  Miura-Ori, a celebrated origami pattern that facilitates functionality in
matter, has found multiple applications in the field of mechanical
metamaterials. Modifications of Miura-Ori pattern can produce curved
configurations during folding, thereby enhancing its potential functionalities.
Thus, a key challenge in designing generalized Miura-Ori structures is to
tailor their folding patterns to achieve desired geometries. In this work, we
address this inverse-design problem by developing a new continuum framework for
the differential geometry of generalized Miura-Ori. By assuming that the
perturbation to the classical Miura-Ori is slowly varying in space, we derive
analytical relations between geometrical properties and the perturbation field.
These relationships are shown to be invertible, allowing us to design complex
curved geometries. Our framework enables porting knowledge, methods and tools
from continuum theories of matter and differential geometry to the field of
origami metamaterials.
