三次非均匀样条上可展面的计算机辅助设计

利用3D射影空间中点和平面间的对偶性可以得到对可展面的一种新的表示，这种表示直接、简单、有效。用这种方式，一个可展面可利用具有非均匀B样条基的控制平面来设计，这种设计方法具有现存曲线设计的特征。本沿用Bodduluri和Ravani的基本思想，把其对三次均匀可展面的设计推广到三次非均匀可展面的设计，并以不同的以中心点表示控制平面的方式对曲面的设计进行了较详细的实例分析，实例表明设计结果良好。

Computer-Aided Design of Nonuniformly Developable Surface

We extend the important idea of duality between plane and point geometries used in the computer-aided design of uniformly developable surface proposed by Bodduluri and Ravani to make it applicable to the case of nonuniformly developable surface. Instead of B-spline basis function of uniform degree 3 used in Ref., we use B-spline basis function of nonuniform degree 3,which is discussed in section 1. We propose two methods for computer-aided design of nonuniformly developable surface: (1) the developable surface is considered as an envelope surface in section 2; (2) the developable surface is considered as the surface composed of the tangent lines to a spine curve, which is discussed in detail in section 3. We applied our two methods successfully to the design of two nonuniformly developable surfaces: the first nonuniformly developable surface was designed as shown in Fig.1 (envelope method) and Fig.3 (spine curve method); the second nonuniformly developable surface was designed as shown in Fig.2 (envelope method) and Fig.4 (spine curve method).Our two methods make it quite simple and intuitive for a designer to design nonuniformly developable surface.