{"publication_status":"published","article_processing_charge":"No","date_published":"2023-08-01T00:00:00Z","volume":42,"month":"08","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_number":"73","publication_identifier":{"eissn":["1557-7368"],"issn":["0730-0301"]},"oa_version":"None","year":"2023","publisher":"Association for Computing Machinery","author":[{"last_name":"Vidulis","first_name":"Michele","full_name":"Vidulis, Michele"},{"first_name":"Yingying","id":"93d68d10-3540-11ef-a265-f748a50dba3d","full_name":"Ren, Yingying","last_name":"Ren"},{"full_name":"Panetta, Julian","first_name":"Julian","last_name":"Panetta"},{"last_name":"Grinspun","first_name":"Eitan","full_name":"Grinspun, Eitan"},{"full_name":"Pauly, Mark","first_name":"Mark","last_name":"Pauly"}],"issue":"4","quality_controlled":"1","abstract":[{"text":"We present an algorithmic approach to discover, study, and design multistable elastic knots. Elastic knots are physical realizations of closed curves embedded in 3-space. When endowed with the material thickness and bending resistance of a physical wire, these knots settle into equilibrium states that balance the forces induced by elastic deformation and self-contacts of the wire. In general, elastic knots can have many distinct equilibrium states, i.e. they are multistable mechanical systems. We propose a computational pipeline that combines randomized spatial sampling and physics simulation to efficiently find stable equilibrium states of elastic knots. Leveraging results from knot theory, we run our pipeline on thousands of different topological knot types to create an extensive data set of multistable knots. By applying a series of filters to this data, we discover new transformable knots with interesting geometric and physical properties. A further analysis across knot types reveals geometric and topological patterns, yielding constructive principles that generalize beyond the currently tabulated knot types. We show how multistable elastic knots can be used to design novel deployable structures and engaging recreational puzzles. Several physical prototypes at different scales highlight these applications and validate our simulation.","lang":"eng"}],"citation":{"ieee":"M. Vidulis, Y. Ren, J. Panetta, E. Grinspun, and M. Pauly, “Computational exploration of multistable elastic knots,” <i>ACM Transactions on Graphics</i>, vol. 42, no. 4. Association for Computing Machinery, 2023.","apa":"Vidulis, M., Ren, Y., Panetta, J., Grinspun, E., &#38; Pauly, M. (2023). Computational exploration of multistable elastic knots. <i>ACM Transactions on Graphics</i>. Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3592399\">https://doi.org/10.1145/3592399</a>","ama":"Vidulis M, Ren Y, Panetta J, Grinspun E, Pauly M. Computational exploration of multistable elastic knots. <i>ACM Transactions on Graphics</i>. 2023;42(4). doi:<a href=\"https://doi.org/10.1145/3592399\">10.1145/3592399</a>","short":"M. Vidulis, Y. Ren, J. Panetta, E. Grinspun, M. Pauly, ACM Transactions on Graphics 42 (2023).","ista":"Vidulis M, Ren Y, Panetta J, Grinspun E, Pauly M. 2023. Computational exploration of multistable elastic knots. ACM Transactions on Graphics. 42(4), 73.","chicago":"Vidulis, Michele, Yingying Ren, Julian Panetta, Eitan Grinspun, and Mark Pauly. “Computational Exploration of Multistable Elastic Knots.” <i>ACM Transactions on Graphics</i>. Association for Computing Machinery, 2023. <a href=\"https://doi.org/10.1145/3592399\">https://doi.org/10.1145/3592399</a>.","mla":"Vidulis, Michele, et al. “Computational Exploration of Multistable Elastic Knots.” <i>ACM Transactions on Graphics</i>, vol. 42, no. 4, 73, Association for Computing Machinery, 2023, doi:<a href=\"https://doi.org/10.1145/3592399\">10.1145/3592399</a>."},"doi":"10.1145/3592399","extern":"1","type":"journal_article","intvolume":"        42","title":"Computational exploration of multistable elastic knots","article_type":"original","language":[{"iso":"eng"}],"scopus_import":"1","date_created":"2024-08-05T06:29:22Z","day":"01","date_updated":"2024-08-12T09:48:36Z","status":"public","publication":"ACM Transactions on Graphics","_id":"17381"}