Naval Architecture School, Universidad Politécnica de Madrid (UPM), Spain.

---

Abstract—The use of developable surfaces in design addresses engineering needs because they can be easily manufactured without stretching or tearing, or without the use of heat treatment. In addition, they also require the minimum strain energy of flexure. This paper presents study cases of ship hulls that are of direct application on shipyards, although the method could be implemented in other fields, such as architecture or furniture design. Our approach is to create a developable B-spline surface between two boundary curves. Between each pair of these curves or directrix lines, the generatrix lines or rulings are created and a quasi-developable B-spline surface containing the rulings is defined. In engineering practice, quasi-developable surfaces can be considered as strictly developable ones, since a tolerance depending on the materials is used. The rulings are obtained by a searching technique based on the warp angle that depends on the material. The creation of a lofting B-spline surface containing the rulings enables the interchange between most common engineering softwares that work with NURBS (Non Uniform Rational B-Spline) surfaces by the use of IGES or STEP standard data exchange files. B-spline curves and surfaces are widely used today in practically all the design softwares. An example of ship hulls entirely created with developable surfaces is presented.

Index Terms—B-splines, developable surfaces, warp angle.

[PDF]

Cite: Francisco Perez-Arribas, Leonardo Fernandez-Jambrina, "Computer-Aided Design of Developable Surfaces: Designing with Developable Surfaces," Journal of Computers vol. 13, no. 10, pp. 1171-1176, 2018.