以已知曲线为渐进线的可展曲面束的设计  

Designing developable surface pencil through given curve as its common asymptotic curve

作　　者：刘羽[1] 王国瑾[1] 

机构地区：[1]浙江大学计算机图像图形研究所,浙江杭州310027

出　　处：《浙江大学学报（工学版）》2013年第7期1246-1252,共7页Journal of Zhejiang University：Engineering Science

基　　金：国家自然科学基金资助项目(61070065;60933007)

摘　　要：研究插值一条任意参数曲线并以其为渐近线的可展以及有理可展曲面束的设计问题.基于插值一条任意参数曲线并以其为渐近线的一般曲面束的表达式,给出该曲面束为可展情形的表达式.讨论所设计的可展曲面束的类型,推导插值Bézier曲线并以其为渐近线的有理Bézier可展曲面束表达式.开展以圆柱螺线、圆锥螺线和Bézier曲线为渐近线的一般可展曲面以及有理Bézier可展曲面的编程实例,验证了该算法的准确性和有效性.Both the general and rational developable surface pencils through an arbitrary parametric curve as its common asymptotic curve were analyzed. By employing the parametric representation of a developable surface pencil taking a given curve as its asymptotic curve, the expression for the case that the pencil is de- veloped was presented and the type of the designed developable surface was discussed. The rational Bezier form of the developable surface pencil through a given Bezier curve as its asymptotic curve was given. Pro- gramming examples for the general and rational developable surfaces through a circular helix, conical helix or Bezier curve as its asymptotic curve were illustrated to verify the correctness and effectivity of the algo- rithm.

关 键 词：渐近线 可展曲面 有理曲面 插值 曲面设计 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]