{"citation":{"mla":"Bächer, Moritz, et al. “Spin-It: Optimizing Moment of Inertia for Spinnable Objects.” <i>ACM Transactions on Graphics</i>, vol. 33, no. 4, 96, ACM, 2014, doi:<a href=\"https://doi.org/10.1145/2601097.2601157\">10.1145/2601097.2601157</a>.","short":"M. Bächer, E. Whiting, B. Bickel, O. Sorkine Hornung, ACM Transactions on Graphics 33 (2014).","ista":"Bächer M, Whiting E, Bickel B, Sorkine Hornung O. 2014. Spin-It: Optimizing moment of inertia for spinnable objects. ACM Transactions on Graphics. 33(4), 96.","chicago":"Bächer, Moritz, Emily Whiting, Bernd Bickel, and Olga Sorkine Hornung. “Spin-It: Optimizing Moment of Inertia for Spinnable Objects.” <i>ACM Transactions on Graphics</i>. ACM, 2014. <a href=\"https://doi.org/10.1145/2601097.2601157\">https://doi.org/10.1145/2601097.2601157</a>.","apa":"Bächer, M., Whiting, E., Bickel, B., &#38; Sorkine Hornung, O. (2014). Spin-It: Optimizing moment of inertia for spinnable objects. <i>ACM Transactions on Graphics</i>. ACM. <a href=\"https://doi.org/10.1145/2601097.2601157\">https://doi.org/10.1145/2601097.2601157</a>","ieee":"M. Bächer, E. Whiting, B. Bickel, and O. Sorkine Hornung, “Spin-It: Optimizing moment of inertia for spinnable objects,” <i>ACM Transactions on Graphics</i>, vol. 33, no. 4. ACM, 2014.","ama":"Bächer M, Whiting E, Bickel B, Sorkine Hornung O. Spin-It: Optimizing moment of inertia for spinnable objects. <i>ACM Transactions on Graphics</i>. 2014;33(4). doi:<a href=\"https://doi.org/10.1145/2601097.2601157\">10.1145/2601097.2601157</a>"},"article_processing_charge":"No","acknowledgement":"This project was supported in part by the ERC Starting Grant iModel (StG-2012-306877). Emily Whiting is supported by the ETH Zurich / Marie Curie COFUND Postdoctoral Fellowship.","author":[{"first_name":"Moritz","full_name":"Bächer, Moritz","last_name":"Bächer"},{"full_name":"Whiting, Emily","last_name":"Whiting","first_name":"Emily"},{"full_name":"Bickel, Bernd","id":"49876194-F248-11E8-B48F-1D18A9856A87","last_name":"Bickel","orcid":"0000-0001-6511-9385","first_name":"Bernd"},{"first_name":"Olga","full_name":"Sorkine Hornung, Olga","last_name":"Sorkine Hornung"}],"day":"01","extern":"1","article_number":"96","intvolume":"        33","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Spin-It: Optimizing moment of inertia for spinnable objects","type":"journal_article","publisher":"ACM","article_type":"original","publication_identifier":{"eissn":["1557-7368"],"issn":["0730-0301"]},"publication_status":"published","publication":"ACM Transactions on Graphics","abstract":[{"text":"Spinning tops and yo-yos have long fascinated cultures around the world with their unexpected, graceful motions that seemingly elude gravity. We present an algorithm to generate designs for spinning objects by optimizing rotational dynamics properties. As input, the user provides a solid 3D model and a desired axis of rotation. Our approach then modifies the mass distribution such that the principal directions of the moment of inertia align with the target rotation frame. We augment the model by creating voids inside its volume, with interior fill represented by an adaptive multi-resolution vox-elization. The discrete voxel fill values are optimized using a continuous, nonlinear formulation. Further, we optimize for rotational stability by maximizing the dominant principal moment. We extend our technique to incorporate deformation and multiple materials for cases where internal voids alone are insufficient. Our method is well-suited for a variety of 3D printed models, ranging from characters to abstract shapes. We demonstrate tops and yo-yos that spin surprisingly stably despite their asymmetric appearance. ","lang":"eng"}],"date_updated":"2025-08-05T14:20:24Z","volume":33,"related_material":{"record":[{"id":"452","status":"public","relation":"later_version"}]},"language":[{"iso":"eng"}],"_id":"2080","status":"public","month":"07","quality_controlled":"1","issue":"4","oa_version":"None","scopus_import":"1","date_published":"2014-07-01T00:00:00Z","doi":"10.1145/2601097.2601157","date_created":"2018-12-11T11:55:35Z","publist_id":"4958","year":"2014"}