以已知曲线为渐进线的可展曲面束的设计

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．

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

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 developed was presented and the type of the designed developable surface was discussed. The rational Bézier form of the developable surface pencil through a given Bézier curve as its asymptotic curve was given. Programming examples for the general and rational developable surfaces through a circular helix, conical helix or Bézier curve as its asymptotic curve were illustrated to verify the correctness and effectivity of the algorithm．