Origami tessellations consisting of repetitively tiled unit cell elements can be used to manufacture cellular three-dimensional structures with interesting mechanical and other properties. In recent years, the search for alternative and innovative core materials for sandwich constructions has resulted in renewed interest in such foldable structures. The ability to simulate the folding process of such structures with one kinematic degree of freedom is essential for their successful design and manufacture. We present an algorithm that allows for the implicit calculation of arbitrary rigid folding states of quadrilateral-based structures with certain topological features. This enables reliable real-time virtual folding of a large number of important tessellation types which has been put to good use in numerous projects.

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