Inspired by the allure of additive fabrication, we pose the problem of origami design from a new perspective: how can we grow a folded surface in three dimensions from a seed so that it is guaranteed to be isometric to the plane? We solve this problem in two steps: by first identifying the geometric conditions for the compatible completion of two separate folds into a single developable four-fold vertex, and then showing how this foundation allows us to grow a geometrically compatible front at the boundary of a given folded seed. This yields a provably complete additive algorithm for the inverse design of the full space of quad origami patterns  . We illustrate the flexibility of our approach by growing ordered, disordered, straight and curved folded origami and fitting surfaces of given curvature with folded approximants. Overall our strategy of replacing a global optimization problem with a local additive algorithm might be more broadly useful in a range of computational fabrication strategies and their physical realizations .
Inspired by the allure of additive fabrication, we pose the problem of origami design from a new perspective: how can we grow a folded surface in three dimensions from a seed so that it is guaranteed to be isometric to the plane? We solve this problem in two steps: by first identifying the geometric conditions for the compatible completion of two separate folds into a single developable four-fold vertex, and then showing how this foundation allows us to grow a geometrically compatible front at the boundary of a given folded seed. This yields a complete marching, or additive, algorithm for the inverse design of the complete space of developable quad origami patterns that can be folded from flat sheets . We illustrate the flexibility of our approach by growing ordered, disordered, straight and curved folded origami and fitting surfaces of given curvature with folded approximants. Overall , our simple shift in perspective from a global search to a local rule has the potential to transform origami-based meta-structure design .
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provably complete additive
complete marching, or additive,
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full space of
complete space of developable
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that can be folded from flat sheets
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our strategy of replacing a global optimization problem with a local additive algorithm might be more broadly useful in a range of computational fabrication strategies and their physical realizations
, our simple shift in perspective from a global search to a local rule has the potential to transform origami-based meta-structure design