λ、μ-B样条上可展曲面的几何设计

Geometric design of λ、μ-B spline developable surface

基于3D射影空间中点和平面间的对偶性这一重要思想,提出了两种直接、简单的可展曲面设计方法。该方法将可展曲面用具有调配函数的控制平面来表示,这种调配函数定义了一种新的带有λ、μ两个局部形状控制参数的分段多项式样条曲线,使新的可展曲面具有灵活的局部形状可调性和更强的描述能力,增加了造型的自由度。通过调节参数λ、μ可得到一族可展曲面,这族可展曲面保留了B样条曲面的特性,在λ、μ为特殊取值时所生成的可展曲面即为均匀B样条可展曲面,为曲面的设计提供了一种有效的新方法。

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.