{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,1,6]],"date-time":"2025-01-06T12:40:35Z","timestamp":1736167235624,"version":"3.32.0"},"reference-count":27,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2024,8,27]],"date-time":"2024-08-27T00:00:00Z","timestamp":1724716800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"DOI":"10.13039\/100009235","name":"Australian Society of Orthodontists Foundation for Research and Education","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100009235","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Orthod Craniofacial Res"],"published-print":{"date-parts":[[2025,2]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:sec><jats:title>Intro<\/jats:title><jats:p>The aim of the current study was to develop and describe a new measuring system for the orientation of a tooth in a digitalized cast of a jaw and provide new angular values for the rotation, torque and tip of maxillary and mandibular teeth.<\/jats:p><\/jats:sec><jats:sec><jats:title>Methods<\/jats:title><jats:p>This retrospective cross\u2010sectional study involved the utilization of a sub\u2010group of extrinsic Euler\u2010angles to derive optimal norm values per tooth in three different planes of orientation (\u2018rotation\u2019, \u2018torque\u2019 and \u2018tip\u2019) by evaluating the digital representations of the teeth derived from a database containing over 17,500 patients. The process involved the entry of the .stl files of the jaw pairs into a fully automated software system (Smyl:Ai, Ulm, Germany) whereupon jaw alignment, teeth segmentation, landmark identification and visual validation of input files was conducted prior to calculation of the norm values for the three different planes of orientation.<\/jats:p><\/jats:sec><jats:sec><jats:title>Results<\/jats:title><jats:p>The digital scans in stereolithography (.STL)\u2010file format of the upper and lower dentitions of 1914 individuals with optimal occlusion were chosen and evaluated. New mean (standard deviation) angular values were determined for the rotation, torque and tip of maxillary and mandibular teeth.<\/jats:p><\/jats:sec><jats:sec><jats:title>Conclusion<\/jats:title><jats:p>The findings facilitate the reappraisal of rotation, torque and tip values currently acceptable as ideal. They will inform anthropologists and dental researchers about occlusion and alignment in orthodontic and non\u2010orthodontic patients and provide baseline data for future studies. The methodology will also enable the evaluation of large numbers of data in relatively short timeframes.<\/jats:p><\/jats:sec>","DOI":"10.1111\/ocr.12848","type":"journal-article","created":{"date-parts":[[2024,8,27]],"date-time":"2024-08-27T09:31:10Z","timestamp":1724751070000},"page":"75-83","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Euler\u2010angle norms for tooth rotation, torque and tip"],"prefix":"10.1111","volume":"28","author":[{"given":"Benjamin","family":"Steinvorth","sequence":"first","affiliation":[{"name":"YOUniquehorns GmbH  Ulm Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stefano","family":"Troiani","sequence":"additional","affiliation":[{"name":"Private Practice  Zurich Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tony","family":"Weir","sequence":"additional","affiliation":[{"name":"Adelaide Dental School, University of Adelaide  Adelaide South Australia Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maurice J.","family":"Meade","sequence":"additional","affiliation":[{"name":"PR Begg Chair in Orthodontics Adelaide Dental School, University of Adelaide  Adelaide South Australia Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2024,8,27]]},"reference":[{"key":"e_1_2_11_2_1","doi-asserted-by":"publisher","DOI":"10.1038\/sj.bdj.4810592"},{"key":"e_1_2_11_3_1","doi-asserted-by":"publisher","DOI":"10.1038\/sj.bdj.4810724"},{"key":"e_1_2_11_4_1","doi-asserted-by":"publisher","DOI":"10.3390\/ijerph19127446"},{"key":"e_1_2_11_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0002-9416(72)90268-0"},{"key":"e_1_2_11_6_1","doi-asserted-by":"publisher","DOI":"10.1093\/ejo\/cjr126"},{"key":"e_1_2_11_7_1","doi-asserted-by":"publisher","DOI":"10.2319\/061421-474.1"},{"key":"e_1_2_11_8_1","first-page":"581","article-title":"2020 JCO study of orthodontic diagnosis and treatment procedures part 1: results and trends","volume":"54","author":"Keim RG","year":"2020","journal-title":"J Clin Orthod"},{"key":"e_1_2_11_9_1","first-page":"138","article-title":"2020 survey of Australian orthodontists' procedures","volume":"36","author":"Miles P","year":"2020","journal-title":"Aust Orthod J"},{"key":"e_1_2_11_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ajodo.2022.08.018"},{"key":"e_1_2_11_11_1","doi-asserted-by":"publisher","DOI":"10.1177\/14653125231204889"},{"key":"e_1_2_11_12_1","doi-asserted-by":"publisher","DOI":"10.1111\/ocr.12517"},{"key":"e_1_2_11_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jormas.2023.101524"},{"key":"e_1_2_11_14_1","doi-asserted-by":"publisher","DOI":"10.1177\/14653125231166015"},{"key":"e_1_2_11_15_1","doi-asserted-by":"publisher","DOI":"10.2319\/111422-783.1"},{"key":"e_1_2_11_16_1","doi-asserted-by":"publisher","DOI":"10.1186\/s40510-022-00402-x"},{"key":"e_1_2_11_17_1","doi-asserted-by":"publisher","DOI":"10.21307\/aoj-2021-011"},{"key":"e_1_2_11_18_1","doi-asserted-by":"publisher","DOI":"10.2319\/022717-147.1"},{"key":"e_1_2_11_19_1","doi-asserted-by":"publisher","DOI":"10.1186\/2196-1042-14-19"},{"key":"e_1_2_11_20_1","doi-asserted-by":"publisher","DOI":"10.2319\/022423-128.1"},{"key":"e_1_2_11_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijsu.2014.07.013"},{"key":"e_1_2_11_22_1","unstructured":"RoseD.Rotations in three\u2010dimensions: euler angles and rotation matrices.2015.http:\/\/danceswithcode.net\/engineeringnotes\/index.html"},{"volume-title":"Total Least Squares CEE 629","year":"2017","author":"Gavin HP","key":"e_1_2_11_23_1"},{"volume-title":"Handbook of Mathematics","year":"1985","author":"Bronshtein IN","key":"e_1_2_11_24_1"},{"key":"e_1_2_11_25_1","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0276302"},{"key":"e_1_2_11_26_1","unstructured":"The Julia Programming Language.https:\/\/julialang.org\/2024."},{"key":"e_1_2_11_27_1","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1016\/j.ajodo.2024.06.008","article-title":"Efficacy of planned moderate to severe torque changes in maxillary central incisors with the Invisalign appliance: a retrospective investigation","volume":"166","author":"Rajan N","year":"2024","journal-title":"Am J Orthod Dentofacial Orthop"},{"key":"e_1_2_11_28_1","doi-asserted-by":"publisher","DOI":"10.3390\/jcm12020532"}],"container-title":["Orthodontics &amp; 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