In this study, we propose a novel computational system called WoodWeaver for fabricating curved surfaces from conventional materials without using moulds. We use a cutting-based material bending method called Dukta. Our system enables a user to design a single free-form curved surface and to fabricate it based on the bending deformation characteristics of the material. The system also indicates an invalid shape; that is, one that will break upon bending deformation. The user can then design a valid shape with this information. We also develop an optimal Dukta pattern that is the smallest-sized gap pattern necessary to represent a user-designed shape. Given a valid shape, the system generates the optimal pattern and a machine cuts four modules with this pattern. Finally, the user assembles these modules to obtain the desired shape.