The Rubik’s Cube was the first in a very long line of complicated 3D puzzles of varying geometries and complexities popularized in the 1980s. But the development of the specialized geometry that makes these “twisty puzzles” work has had far more uses than just making children’s games.
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Computational Design of Twisty Joints and Puzzles (SIGGRAPH 2015)
by Timothy Sun and Changxi Zheng
Technical Paper at SIGGRAPH 2015
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.