Curved-crease (CC) origami differs from prismatic, or straight-crease origami, in that the folded surface of the pattern is bent during the folding process. Limited studies on the mechanical performance of such geometries have been conducted, in part because of the difficulty in parametrizing and modeling the pattern geometry. This paper presents a new method for generating and parametrizing rigid-foldable, CC geometries from Miura-derivative prismatic base patterns. The two stages of the method, the ellipse creation stage and rigid subdivision stage, are first demonstrated on a Miura-base pattern to generate a CC Miura pattern. It is shown that a single additional parameter to that required for the straight-crease pattern is sufficient to completely define the CC variant. The process is then applied to tapered Miura, Arc, Arc-Miura, and piecewise patterns to generate CC variants of each. All parametrizations are validated by comparison with physical prototypes and compiled into a matlab Toolbox for subsequent work.