],"to":[30,38,101,109,115,135,154,166,174,183],"case":[32,103],"shading":[34,111,168],"integrals":[35],"in":[36],"order":[37],"predict":[39],"and":[40,66,73,144,162],"analyze":[41],"performances":[43],"methods.":[46],"show":[48],"spectral":[51,79],"distribution":[52,65],"error":[56,83],"depends":[57],"not":[58],"only":[59],"samples":[62],"set":[63,197],"size,":[64],"weights,":[67],"but":[68],"also":[69,97],"BRDF":[72],"integrand":[75],"smoothness.":[76],"The":[77],"proposed":[78,149],"better":[87],"understanding":[88],"how":[90],"above":[92],"different":[93],"factors":[94],"interact.":[95],"extend":[98],"our":[99,148],"Fourier":[105],"truncation-based":[106,163],"techniques":[107],"applied":[108,165],"integral,":[112],"so":[113],"as":[114,140],"find":[116],"smallest":[118],"spherical/hemispherical":[119],"harmonics":[120,178],"degree":[121,179],"L":[122,180],"(truncation)":[123],"entails":[125],"targeted":[127],"error.":[129],"This":[130,170],"application":[131],"is":[132,151],"very":[133],"beneficial":[134],"global":[136],"illumination":[137],"methods":[138,164],"such":[139],"Precomputed":[141],"Radiance":[142,145],"Transfer":[143],"Caching.":[146],"Finally,":[147],"first":[153],"allow":[155],"direct":[157],"comparison":[159],"between":[160],"quadrature-":[161],"integral.":[169],"enables,":[171],"example,":[173],"determine":[175],"spherical":[177],"which":[181],"corresponds":[182],"quadrature-based":[185],"with":[187],"N":[188],"samples.":[189],"Our":[190],"findings":[192],"are":[193],"validated":[194],"by":[195],"rendering":[199],"experiments.":[200]},"counts_by_year":[{"year":2022,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}