This paper introduces a novel method for weaving 3D shell-shaped fabrics directly on the loom by using the Variable Reed, a hardware modification that allows variable dent positioning along the warp. With this reed, we weave discontinuous wefts (partial weft rows) and then apply different curved profiles to the weft yarns to dynamically alter the angle between the warp and weft during weaving. This technique enables the fabric to be folded and deformed into a 3D surface after it is removed from the loom. We demonstrate our method using a series of 3D woven samples and provide a computational design tool for creating 3D shell-shaped fabrics from an input surface, illustrated by examples of a wing and a half-dome. Our approach can be used to produce 3D-shaped woven fabric for garments, upholstery, architecture, and composites.