{"id":"https://openalex.org/W3046704612","doi":"https://doi.org/10.34768/amcs-2020-0012","title":"An algorithm for quaternion-based 3D rotation","display_name":"An algorithm for quaternion-based 3D rotation","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3046704612","doi":"https://doi.org/10.34768/amcs-2020-0012","mag":"3046704612"},"language":"en","primary_location":{"id":"doi:10.34768/amcs-2020-0012","is_oa":true,"landing_page_url":"https://doi.org/10.34768/amcs-2020-0012","pdf_url":"https://sciendo.com/pdf/10.34768/amcs-2020-0012","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://sciendo.com/pdf/10.34768/amcs-2020-0012","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019629900","display_name":"Aleksandr Cariow","orcid":"https://orcid.org/0000-0002-4513-4593"},"institutions":[{"id":"https://openalex.org/I155313962","display_name":"West Pomeranian University of Technology","ror":"https://ror.org/0596m7f19","country_code":"PL","type":"education","lineage":["https://openalex.org/I155313962"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Aleksandr Cariow","raw_affiliation_strings":["Faculty of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin"],"affiliations":[{"raw_affiliation_string":"Faculty of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin","institution_ids":["https://openalex.org/I155313962"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053225722","display_name":"Galina Cariowa","orcid":"https://orcid.org/0000-0002-3859-484X"},"institutions":[{"id":"https://openalex.org/I155313962","display_name":"West Pomeranian University of Technology","ror":"https://ror.org/0596m7f19","country_code":"PL","type":"education","lineage":["https://openalex.org/I155313962"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Galina Cariowa","raw_affiliation_strings":["Faculty of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin"],"affiliations":[{"raw_affiliation_string":"Faculty of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin","institution_ids":["https://openalex.org/I155313962"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036530734","display_name":"Dorota Majorkowska-Mech","orcid":"https://orcid.org/0000-0002-2123-0521"},"institutions":[{"id":"https://openalex.org/I155313962","display_name":"West Pomeranian University of Technology","ror":"https://ror.org/0596m7f19","country_code":"PL","type":"education","lineage":["https://openalex.org/I155313962"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Dorota Majorkowska-Mech","raw_affiliation_strings":["Faculty of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin"],"affiliations":[{"raw_affiliation_string":"Faculty of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin","institution_ids":["https://openalex.org/I155313962"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5036530734"],"corresponding_institution_ids":["https://openalex.org/I155313962"],"apc_list":{"value":4080,"currency":"PLN","value_usd":1100},"apc_paid":{"value":4080,"currency":"PLN","value_usd":1100},"fwci":1.5881,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.87208681,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"30","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9747999906539917,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9747999906539917,"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9726999998092651,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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":0.96670001745224,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/quaternion","display_name":"Quaternion","score":0.9538928270339966},{"id":"https://openalex.org/keywords/rotation","display_name":"Rotation (mathematics)","score":0.7455234527587891},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5918969511985779},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.574439525604248},{"id":"https://openalex.org/keywords/rotation-matrix","display_name":"Rotation matrix","score":0.5286422371864319},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4407520294189453},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33832669258117676},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10550928115844727}],"concepts":[{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.9538928270339966},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.7455234527587891},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5918969511985779},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.574439525604248},{"id":"https://openalex.org/C83633838","wikidata":"https://www.wikidata.org/wiki/Q1256564","display_name":"Rotation matrix","level":2,"score":0.5286422371864319},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4407520294189453},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33832669258117676},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10550928115844727}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.34768/amcs-2020-0012","is_oa":true,"landing_page_url":"https://doi.org/10.34768/amcs-2020-0012","pdf_url":"https://sciendo.com/pdf/10.34768/amcs-2020-0012","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:421961f6772640d780828f8218470e73","is_oa":true,"landing_page_url":"https://doaj.org/article/421961f6772640d780828f8218470e73","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Applied Mathematics and Computer Science, Vol 30, Iss 1, Pp 149-160 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.34768/amcs-2020-0012","is_oa":true,"landing_page_url":"https://doi.org/10.34768/amcs-2020-0012","pdf_url":"https://sciendo.com/pdf/10.34768/amcs-2020-0012","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W3046704612.pdf"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W28559072","https://openalex.org/W260898655","https://openalex.org/W334428825","https://openalex.org/W584835857","https://openalex.org/W605887985","https://openalex.org/W1527786550","https://openalex.org/W1530680819","https://openalex.org/W1575685434","https://openalex.org/W1586011495","https://openalex.org/W1596451335","https://openalex.org/W1807725195","https://openalex.org/W1936177838","https://openalex.org/W1972673941","https://openalex.org/W1994236486","https://openalex.org/W2007876834","https://openalex.org/W2015733920","https://openalex.org/W2016959837","https://openalex.org/W2097854005","https://openalex.org/W2098748390","https://openalex.org/W2100506000","https://openalex.org/W2125120409","https://openalex.org/W2132518575","https://openalex.org/W2135882834","https://openalex.org/W2145412836","https://openalex.org/W2145741013","https://openalex.org/W2149448901","https://openalex.org/W2151735125","https://openalex.org/W2152816064","https://openalex.org/W2161469547","https://openalex.org/W2162334919","https://openalex.org/W2170065176","https://openalex.org/W2277883734","https://openalex.org/W2284467420","https://openalex.org/W2293451440","https://openalex.org/W2297059176","https://openalex.org/W2482637621","https://openalex.org/W2601557837","https://openalex.org/W2901775224","https://openalex.org/W3101105363","https://openalex.org/W4229748564","https://openalex.org/W4244978400","https://openalex.org/W4247824879","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2388930076","https://openalex.org/W2511668269","https://openalex.org/W2091132606","https://openalex.org/W2106549822","https://openalex.org/W2348328811","https://openalex.org/W1544024058","https://openalex.org/W2074615279","https://openalex.org/W4320038180","https://openalex.org/W1490500322","https://openalex.org/W2382267983"],"abstract_inverted_index":{"In":[0],"this":[1],"work":[2],"a":[3,23,27,64],"new":[4],"algorithm":[5,51],"for":[6],"quaternion-based":[7,24],"spatial":[8],"rotation":[9,25,28],"is":[10],"presented":[11],"which":[12],"reduces":[13],"the":[14,49,54],"number":[15],"of":[16,22,45],"underlying":[17],"real":[18,46,60],"multiplications.":[19],"The":[20],"performing":[21],"using":[26],"matrix":[29],"takes":[30],"15":[31],"ordinary":[32],"multiplications,":[33],"6":[34],"trivial":[35],"multiplications":[36,61],"by":[37,73,79],"2":[38],"(left-shifts),":[39],"21":[40],"additions,":[41,69],"and":[42,75],"4":[43,70],"squarings":[44],"numbers,":[47],"while":[48],"proposed":[50],"can":[52],"compute":[53],"same":[55],"result":[56],"in":[57],"only":[58],"14":[59],"(or":[62],"multipliers\u2014in":[63],"hardware":[65],"implementation":[66],"case),":[67],"43":[68],"right-shifts":[71],"(multiplications":[72,78],"1/4),":[74],"3":[76],"left-shifts":[77],"2).":[80]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4}],"updated_date":"2026-03-31T07:56:22.981413","created_date":"2025-10-10T00:00:00"}
