video: The popular Rubik's cube is a 3-D puzzle composed of 26 separate interlocking pieces that rotate along six rotation axes, each of which can be moved independently. While the most well-known Rubik's cube is a square, others are constructed using different geometric shapes (tetrahedron, octahedron, dodecahedron, icosahedron); together they compose a class of twisty joint puzzles. Now two Columbia Engineering researchers have greatly expanded what else can be included in this class of puzzles. Changxi Zheng, assistant professor of computer science, and his PHD student Timothy Sun have developed an algebraic method that makes it possible for ordinary users to create twisty joint puzzles out of almost any arbitrary 3D object. Given rotation axes defined by the user, the method automatically adjusts the supplied axes while adding others to ensure all parts rotate freely. So that rotating pieces do not block or collide with one another, all possible configurations of pairs of pieces are enumerated (by defining a group structure on the pieces). Should a possible collision be detected, the pieces are automatically deformed--while retaining as much of the original form as possible--to ensure free rotation of all parts and yield a workable twisty joint. Holding all pieces together is an internal mechanism where the centers (which rotate in place) of each rotation axis are connected together. This internal mechanism is generated so that all pieces, once assembled, snap together and interlock with one another to form a working puzzle. No screws or springs are needed, thereby facilitating 3D printing of the snapping mechanism. The work is both original--representing a new theoretical result--and sophisticated, drawing on algebraic methods to determine the best places to put rotation axes. Wednesday, August 12, 10:45 am to 12:15 pm Links: http://www.cs.columbia.edu/cg/twisty/ VIDEO: https://youtu.be/M6OI8qjeNnE ZHENG: http://www.cs.columbia.edu/~cxz/ SUN: http://www.cs.columbia.edu/~tim/ view more
Credit: Changxi Zheng + Timothy Sun/Columbia Engineering