Rigidly Foldable Quadrilateral Meshes from Angle Arrays

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We present a design technique for generating rigidly fold- able quadrilateral meshes, taking as input four arrays of direc- tion angles and fold angles for horizontal and vertical folds. By starting with angles, rather than vertex coordinates, and enforc- ing the fold-angle-multiplier condition at each vertex, it is pos- sible to achieve arbitrarily large and complex panel arrays that flex from unfolded to flatly folded with a single degree of freedom. Furthermore, the design technique is computationally simple, re- ducing for some cases to a simple linear programming problem. The resulting mechanisms have applications in architectural fa- cades, furniture design, and more.