{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/arbitrary-unitary-rotation-of-three","title":"Arbitrary unitary rotation of three-dimensional pixellated images","arxiv_id":"2207.13308","date":"2022-07-27","proceeding":null,"authors":["Alejandro R. Urzúa","Kurt Bernardo Wolf"],"abstract":"Using the coefficients introduced by Bargmann and Moshinsky for the reduction of the su($3$) algebra of Cartesian three-dimensional oscillator multiplet states into so($3$) angular momentum submultiplets, we implement unitary rotations of three-dimensional Cartesian arrays that form finite pixellated \"volume images.\" Transforming between the Cartesian and spherical bases, the subgroup of rotations in the latter is converted into rotations of the former, allowing for proper concatenation and inversion of these unitary transformations, which entail no loss of information.","url_abs":"https://arxiv.org/abs/2207.13308v2","url_pdf":"https://arxiv.org/pdf/2207.13308v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"arbitrary-unitary-rotation-of-three","repo_url":"https://github.com/rurz/UnitRots","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}