关键词: 可展曲面, 对偶性, 局部形状参数, 曲线设计, B样条

Abstract: Two direct and simple design methods of developable surface are developed based on the duality of the mid-point of 3D projective space and the plane.The method makes the developable surface expressed by the control plane of blending function.A new piecewise polynomial spline curve with two local shape parameters λ and μ is defined by this blending function.Therefore the new developable surface has tunability of flexible local shape and more strong description ability，and increases degree of freedom of the modeling.A class of developable surface is obtained by regulating the parameters λ and μ and the class of developable surface keeps characteristics of B-spline surface，that is uniform B-spline surface is formed by special value of λ and μ.This provides a new method for the design of the surface.

Key words: developable surface, duality, local shape parameter, curve design, B-spline