{"doi":"10.1002/cav.1529","title":"Euler angles: conversion of arbitrary rotation sequences to specific rotation sequence","abstract":"<jats:title>ABSTRACT</jats:title><jats:p>Euler angles have been used to describe the orientation of objects in two‐dimensional and three‐dimensional spaces since its formulation by Leonhard Euler. Many applications intended to represent the rotation of a body have been developed on the basis of Euler angles. Two‐dimensional rotations are combined in sequence to represent three‐dimensional rotations. Because there are three axes in a three‐dimensional Euclidean space (<jats:italic>X</jats:italic>, <jats:italic>Y</jats:italic> and <jats:italic>Z</jats:italic>), 12 rotation sequences in three dimensions are possible: <jats:italic>XYZ</jats:italic>, <jats:italic>XZY</jats:italic>, <jats:italic>YXZ</jats:italic>, <jats:italic>YZX</jats:italic>, <jats:italic>ZXY</jats:italic>, <jats:italic>ZYX</jats:italic>, <jats:italic>XYX</jats:italic>, <jats:italic>ZYZ</jats:italic>, <jats:italic>ZXZ</jats:italic>, <jats:italic>YXY</jats:italic>, <jats:italic>XZX</jats:italic> and <jats:italic>YZY</jats:italic>. Each rotation sequence yields different results, and different applications implement a different rotation sequence. Thus, conversion between different rotation sequences becomes essential to make applications developed in different rotation sequences compatible with each other. In this paper, a new method is introduced to convert arbitrary rotation sequences to a specific rotation sequence of choice. A sample program is also developed in a MATLAB‐Simulink environment to demonstrate the use of the new method in converting an arbitrary Euler rotation sequence to the specific Euler rotation sequence of <jats:italic>XYZ</jats:italic>. A six‐degrees‐of‐freedom animation block is used in the program to aid users to graphically see the rotation of a body in three‐dimensional space. Copyright © 2013 John Wiley &amp; Sons, Ltd.</jats:p>","journal":"Computer Animation and Virtual Worlds","year":2014,"id":595365,"datarank":0.29188652235829704,"base_score":1.9459101490553132,"endowment":1.9459101490553132,"self_citation_contribution":0.29188652235829704,"citation_network_contribution":0.0,"self_endowment_contribution":0.29188652235829704,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":6,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":null,"is_data_producer":false,"deposit_databanks":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":null,"fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":1524514,"name":"Logah Perumal","orcid":null,"position":0,"is_corresponding":false}],"reference_count":0,"raw_metadata":{"has_enrichment":true,"resolved":true,"title":"Euler angles: conversion of arbitrary rotation sequences to specific rotation sequence","abstract":"<jats:title>ABSTRACT</jats:title><jats:p>Euler angles have been used to describe the orientation of objects in two‐dimensional and three‐dimensional spaces since its formulation by Leonhard Euler. Many applications intended to represent the rotation of a body have been developed on the basis of Euler angles. Two‐dimensional rotations are combined in sequence to represent three‐dimensional rotations. Because there are three axes in a three‐dimensional Euclidean space (<jats:italic>X</jats:italic>, <jats:italic>Y</jats:italic> and <jats:italic>Z</jats:italic>), 12 rotation sequences in three dimensions are possible: <jats:italic>XYZ</jats:italic>, <jats:italic>XZY</jats:italic>, <jats:italic>YXZ</jats:italic>, <jats:italic>YZX</jats:italic>, <jats:italic>ZXY</jats:italic>, <jats:italic>ZYX</jats:italic>, <jats:italic>XYX</jats:italic>, <jats:italic>ZYZ</jats:italic>, <jats:italic>ZXZ</jats:italic>, <jats:italic>YXY</jats:italic>, <jats:italic>XZX</jats:italic> and <jats:italic>YZY</jats:italic>. Each rotation sequence yields different results, and different applications implement a different rotation sequence. Thus, conversion between different rotation sequences becomes essential to make applications developed in different rotation sequences compatible with each other. In this paper, a new method is introduced to convert arbitrary rotation sequences to a specific rotation sequence of choice. A sample program is also developed in a MATLAB‐Simulink environment to demonstrate the use of the new method in converting an arbitrary Euler rotation sequence to the specific Euler rotation sequence of <jats:italic>XYZ</jats:italic>. A six‐degrees‐of‐freedom animation block is used in the program to aid users to graphically see the rotation of a body in three‐dimensional space. Copyright © 2013 John Wiley &amp; Sons, Ltd.</jats:p>","is_dataset_classified":null,"base_score":1.9459101490553132,"endowment":1.9459101490553132,"datacite_reuse_total":0,"file_count":0,"downloads":0,"views":0,"has_version_chain":false,"is_dataset":false,"is_oa":false,"pmid":"21097893","pmcid":null,"openalex_id":"https://openalex.org/W1955447130","authors":[],"funders":[],"total_grants":0,"fwci":0.0,"citation_percentile":0.48590232,"influential_citations":0,"citation_trend":[{"year":2017,"count":1},{"year":2018,"count":1},{"year":2023,"count":1},{"year":2025,"count":1},{"year":2026,"count":2}],"oa_status":"closed","license":"http://onlinelibrary.wiley.com/termsAndConditions#vor","oa_locations":[{"url":"https://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1002%2Fcav.1529","host_type":"publisher"},{"url":"https://onlinelibrary.wiley.com/doi/pdf/10.1002/cav.1529","host_type":"publisher"},{"url":"https://doi.org/10.1002/cav.1529","host_type":"journal"},{"url":"http://shdl.mmu.edu.my/5836/","host_type":"repository"}],"fields_of_study":["Aerospace Engineering and Control Systems","Mathematics and Applications","Algebraic and Geometric Analysis"],"mesh_terms":[],"keywords":["Rotation (mathematics)","Euler angles","Euler's rotation theorem","Euler's formula","Sequence (biology)","Computer science","Orientation (vector space)","Translation (biology)","Block (permutation group theory)","Rotation around a fixed axis","Euclidean space","Angle of rotation","Algorithm","Geometry","Mathematics","Mathematical analysis","Physics","Computer vision","Classical mechanics"],"sdg_mappings":[{"sdg_number":0,"sdg_label":"Peace, Justice and strong institutions"}],"linked_datasets":[],"clinical_trials":[],"software_tools":[],"database_accessions":[],"source":"live","citation_network_status":"fetched"},"created_at":"2026-07-27T17:18:22.824046Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}