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Research on the Subdivision Algorithm about the Approximate Development of the Undevelopable Surfaces

Modern industrial manufacturing contains different kinds of surface modeling, which is processed by planar materials. For the principle of the most efficient materials using, how to optimize subdivision undevelopable surface before development becomes an important topic in CAM design and manufacturing industries. The paper transforms the basic parameters of surface before subdivision, and gives the standards of subdivision surfaces. We proved the feasibility and the existence of triangle subdivision algorithm. By introducing double parameters MÖbius transformation , the subdivision surface is more uniform. At last, numerical examples prove that the algorithm about the approximate development of the undevelopable surfaces is effective and practical.