Computational Design of Twisty Joints and Puzzles

摘要

We present the first computational method that allows ordinaryrnusers to create complex twisty joints and puzzles inspired byrnthe Rubik’s Cube mechanism. Given a user-supplied 3D modelrnand a small subset of rotation axes, our method automaticallyrnadjusts those rotation axes and adds others to construct a “nonblocking”rntwisty joint in the shape of the 3D model. Our methodrnoutputs the shapes of pieces which can be directly 3D printedrnand assembled into an interlocking puzzle. We develop a grouptheoreticrnapproach to representing a wide class of twisty puzzlesrnby establishing a connection between non-blocking twisty jointsrnand the finite subgroups of the rotation group SO(3). The theoreticalrnfoundation enables us to build an efficient system forrnautomatically completing the set of rotation axes and fast collisionrndetection between pieces. We also generalize the Rubik’srnCube mechanism to a large family of twisty puzzles.