On increasing the developability of a trimmed NURBS surface

Developable surfaces are desired in designing products manufactured from planar sheets. Trimmed non-uniform rational B-spline (NURBS) surface patches are widely adopted to represent 3D products in CAD/CAM. This paper presents a new method to increase the developability of an arbitrarily trimmed NURBS surface patch. With this tool, designers can first create and modify the shape of a product without thinking about the developable constraint. When the design is finished, our approach is applied to increase the developability of the designed surface patches. Our method is an optimisation-based approach. After defining a function to identify the developability of a surface patch, the objective function for increasing the developability is derived. During the optimisation, the positions and weights of the free control points are adjusted. When increasing the developability of a given surface patch, its deformation is also minimised and the singular points are avoided. G⁰ continuity is reserved on the boundary curves during the optimisetion, and the method to reserve G¹ continuity across the boundaries is also discussed in this paper. Compared to other existing methods, our approach solves the problem in a novel way that is close to the design convention, and we are dealing with the developability problem of an arbitrarily trimmed NURBS patch.