与给定切线多边形相切的3次Bézier样条曲线
来源期刊：中南大学学报(自然科学版)2001年第1期
论文作者：文锦
文章页码：108 - 110
关键词：Bézier曲线;切线多边形;保形
Key words：Bézier curve; tangent polygon; shape preserving
摘 要：讨论了与给定切线多边形相切的3次Bézier样条曲线.对于给定的切线多边形,在每条边上定义1个切点及2个Bézier点,从而在2个切点之间构造2段3次Bézier曲线,通过选取合适的调节参数λi,μi,ρi,3次Bézier曲线段是2阶几何连续的.此外,证明了该3次Bézier样条曲线对切线多边形是保形的,该样条曲线有利于凸轮的计算机辅助设计.
Abstract: In this paper, a planar piecewise cubic Bézier curve is discussed which has edges of a given polygons as tangents. For a given tangent polygon, a tangent point and two Bézier points are defined, two cubic Bézier curve segments are constructed. By choosing approarite adjustable parameters λi,μi,ρi, the cubic Bézier spline curve is C2-Continu-ous, which proves thatthe cubic Bézier spline curve is shape preserving to the given tangent polygon. The shape preserving spling curve has important role in the computer aided design for the cam.
