Moritz Bächer
Emily Whiting
Bernd Bickel
Olga Sorkine-Hornung
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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 voxelization. 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.
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Supplemental material.
- Bächer, M., Bickel, B., James, D. L., and Pfister, H. 2012. Fabricating articulated characters from skinned meshes. ACM Trans. Graph. 31, 4, 47:1--47:9. Google Scholar
Digital Library
- Bendsøe, M., and Sigmund, O. 2012. Topology Optimization: Theory, Methods and Applications. Engineering online library. Springer.Google Scholar
- Bickel, B., Bächer, M., Otaduy, M. A., Lee, H. R., Pfister, H., Gross, M., and Matusik, W. 2010. Design and fabrication of materials with desired deformation behavior. ACM Trans. Graph. 29, 4. Google ScholarDigital Library
- Byrd, R. H., Nocedal, J., and Waltz, R. A. 2006. Knitro: An integrated package for nonlinear optimization. In Large-scale nonlinear optimization. Springer, 35--59.Google Scholar
- Calì, J., Calian, D. A., Amati, C., Kleinberger, R., Steed, A., Kautz, J., and Weyrich, T. 2012. 3D-printing of non-assembly, articulated models. ACM Trans. Graph. 31, 6, 130:1--130:8. Google ScholarDigital Library
- Ceylan, D., Li, W., Mitra, N., Agrawala, M., and Pauly, M. 2013. Designing and fabricating mechanical automata from mocap sequences. ACM Trans. Graph. 32, 6. Google ScholarDigital Library
- Chen, D., Levin, D. I. W., Didyk, P., Sitthi-Amorn, P., and Matusik, W. 2013. Spec2Fab: A reducer-tuner model for translating specifications to 3D prints. ACM Trans. Graph. 32, 4, 135:1--135:10. Google ScholarDigital Library
- Cohen, R. J. 1977. The tippe top revisited. American Journal of Physics 45, 1, 12--17.Google ScholarCross Ref
- Coros, S., Thomaszewski, B., Noris, G., Sueda, S., Forberg, M., Sumner, R. W., Matusik, W., and Bickel, B. 2013. Computational design of mechanical characters. ACM Trans. Graph. 32, 4, 83:1--83:12. Google ScholarDigital Library
- Crabtree, H. 1909. An Elementary Treatment of the Theory of Spinning Tops. Longmans, Green and Co.Google Scholar
- Cross, R. 2013. The rise and fall of spinning tops. American Journal of Physics 81, 280.Google ScholarCross Ref
- DeRose, G. C. J., and Díaz, A. R. 1996. Hierarchical solution of large-scale three-dimensional topology optimization problems. In ASME Design Engineering Technical Conferences and Computers in Engineering Conference.Google Scholar
- Eberly, D. H. 2003. Game Physics. Elsevier Science Inc. Google ScholarDigital Library
- Fletcher, R. 1987. Practical Methods of Optimization; (2Nd Ed.). Wiley-Interscience, New York, NY, USA. Google ScholarCross Ref
- Furuta, Y., Mitani, J., Igarashi, T., and Fukui, Y. 2010. Kinetic art design system comprising rigid body simulation. Computer-Aided Design and Applications 7, 4, 533--546.Google ScholarCross Ref
- Gajamohan, M., Merz, M., Thommen, I., and D'Andrea, R. 2012. The Cubli: A cube that can jump up and balance. In Proc. IROS, IEEE, 3722--3727.Google ScholarCross Ref
- Goldstein, H., Poole, C., and Safko, J. 2001. Classical Mechanics, 3rd ed. Addison Wesley.Google Scholar
- Gould, D. 1975. The Top: Universal Toy Enduring Pastime. Bailey Brothers and Swinfen Ltd.Google Scholar
- Hirose, M., Mitani, J., Kanamori, Y., and Fukui, Y. 2011. An interactive design system for sphericon-based geometric toys using conical voxels. In Proc. International Conference on Smart Graphics, 37--47. Google ScholarDigital Library
- Hullin, M. B., Ihrke, I., Heidrich, W., Weyrich, T., Damberg, G., and Fuchs, M. 2013. Computational fabrication and display of material appearance. In Eurographics State-of-the-Art Reports (STAR), 17 pages.Google Scholar
- Jacobson, A., Baran, I., Popović, J., and Sorkine, O. 2011. Bounded biharmonic weights for real-time deformation. ACM Trans. Graph. 30, 4, 78:1--78:8. Google ScholarDigital Library
- Jacobson, A., Baran, I., Kavan, L., Popović, J., and Sorkine, O. 2012. Fast automatic skinning transformations. ACM Transactions on Graphics (proceedings of ACM SIGGRAPH) 31, 4, 77:1--77:10. Google ScholarDigital Library
- Kang, Z., Wang, X., and Wang, R. 2009. Topology optimization of space vehicle structures considering attitude control effort. Finite Elements in Analysis and Design 45, 431--438. Google ScholarDigital Library
- König, O., and Wintermantel, M., 2004. CAD-based evolutionary design optimization with CATIA V5. 1st Weimar Optimization and Stochastic Days.Google Scholar
- Lewis, D., Ratiu, T., Simo, J. C., and Marsden, J. E. 1992. The heavy top: a geometric treatment. Nonlinearity 5, 1, 1.Google ScholarCross Ref
- Luo, L., Baran, I., Rusinkiewicz, S., and Matusik, W. 2012. Chopper: partitioning models into 3D-printable parts. ACM Trans. Graph. 31, 6, 129:1--129:9. Google ScholarDigital Library
- Macchietto, A., Zordan, V., and Shelton, C. R. 2009. Momentum control for balance. ACM Trans. Graph. 28, 3. Google ScholarDigital Library
- Malko, G. 1978. The One and Only Yo-Yo Book. Avon.Google Scholar
- Nocedal, J., and Wright, S. J. 2000. Numerical Optimization. Springer.Google Scholar
- Perry, J. 1957. Spinning Tops and Gyroscopic Motion. Dover Publications.Google Scholar
- Prévost, R., Whiting, E., Lefebvre, S., and Sorkine-Hornung, O. 2013. Make It Stand: Balancing shapes for 3D fabrication. ACM Trans. Graph. 32, 4, 81:1--81:10. Google ScholarDigital Library
- Proos, K., Steven, G., Querin, O., and Xie, Y. 2001. Stiffness and inertia multicriteria evolutionary structural optimisation. Engineering Computations 18, 7, 1031--1054.Google ScholarCross Ref
- Provatidis, C. G. 2012. Revisiting the spinning top. International Journal of Material and Mechanical Engineering (IJMME) 1, 4, 71--88.Google Scholar
- Skouras, M., Thomaszewski, B., Coros, S., Bickel, B., and Gross, M. 2013. Computational design of actuated deformable characters. ACM Trans. Graph. 32, 4, 82:1--82:10. Google ScholarDigital Library
- Sorkine, O., Cohen-Or, D., Lipman, Y., Alexa, M., Rössl, C., and Seidel, H.-P. 2004. Laplacian surface editing. In Proc. Symposium on Geometry Processing, 179--188. Google ScholarDigital Library
- Stava, O., Vanek, J., Benes, B., Carr, N., and Měch, R. 2012. Stress relief: Improving structural strength of 3D printable objects. ACM Trans. Graph. 31, 4, 48:1--48:11. Google ScholarDigital Library
- Umetani, N., and Schmidt, R. 2013. Cross-sectional structural analysis for 3D printing optimization. In SIGGRAPH Asia 2013 Technical Briefs, 5:1--5:4. Google ScholarDigital Library
- Vidimče, K., Wang, S.-P., Ragan-Kelley, J., and Matusik, W. 2013. OpenFab: A programmable pipeline for multi-material fabrication. ACM Trans. Graph. 32, 4, 136:1--136:12. Google ScholarDigital Library
- Wang, W., Wang, T. Y., Yang, Z., Liu, L., Tong, X., Tong, W., Deng, J., Chen, F., and Liu, X. 2013. Cost-effective printing of 3D objects with skin-frame structures. ACM Trans. Graph. 32, 6, 177:1--177:10. Google ScholarDigital Library
- Zhou, Q., Panetta, J., and Zorin, D. 2013. Worst-case structural analysis. ACM Trans. Graph. 32, 4, 137:1--137:12. Google ScholarDigital Library
- Zhou, Y., Sueda, S., Matusik, W., and Shamir, A. 2014. Boxelization: Folding 3d objects into boxes. ACM Trans. Graph. 33, 4 (Jul), (to appear). Google ScholarDigital Library
- Zhu, L., Xu, W., Snyder, J., Liu, Y., Wang, G., and Guo, B. 2012. Motion-guided mechanical toy modeling. ACM Trans. Graph. 31, 6, 127. Google ScholarDigital Library
Index Terms
- Spin-it: optimizing moment of inertia for spinnable objects
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