Developable surfaces are widely used in manufacturing with materials that are not amenable to stretching. Applications include the formation of ship hulls, ducts, shoes, clothing and automobile parts such as upholstery and body panels. In shipbuilding, developable surfaces are shaped using only rollers or presses. Heat treatment is then used only to remove distortion induced by welding or other means. Doubly curved surfaces, on the other hand, must be heat treated after rolling to induce the additional curvature. The heat treatment is normally done by hand, by a skilled artisan with years of training to achieve the correct amount of bending. This is an extremely time consuming, labor intensive and thus expensive process. According to Avondale/IHI Shipbuilding Technology Transfer data for a tanker, only 15.1% of the curved plates in a ship hull are singly curved, while 65.8% of the plates are doubly curved, requiring roller and heat treatment processes. An intensive effort to increase the amount of developable surfaces in the hulls of merchant ships at Burmeister & Wain Shipyard has resulted in a reported 20% reduction in manhours required to produce a hull. Designing a ship entirely of singly curved, or developable, surfaces would reduce construction costs even more. The main goal of this research is to develop a user-friendly method of designing developable surfaces with a B-spline representation. The effort is then extended to address some common differential geometry properties that will be useful in the design and manufacturing process. The ultimate goal is to provide a method to design a complete ship hull from developable surfaces and to generate cutting and bending information in a format that is user friendly for both the engineer and the worker. Although this thesis does not go that far, it takes a major step toward this goal
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