{"id":"https://openalex.org/W2017427737","doi":"https://doi.org/10.1080/10867651.1999.10487513","title":"Building an Orthonormal Basis from a Unit Vector","display_name":"Building an Orthonormal Basis from a Unit Vector","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2017427737","doi":"https://doi.org/10.1080/10867651.1999.10487513","mag":"2017427737"},"language":"en","primary_location":{"id":"doi:10.1080/10867651.1999.10487513","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10867651.1999.10487513","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/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":true,"raw_author_name":"John F. Hughes","raw_affiliation_strings":["Brown University, Computer Science Department , 115 Waterman Street, Providence , RI , 02912 E-mail: Uth@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: Uth@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"]}]},{"author_position":"last","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":false,"raw_author_name":"Tomas Moller","raw_affiliation_strings":["Chalmers University of Technology, Department of Computer Engineering , 412 96 , Gothenburg , 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 Engineering , 412 96 , Gothenburg , 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"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5103642464"],"corresponding_institution_ids":["https://openalex.org/I27804330"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.13731842,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"4","issue":"4","first_page":"33","last_page":"35"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10571","display_name":"Robotic Mechanisms and Dynamics","score":0.9513999819755554,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T10571","display_name":"Robotic Mechanisms and Dynamics","score":0.9513999819755554,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/orthonormal-basis","display_name":"Orthonormal basis","score":0.9751644134521484},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.8414050340652466},{"id":"https://openalex.org/keywords/orthonormality","display_name":"Orthonormality","score":0.7724131345748901},{"id":"https://openalex.org/keywords/unit-vector","display_name":"Unit vector","score":0.7257150411605835},{"id":"https://openalex.org/keywords/unit","display_name":"Unit (ring theory)","score":0.6590533256530762},{"id":"https://openalex.org/keywords/vector","display_name":"Vector (molecular biology)","score":0.5558832883834839},{"id":"https://openalex.org/keywords/vector-space","display_name":"Vector space","score":0.5028654932975769},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5015468597412109},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43427175283432007},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.401811808347702},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.31916821002960205},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2097814381122589},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13662827014923096},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11456283926963806},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.11115497350692749},{"id":"https://openalex.org/keywords/mathematics-education","display_name":"Mathematics education","score":0.057670801877975464}],"concepts":[{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.9751644134521484},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.8414050340652466},{"id":"https://openalex.org/C92951342","wikidata":"https://www.wikidata.org/wiki/Q1411166","display_name":"Orthonormality","level":3,"score":0.7724131345748901},{"id":"https://openalex.org/C84316537","wikidata":"https://www.wikidata.org/wiki/Q36255","display_name":"Unit vector","level":2,"score":0.7257150411605835},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.6590533256530762},{"id":"https://openalex.org/C92087593","wikidata":"https://www.wikidata.org/wiki/Q427389","display_name":"Vector (molecular biology)","level":4,"score":0.5558832883834839},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.5028654932975769},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5015468597412109},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43427175283432007},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.401811808347702},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.31916821002960205},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2097814381122589},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13662827014923096},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11456283926963806},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.11115497350692749},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.057670801877975464},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C40767141","wikidata":"https://www.wikidata.org/wiki/Q285697","display_name":"Recombinant DNA","level":3,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10867651.1999.10487513","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10867651.1999.10487513","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":[{"display_name":"Sustainable cities and communities","score":0.6200000047683716,"id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":2,"referenced_works":["https://openalex.org/W2041064634","https://openalex.org/W2798799102"],"related_works":["https://openalex.org/W2013801824","https://openalex.org/W1529452180","https://openalex.org/W1496788307","https://openalex.org/W2149054915","https://openalex.org/W2163754877","https://openalex.org/W4247890333","https://openalex.org/W151849613","https://openalex.org/W2799109646","https://openalex.org/W2017427737","https://openalex.org/W3023563117"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"show":[2],"how":[3],"to":[4],"easily":[5],"create":[6],"a":[7,12],"right-handed":[8],"orthonormal":[9],"basis,":[10],"given":[11],"unit":[13],"vector,":[14],"in":[15],"2\u2212,":[16],"3\u2212,":[17],"and":[18],"4-space.":[19]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
