Computational Design of Twisty Joints and Puzzles

Timothy Sun and Changxi Zheng


We present the first computational method that allows ordinary users to create complex twisty joints and puzzles inspired by the Rubik's Cube mechanism. Given a user-supplied 3D model and a small subset of rotation axes, our method automatically adjusts those rotation axes and adds others to construct a "non-blocking" twisty joint in the shape of the 3D model. Our method outputs the shapes of pieces which can be directly 3D printed and assembled into an interlocking puzzle. We develop a group-theoretic approach to representing a wide class of twisty puzzles by establishing a connection between non-blocking twisty joints and the finite subgroups of the rotation group SO(3). The theoretical foundation enables us to build an efficient system for automatically completing the set of rotation axes and fast collision detection between pieces. We also generalize the Rubik's Cube mechanism to a large family of twisty puzzles.




bibtex Timothy Sun, Changxi Zheng, Computational Design of Twisty Joints and Puzzles, ACM Transactions on Graphics 34(4) (Proc. SIGGRAPH 2015), Aug, 2015.


We thank the anonymous reviewers for their feedback. We also thank Yun Fei for assistance in preparing the video, Dingzeyu Li for help on making figures, and Akash Garg, Yonghao Yue, and Shuang Zhao for their comments on earlier drafts. This research was supported in part by the National Science Foundation (CAREER-1453101) and generous gifts from Intel. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of funding agencies or others.


Columbia University

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