Origami describes rules for creating folded structures from patterns on a flat sheet, but does not prescribe how patterns can
be designed to fit target shapes. Here, starting from the simplest periodic origami pattern that yields one-degree-of-freedom
collapsible structures—we show that scale-independent elementary geometric constructions and constrained optimization
algorithms can be used to determine spatially modulated patterns that yield approximations to given surfaces of constant or
varying curvature. Paper models confirm the feasibility of our calculations. We also assess the diculty of realizing these
geometric structures by quantifying the energetic barrier that separates the metastable flat and folded states. Moreover, we
characterize the trade-o between the accuracy to which the pattern conforms to the target surface, and the eort associated
with creating finer folds. Our approach enables the tailoring of origami patterns to drape complex surfaces independent of
absolute scale, as well as the quantification of the energetic and material cost of doing so.