A computational algorithm for origami design
Proceedings of the twelfth annual symposium on Computational geometry
Folding flat silhouettes and wrapping polyhedral packages: new results in computational origami
Computational Geometry: Theory and Applications
Geometric Folding Algorithms: Linkages, Origami, Polyhedra
Geometric Folding Algorithms: Linkages, Origami, Polyhedra
Origamizing Polyhedral Surfaces
IEEE Transactions on Visualization and Computer Graphics
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We propose an original and novel algorithm for the automatic development of crease patterns for certain polyhedra with discrete rotational symmetry by composing right frusta. Unlike existing algorithms, the folded product will conform to the surface of the target polyhedron without external flaps. The crease patterns of frusta are drawn first and then composed by the algorithm to draw the crease pattern of the rotationally symmetric polyhedron. The composition is performed by splitting creases that were folded on pleats from frustum crease patterns. A CAD program has been written to implement the algorithm automatically, allowing users to specify a target polyhedron and generate a crease pattern that folds into it.