三角B样条上可展曲面的设计与形状调节

提出了计算机辅助设计可展曲面的新方法,利用该文的方法,可展曲面可用具有三角B样条基函数的控制平面来设计,这种设计方法具有现存曲线设计方法的特征。同时,通过引入形状控制参数,使生成的可展曲面在较大的范围内可进行调节和控制,增加了造型的自由度。该文的设计方法直接、简单、有效,不仅能克服传统方法在可展曲面设计方法上的缺陷,而且能方便地解决工程中经常遇到的可展曲面的形状难以调节和控制的问题。

Design for Adjustably Developable Surfaces Based on Triangle-B Spline

In this paper,using the important idea of duality between plane and point geometries,we propose a direct explicit and efficient method of computer-aided design for developable surfaces based on triangle-B spline.The developable surfaces are represented using control planes with appropriate basis functions.The shapes of developable surfaces can be adjusted using a control parameter.When adjusting parameter,a family of developable surfaces can be constructed,they can keep the characteristics of B spline surfaces.Meanwhile,we show that the techniques for the geometric design of developable surfaces in this paper have all the characteristics of existing approaches for curves design.The new algorithm can not only overcome the difficulties in representation of developable surfaces utilizing traditional approaches,but also resolve the problems in adjusting and controlling the shape of developable surfaces that often faced in Engineering.The algorithms are explained in detail,and demonstrated with the examples in the paper.We expect our methods can fill the gaps in research of developable surfaces.