Bächer, Moritz; Bickel, BerndISTA ; Whiting, Emily; Sorkine Hornung, Olga
Spinning tops and yo-yos have long fascinated cultures around the world with their unexpected, graceful motions that seemingly elude gravity. Yet, due to the exceeding difficulty of creating stably spinning objects of asymmetric shape in a manual trial-and-error process, there has been little departure from rotationally symmetric designs. With modern 3D printing technologies, however, we can manufacture shapes of almost unbounded complexity at the press of a button, shifting this design complexity toward computation. In this article, we describe an algorithm to generate designs for spinning objects by optimizing their mass distribution: as input, the user provides a solid 3D model and a desired axis of rotation. Our approach then modifies the interior mass distribution such that the principal directions of the moment of inertia align with the target rotation frame. To create voids inside the model, we represent its volume with an adaptive multiresolution voxelization and optimize the discrete voxel fill values using a continuous, nonlinear formulation. We further optimize for rotational stability by maximizing the dominant principal moment. 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.
Communications of the ACM
This project was supported in part by the ERC Starting Grant iModel (StG-2012-306877). Emily Whiting was supported by the ETH Zurich/Marie Curie COFUND Postdoctoral Fellowship. First and foremost, we would like to thank our editor Steve Marschner for his invaluable feedback. We were fortunate to get further help from Maurizio Nitti for model design, Romain Prévost for Make-It-Stand comparisons, Alexander Sorkine-Hornung, Kaan Yücer, and Changil Kim for video and photo assistance, Ronnie Gänsli for metal casting, Alec Jacobson for the posed Elephant and Armadillo models, and Romain Prévost and Amit Bermano for print preparation. Model sources include: Woven Ring: generated by “Sculpture Generator 1” by Carlo H. Séquin, UC Berkeley; Elephant: De Espona model library, courtesy of Robert Sumner; T-Rex: TurboSquid; Armadillo: Stanford Computer Graphics Laboratory; and Utah Teapot: Martin Newell, University of Utah.
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Bächer M, Bickel B, Whiting E, Sorkine Hornung O. Spin it: Optimizing moment of inertia for spinnable objects. Communications of the ACM. 2017;60(8):92-99. doi:10.1145/3068766
Bächer, M., Bickel, B., Whiting, E., & Sorkine Hornung, O. (2017). Spin it: Optimizing moment of inertia for spinnable objects. Communications of the ACM. ACM. https://doi.org/10.1145/3068766
Bächer, Moritz, Bernd Bickel, Emily Whiting, and Olga Sorkine Hornung. “Spin It: Optimizing Moment of Inertia for Spinnable Objects.” Communications of the ACM. ACM, 2017. https://doi.org/10.1145/3068766.
M. Bächer, B. Bickel, E. Whiting, and O. Sorkine Hornung, “Spin it: Optimizing moment of inertia for spinnable objects,” Communications of the ACM, vol. 60, no. 8. ACM, pp. 92–99, 2017.
Bächer M, Bickel B, Whiting E, Sorkine Hornung O. 2017. Spin it: Optimizing moment of inertia for spinnable objects. Communications of the ACM. 60(8), 92–99.
Bächer, Moritz, et al. “Spin It: Optimizing Moment of Inertia for Spinnable Objects.” Communications of the ACM, vol. 60, no. 8, ACM, 2017, pp. 92–99, doi:10.1145/3068766.