{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T17:11:05Z","timestamp":1779210665992,"version":"3.51.4"},"reference-count":97,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T00:00:00Z","timestamp":1778889600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["JEMR"],"abstract":"<jats:p>Human eyes do not have perfectly aligned optical components; the fovea is displaced from the posterior pole, and the crystalline lens is tilted away from the eye\u2019s optical axis. Important in the study of vision quality, it is included here in binocular and oculomotor research. In the binocular system, with the eye\u2019s optical asymmetry, all axes differ. The eye\u2019s posture change is decomposed into the torsion-free part that gives the change in visual axis direction and the torsional part that best approximates the rotation about the lens\u2019s optical axis. This geometric formulation, supported by computer simulations and modern ophthalmology studies, leads to binocular Listing\u2019s law and the related half-angle rule, important for oculomotor control by constraining the eye\u2019s redundant torsional degree of freedom. The eye\u2019s primary position and the Listing plane, indispensable ingredients of Listing\u2019s law, are replaced with the binocular eyes\u2019 posture corresponding to the eye muscles\u2019 natural tonus resting position, which serves as a zero-reference level for convergence effort. Further, the binocular constraints couple 3D changes in the torsional positions of the eyes within the ab initio formulation of Listing\u2019s law here, which was previously proposed ad hoc. Finally, the noncommutativity rule underlying Listing\u2019s law and the half-angle rule are discussed by specifying the configuration space of sequences of fixations of binocularly constrained eyes, which are visualized in 3D simulations. The results obtained in this study should be a part of the answers to the questions posted in the literature on the relevance of Listing\u2019s law to clinical practices.<\/jats:p>","DOI":"10.3390\/jemr19030056","type":"journal-article","created":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T16:07:26Z","timestamp":1779206846000},"page":"56","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Ab Initio Binocular Formulation of Listing\u2019s Law"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7968-3980","authenticated-orcid":false,"given":"Jacek","family":"Turski","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, University of Houston-Downtown, One Main Street, Houston, TX 77002, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,5,16]]},"reference":[{"key":"ref_1","unstructured":"Southhall, J.P.C. 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