{"id":"https://openalex.org/W2625488966","doi":"https://doi.org/10.1145/3095140.3097284","title":"A hybrid approach for computing products of high-dimensional geometric algebras","display_name":"A hybrid approach for computing products of high-dimensional geometric algebras","publication_year":2017,"publication_date":"2017-06-13","ids":{"openalex":"https://openalex.org/W2625488966","doi":"https://doi.org/10.1145/3095140.3097284","mag":"2625488966"},"language":"en","primary_location":{"id":"doi:10.1145/3095140.3097284","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3095140.3097284","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Computer Graphics International Conference","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-01552462v1/file/breuils_engage_2017.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047133071","display_name":"St\u00e9phane Breuils","orcid":"https://orcid.org/0000-0002-8636-4977"},"institutions":[{"id":"https://openalex.org/I4210152518","display_name":"Laboratoire d'Informatique Gaspard-Monge","ror":"https://ror.org/04t50yk91","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I142631665","https://openalex.org/I4210145102","https://openalex.org/I4210152518","https://openalex.org/I4210154111","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"St\u00e9phane Breuils","raw_affiliation_strings":["LIGM, Marne-la-Vall\u00e9e, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LIGM, Marne-la-Vall\u00e9e, France","institution_ids":["https://openalex.org/I4210152518"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083779733","display_name":"Vincent Nozick","orcid":"https://orcid.org/0000-0001-8792-7164"},"institutions":[{"id":"https://openalex.org/I176979517","display_name":"International Research Center for Japanese Studies","ror":"https://ror.org/04861vz74","country_code":"JP","type":"education","lineage":["https://openalex.org/I1319490839","https://openalex.org/I176979517","https://openalex.org/I4210148627"]},{"id":"https://openalex.org/I4387152154","display_name":"Japanese-French Laboratory for Informatics","ror":"https://ror.org/007xn7v02","country_code":"JP","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I203951103","https://openalex.org/I39804081","https://openalex.org/I4387152154","https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Vincent Nozick","raw_affiliation_strings":["JFLI, Tokyo, Japan","JFLI - Japanese French Laboratory for Informatics (Japan)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"JFLI, Tokyo, Japan","institution_ids":[]},{"raw_affiliation_string":"JFLI - Japanese French Laboratory for Informatics (Japan)","institution_ids":["https://openalex.org/I176979517","https://openalex.org/I4387152154"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043245355","display_name":"Laurent Fuchs","orcid":"https://orcid.org/0000-0002-0684-6467"},"institutions":[{"id":"https://openalex.org/I32881790","display_name":"Universit\u00e9 de Poitiers","ror":"https://ror.org/04xhy8q59","country_code":"FR","type":"education","lineage":["https://openalex.org/I32881790"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Laurent Fuchs","raw_affiliation_strings":["Universit\u00e9 de Poitiers, Poitiers, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Poitiers, Poitiers, France","institution_ids":["https://openalex.org/I32881790"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049711176","display_name":"Dietmar Hildenbrand","orcid":"https://orcid.org/0000-0002-6384-4345"},"institutions":[{"id":"https://openalex.org/I4829542","display_name":"RheinMain University of Applied Sciences","ror":"https://ror.org/0378gm372","country_code":"DE","type":"education","lineage":["https://openalex.org/I4829542"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Dietmar Hildenbrand","raw_affiliation_strings":["Hochschule RheinMain, R\u00fcsselsheim, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hochschule RheinMain, R\u00fcsselsheim, Germany","institution_ids":["https://openalex.org/I4829542"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054314843","display_name":"Werner Benger","orcid":"https://orcid.org/0000-0003-2782-175X"},"institutions":[{"id":"https://openalex.org/I121820613","display_name":"Louisiana State University","ror":"https://ror.org/05ect4e57","country_code":"US","type":"education","lineage":["https://openalex.org/I121820613"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Werner Benger","raw_affiliation_strings":["Louisiana State University","LSU - Department of Physics & Astronomy [Louisiana State University] (Department of Physics & Astronomy, Louisiana State University, Baton Rouge, LA 70803, USA - United States)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Louisiana State University","institution_ids":["https://openalex.org/I121820613"]},{"raw_affiliation_string":"LSU - Department of Physics & Astronomy [Louisiana State University] (Department of Physics & Astronomy, Louisiana State University, Baton Rouge, LA 70803, USA - United States)","institution_ids":["https://openalex.org/I121820613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032881514","display_name":"Christian J. Steinmetz","orcid":"https://orcid.org/0000-0002-0971-5729"},"institutions":[{"id":"https://openalex.org/I31512782","display_name":"Technical University of Darmstadt","ror":"https://ror.org/05n911h24","country_code":"DE","type":"education","lineage":["https://openalex.org/I31512782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Christian Steinmetz","raw_affiliation_strings":["TU Darmstadt, Darmstadt, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"TU Darmstadt, Darmstadt, Germany","institution_ids":["https://openalex.org/I31512782"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5047133071"],"corresponding_institution_ids":["https://openalex.org/I4210152518"],"apc_list":null,"apc_paid":null,"fwci":1.5002,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.80667694,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9648000001907349,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9556000232696533,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/conformal-geometric-algebra","display_name":"Conformal geometric algebra","score":0.9492913484573364},{"id":"https://openalex.org/keywords/geometric-algebra","display_name":"Geometric algebra","score":0.8570852875709534},{"id":"https://openalex.org/keywords/universal-geometric-algebra","display_name":"Universal geometric algebra","score":0.7076541185379028},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.6264212727546692},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5129375457763672},{"id":"https://openalex.org/keywords/symbolic-computation","display_name":"Symbolic computation","score":0.5065256357192993},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.47983333468437195},{"id":"https://openalex.org/keywords/quadric","display_name":"Quadric","score":0.4483734369277954},{"id":"https://openalex.org/keywords/algebra-representation","display_name":"Algebra representation","score":0.43899279832839966},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3460274934768677},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.26642924547195435}],"concepts":[{"id":"https://openalex.org/C147898140","wikidata":"https://www.wikidata.org/wiki/Q5160252","display_name":"Conformal geometric algebra","level":5,"score":0.9492913484573364},{"id":"https://openalex.org/C180671464","wikidata":"https://www.wikidata.org/wiki/Q1186649","display_name":"Geometric algebra","level":4,"score":0.8570852875709534},{"id":"https://openalex.org/C64228544","wikidata":"https://www.wikidata.org/wiki/Q17152794","display_name":"Universal geometric algebra","level":5,"score":0.7076541185379028},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.6264212727546692},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5129375457763672},{"id":"https://openalex.org/C110812573","wikidata":"https://www.wikidata.org/wiki/Q175515","display_name":"Symbolic computation","level":2,"score":0.5065256357192993},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.47983333468437195},{"id":"https://openalex.org/C2779219049","wikidata":"https://www.wikidata.org/wiki/Q852117","display_name":"Quadric","level":2,"score":0.4483734369277954},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.43899279832839966},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3460274934768677},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26642924547195435},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3095140.3097284","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3095140.3097284","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Computer Graphics International Conference","raw_type":"proceedings-article"},{"id":"pmh:oai:HAL:hal-01552462v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01552462","pdf_url":"https://hal.science/hal-01552462v1/file/breuils_engage_2017.pdf","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":"CGI / ENGAGE 2017, Jun 2017, Hiyoshi, Japan. pp.1 - 6, ⟨10.1145/3095140.3097284⟩","raw_type":"Conference papers"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-01552462v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01552462","pdf_url":"https://hal.science/hal-01552462v1/file/breuils_engage_2017.pdf","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":"CGI / ENGAGE 2017, Jun 2017, Hiyoshi, Japan. pp.1 - 6, ⟨10.1145/3095140.3097284⟩","raw_type":"Conference papers"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2625488966.pdf","grobid_xml":"https://content.openalex.org/works/W2625488966.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W194472640","https://openalex.org/W1586781146","https://openalex.org/W1600874933","https://openalex.org/W1984648584","https://openalex.org/W2008609482","https://openalex.org/W2014171255","https://openalex.org/W2039117545","https://openalex.org/W2050174852","https://openalex.org/W2116021467","https://openalex.org/W2116418869","https://openalex.org/W2167406894","https://openalex.org/W2258959657","https://openalex.org/W2285532564","https://openalex.org/W2339553700","https://openalex.org/W2595105991","https://openalex.org/W2766270335","https://openalex.org/W2894711301","https://openalex.org/W6696061862"],"related_works":["https://openalex.org/W2579897398","https://openalex.org/W4297796763","https://openalex.org/W2795258309","https://openalex.org/W4292411538","https://openalex.org/W2800834093","https://openalex.org/W2952712267","https://openalex.org/W2120019850","https://openalex.org/W288435025","https://openalex.org/W2740005812","https://openalex.org/W1538240564"],"abstract_inverted_index":{"Geometric":[0,33,74,85,89,107],"Algebra":[1,34,90,108],"is":[2,120,183,217],"considered":[3],"as":[4,41,57,195,197,211],"a":[5,106,121,143,148,212,218],"very":[6,219],"intuitive":[7],"tool":[8],"to":[9,17,23,78,158,165,230],"deal":[10,24],"with":[11,25,127,133,147],"geometric":[12],"problems":[13],"and":[14,21,39,44,65,114,130,171],"it":[15],"appears":[16],"be":[18,63,66],"increasingly":[19],"efficient":[20,98],"useful":[22],"computer":[26],"graphics":[27],"solutions.":[28],"For":[29],"example,":[30],"the":[31,72,139,160,166,169,172,178,205,232],"Conformal":[32],"includes":[35],"circles,":[36],"spheres,":[37],"planes":[38],"lines":[40],"algebraic":[42,51],"objects,":[43],"intersections":[45],"between":[46],"these":[47,101],"objects":[48,55],"are":[49,92,156],"also":[50,62,226],"objects.":[52,102],"More":[53,137],"complex":[54],"such":[56],"conics,":[58],"quadric":[59],"surfaces":[60],"can":[61],"expressed":[64],"manipulated":[67],"using":[68,151],"an":[69],"extension":[70],"of":[71,81,88,100,168,174,192,207,234],"conformal":[73],"Algebra.":[75],"However":[76],"due":[77],"high":[79,115,187,239],"dimension":[80,167,193],"their":[82],"representations":[83],"in":[84,177,238],"Algebra,":[86],"implementations":[87],"that":[91],"currently":[93],"available":[94],"do":[95],"not":[96],"allow":[97],"realizations":[99],"This":[103,202,224],"paper":[104,203,225],"presents":[105,227],"implementation":[109,182],"dedicated":[110],"for":[111,124,186,198],"both":[112],"low":[113,134],"dimensions.":[116],"The":[117,180],"proposed":[118,140],"method":[119,141,150,210],"hybrid":[122,209],"solution":[123],"precomputed":[125,144],"code":[126,222],"fast":[128],"execution":[129],"runtime":[131],"computations":[132],"memory":[135],"requirement.":[136],"specifically,":[138],"combines":[142],"table":[145],"approach":[146],"recursive":[149],"binary":[152],"trees.":[153],"Some":[154],"rules":[155],"defined":[157],"select":[159],"most":[161],"appropriate":[162],"choice,":[163],"according":[164],"algebra":[170,191],"type":[173],"multivectors":[175],"involved":[176],"product.":[179],"resulting":[181],"well":[184,196],"suited":[185],"dimensional":[188,200,240],"spaces":[189],"(e.g.":[190],"15)":[194],"lower":[199],"space.":[201],"details":[204],"integration":[206],"this":[208],"plug-in":[213],"into":[214],"Gaalop,":[215],"which":[216],"advanced":[220],"optimizing":[221],"generator.":[223],"some":[228],"benchmarks":[229],"show":[231],"performances":[233],"our":[235],"method,":[236],"especially":[237],"spaces.":[241]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2}],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2025-10-10T00:00:00"}