{"id":"https://openalex.org/W2057334693","doi":"https://doi.org/10.1080/10867651.1999.10487509","title":"Efficiently Building a Matrix to Rotate One Vector to Another","display_name":"Efficiently Building a Matrix to Rotate One Vector to Another","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2057334693","doi":"https://doi.org/10.1080/10867651.1999.10487509","mag":"2057334693"},"language":"en","primary_location":{"id":"doi:10.1080/10867651.1999.10487509","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10867651.1999.10487509","pdf_url":null,"source":{"id":"https://openalex.org/S4210240212","display_name":"Journal of Graphics Tools","issn_l":"1086-7651","issn":["1086-7651"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graphics Tools","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/A5104063365","display_name":"Tomas M\u00f6ller","orcid":null},"institutions":[{"id":"https://openalex.org/I66862912","display_name":"Chalmers University of Technology","ror":"https://ror.org/040wg7k59","country_code":"SE","type":"education","lineage":["https://openalex.org/I66862912"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Tomas M\u00f6ller","raw_affiliation_strings":["Chalmers University of Technology, Department of Computer Engincering , 412 90 , Gothcnlmrg , Sweden E-mail: tompa@acm.org","U.C. Berkeley and Chalmers University of Technology, Department of Computer Engineering, 412 96 Gothenburg, Sweden"],"affiliations":[{"raw_affiliation_string":"Chalmers University of Technology, Department of Computer Engincering , 412 90 , Gothcnlmrg , Sweden E-mail: tompa@acm.org","institution_ids":["https://openalex.org/I66862912"]},{"raw_affiliation_string":"U.C. Berkeley and Chalmers University of Technology, Department of Computer Engineering, 412 96 Gothenburg, Sweden","institution_ids":["https://openalex.org/I66862912"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103642464","display_name":"John F. Hughes","orcid":null},"institutions":[{"id":"https://openalex.org/I27804330","display_name":"Brown University","ror":"https://ror.org/05gq02987","country_code":"US","type":"education","lineage":["https://openalex.org/I27804330"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"John F. Hughes","raw_affiliation_strings":["Brown University, Computer Science Department , 115 Waterman Street, Providence , RI , 02912 E-mail: jfll@cs.brown.edu","Brown University, Computer Science Department, 115 Waterman Street, Providence, RI"],"affiliations":[{"raw_affiliation_string":"Brown University, Computer Science Department , 115 Waterman Street, Providence , RI , 02912 E-mail: jfll@cs.brown.edu","institution_ids":["https://openalex.org/I27804330"]},{"raw_affiliation_string":"Brown University, Computer Science Department, 115 Waterman Street, Providence, RI","institution_ids":["https://openalex.org/I27804330"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5104063365"],"corresponding_institution_ids":["https://openalex.org/I66862912"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":43,"citation_normalized_percentile":{"value":0.18519506,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"4","issue":"4","first_page":"1","last_page":"4"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9322999715805054,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9322999715805054,"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"}},{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9289000034332275,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/trigonometry","display_name":"Trigonometry","score":0.7257332801818848},{"id":"https://openalex.org/keywords/trigonometric-functions","display_name":"Trigonometric functions","score":0.7150038480758667},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6694452166557312},{"id":"https://openalex.org/keywords/unit-vector","display_name":"Unit vector","score":0.6554174423217773},{"id":"https://openalex.org/keywords/unit","display_name":"Unit (ring theory)","score":0.6467702984809875},{"id":"https://openalex.org/keywords/vector-valued-function","display_name":"Vector-valued function","score":0.4367177486419678},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42791467905044556},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36710143089294434},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.34577351808547974},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.29386597871780396},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2382424771785736},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18499431014060974}],"concepts":[{"id":"https://openalex.org/C29001434","wikidata":"https://www.wikidata.org/wiki/Q8084","display_name":"Trigonometry","level":2,"score":0.7257332801818848},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.7150038480758667},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6694452166557312},{"id":"https://openalex.org/C84316537","wikidata":"https://www.wikidata.org/wiki/Q36255","display_name":"Unit vector","level":2,"score":0.6554174423217773},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.6467702984809875},{"id":"https://openalex.org/C2456702","wikidata":"https://www.wikidata.org/wiki/Q1375954","display_name":"Vector-valued function","level":2,"score":0.4367177486419678},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42791467905044556},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36710143089294434},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.34577351808547974},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29386597871780396},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2382424771785736},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18499431014060974},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10867651.1999.10487509","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10867651.1999.10487509","pdf_url":null,"source":{"id":"https://openalex.org/S4210240212","display_name":"Journal of Graphics Tools","issn_l":"1086-7651","issn":["1086-7651"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graphics Tools","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":6,"referenced_works":["https://openalex.org/W181787642","https://openalex.org/W1490482062","https://openalex.org/W1663723700","https://openalex.org/W2147774191","https://openalex.org/W2798909945","https://openalex.org/W4239377895"],"related_works":["https://openalex.org/W2987292777","https://openalex.org/W634571496","https://openalex.org/W579400037","https://openalex.org/W2951578208","https://openalex.org/W1570037808","https://openalex.org/W4298173607","https://openalex.org/W3020816813","https://openalex.org/W4386784405","https://openalex.org/W115184939","https://openalex.org/W4285286257"],"abstract_inverted_index":{"Abstract":[0],"We":[1,38],"describe":[2],"an":[3],"efficient":[4],"(no":[5],"square":[6],"roots":[7],"or":[8],"trigonometric":[9],"functions)":[10],"method":[11,45],"to":[12],"const":[13],"ruct":[14],"the":[15,33],"3":[16,18],"\u00d7":[17,36],"matrix":[19],"that":[20],"rotates":[21],"a":[22],"unit":[23,28],"vector":[24,29],"f":[25,35],"into":[26],"another":[27],"t,":[30],"rotating":[31],"about":[32],"axis":[34],"t.":[37],"give":[39],"experiment":[40],"al":[41],"results":[42],"showing":[43],"this":[44],"is":[46,56],"faster":[47],"than":[48],"previously":[49],"known":[50],"methods.":[51],"An":[52],"implementation":[53],"in":[54],"C":[55],"provided.":[57]},"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}