Developability of Subdivision Surfaces

Min Zhou, Zhenglin Ye, Guohua Peng, Junqing Yang, and Shuili Ren
Department of Mathematics, Northwestern Polytechinical University,
Xi'an, 710072,
P.R.China

Abstract    
In this paper, by analysis Gaussian curvature of subdivision surfaces, we present a new approach to represent and design developable surfaces, and derive necessary and sufficient conditions which guarantee that the limiting surface is developable. Our approach has both flexibility of net type surfaces and accuracy of parametric surfaces, but also is efficient tool to apply in engineering. We expect it can fill the gaps in research of developable surfaces.