Unfolding Polyhedra Method for the Design of Origami Structures with Creased Folds

After addressing the kinematics of origami structures with creased folds in the previous chapter, here we present a method for their design to achieve targeted three-dimensional shapes. This chapter addresses the method of unfolding polyhedra. The goal shape is represented in this method as a three-dimensional polygonal mesh, termed as the goal mesh. The objective in unfolding polyhedra is to find the shape and fold pattern of a planar sheet that can be folded towards a configuration that matches the goal mesh. We examine the theory and computational implementation aspects of the unfolding polyhedra method and provide various representative examples.

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