{"id":"https://openalex.org/W2737593009","doi":"https://doi.org/10.1145/3072959.3073694","title":"A spherical cap preserving parameterization for spherical distributions","display_name":"A spherical cap preserving parameterization for spherical distributions","publication_year":2017,"publication_date":"2017-07-20","ids":{"openalex":"https://openalex.org/W2737593009","doi":"https://doi.org/10.1145/3072959.3073694","mag":"2737593009"},"language":"en","primary_location":{"id":"doi:10.1145/3072959.3073694","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3072959.3073694","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":true,"oa_status":"green","oa_url":"https://hal.science/hal-01523333","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075865950","display_name":"Jonathan Dupuy","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jonathan Dupuy","raw_affiliation_strings":["Unity Technologies","Unity Technologies (United States)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Unity Technologies","institution_ids":[]},{"raw_affiliation_string":"Unity Technologies (United States)","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082483572","display_name":"Eric Heitz","orcid":"https://orcid.org/0000-0002-9323-3318"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Eric Heitz","raw_affiliation_strings":["Unity Technologies","Unity Technologies (United States)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Unity Technologies","institution_ids":[]},{"raw_affiliation_string":"Unity Technologies (United States)","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037928047","display_name":"Laurent Belcour","orcid":"https://orcid.org/0000-0002-1982-0717"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Laurent Belcour","raw_affiliation_strings":["Unity Technologies","Unity Technologies (United States)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Unity Technologies","institution_ids":[]},{"raw_affiliation_string":"Unity Technologies (United States)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.0616,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.97319224,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"36","issue":"4","first_page":"1","last_page":"12"},"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/T10531","display_name":"Advanced Vision and Imaging","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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":0.9995999932289124,"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/rendering","display_name":"Rendering (computer graphics)","score":0.6482841372489929},{"id":"https://openalex.org/keywords/spherical-coordinate-system","display_name":"Spherical coordinate system","score":0.5771104097366333},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.5613470077514648},{"id":"https://openalex.org/keywords/spherical-harmonics","display_name":"Spherical harmonics","score":0.5538794994354248},{"id":"https://openalex.org/keywords/spherical-model","display_name":"Spherical model","score":0.5274011492729187},{"id":"https://openalex.org/keywords/spherical-cap","display_name":"Spherical cap","score":0.4813431203365326},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.43648645281791687},{"id":"https://openalex.org/keywords/spherical-mean","display_name":"Spherical mean","score":0.435655802488327},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.43296435475349426},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42492809891700745},{"id":"https://openalex.org/keywords/spherical-geometry","display_name":"Spherical geometry","score":0.4133346974849701},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4007706642150879},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3611270785331726},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29334139823913574},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics (images)","score":0.18919217586517334},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16612431406974792}],"concepts":[{"id":"https://openalex.org/C205711294","wikidata":"https://www.wikidata.org/wiki/Q176953","display_name":"Rendering (computer graphics)","level":2,"score":0.6482841372489929},{"id":"https://openalex.org/C126990412","wikidata":"https://www.wikidata.org/wiki/Q203218","display_name":"Spherical coordinate system","level":2,"score":0.5771104097366333},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5613470077514648},{"id":"https://openalex.org/C3768446","wikidata":"https://www.wikidata.org/wiki/Q877100","display_name":"Spherical harmonics","level":2,"score":0.5538794994354248},{"id":"https://openalex.org/C2778084274","wikidata":"https://www.wikidata.org/wiki/Q7576711","display_name":"Spherical model","level":2,"score":0.5274011492729187},{"id":"https://openalex.org/C2778664614","wikidata":"https://www.wikidata.org/wiki/Q575597","display_name":"Spherical cap","level":2,"score":0.4813431203365326},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.43648645281791687},{"id":"https://openalex.org/C137665795","wikidata":"https://www.wikidata.org/wiki/Q7576710","display_name":"Spherical mean","level":2,"score":0.435655802488327},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.43296435475349426},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42492809891700745},{"id":"https://openalex.org/C77730005","wikidata":"https://www.wikidata.org/wiki/Q326905","display_name":"Spherical geometry","level":2,"score":0.4133346974849701},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4007706642150879},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3611270785331726},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29334139823913574},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.18919217586517334},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16612431406974792},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3072959.3073694","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3072959.3073694","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"},{"id":"pmh:oai:HAL:hal-01523333v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01523333","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ACM Transactions on Graphics, 2017, ⟨10.1145/3072959.3073694⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-01523333v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01523333","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ACM Transactions on Graphics, 2017, ⟨10.1145/3072959.3073694⟩","raw_type":"Journal articles"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.4300000071525574}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W5886489","https://openalex.org/W65018654","https://openalex.org/W189266126","https://openalex.org/W608395726","https://openalex.org/W1982519631","https://openalex.org/W1983453594","https://openalex.org/W1999182952","https://openalex.org/W2001909619","https://openalex.org/W2024913359","https://openalex.org/W2033102965","https://openalex.org/W2037057571","https://openalex.org/W2037418484","https://openalex.org/W2059734713","https://openalex.org/W2066334759","https://openalex.org/W2092360980","https://openalex.org/W2095606974","https://openalex.org/W2095800081","https://openalex.org/W2111999986","https://openalex.org/W2138624212","https://openalex.org/W2142380402","https://openalex.org/W2146556997","https://openalex.org/W2170399863","https://openalex.org/W2200117061","https://openalex.org/W2293451440","https://openalex.org/W2473283942","https://openalex.org/W2971987237","https://openalex.org/W4205113243","https://openalex.org/W4245933748","https://openalex.org/W4285719527","https://openalex.org/W6602647839"],"related_works":["https://openalex.org/W2007132916","https://openalex.org/W2024558872","https://openalex.org/W2064332257","https://openalex.org/W2023619979","https://openalex.org/W2022069221","https://openalex.org/W4382058375","https://openalex.org/W4321637725","https://openalex.org/W2125110984","https://openalex.org/W1991486201","https://openalex.org/W2091451126"],"abstract_inverted_index":{"We":[0,94],"introduce":[1],"a":[2,12,21,30,85],"novel":[3,53],"parameterization":[4,100],"for":[5,107],"spherical":[6,46,55,86,104],"distributions":[7,47,56,66],"that":[8,33,57,74,124],"is":[9,125],"based":[10],"on":[11],"point":[13],"located":[14],"inside":[15],"the":[16,27,38,42,64,76,91,96],"sphere,":[17],"which":[18],"we":[19,51,72],"call":[20],"pivot.":[22],"The":[23],"pivot":[24],"serves":[25],"as":[26],"center":[28],"of":[29,41,98],"straight-line":[31],"projection":[32],"maps":[34],"solid":[35],"angles":[36],"onto":[37],"opposite":[39],"side":[40],"sphere.":[43],"By":[44],"transforming":[45],"in":[48],"this":[49],"way,":[50],"derive":[52,102],"parametric":[54],"can":[58,79,90],"be":[59,80],"evaluated":[60],"and":[61,110,121],"importance-sampled":[62],"from":[63],"original":[65,77],"using":[67],"simple,":[68],"closed-form":[69],"expressions.":[70],"Moreover,":[71],"prove":[73],"if":[75],"distribution":[78],"sampled":[81],"and/or":[82],"integrated":[83],"over":[84],"cap,":[87],"then":[88],"so":[89],"transformed":[92],"distribution.":[93],"exploit":[95],"properties":[97],"our":[99],"to":[101,119,127],"efficient":[103],"lighting":[105],"techniques":[106,114],"both":[108],"real-time":[109],"offline":[111],"rendering.":[112],"Our":[113],"are":[115],"robust,":[116],"fast,":[117],"easy":[118],"implement,":[120],"achieve":[122],"quality":[123],"superior":[126],"previous":[128],"work.":[129]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":5}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}