带有给定切线多边形的四次C-曲线

Quartic C-curves with given tangent polygons

四次C-曲线是由{sint,cost,t2,t,1}生成的曲线,包括四次C-Bézier曲线和四次C-B样条曲线,具有很多类似于Bézier曲线和B样条曲线的优良性质。文章讨论了与给定切线多边形相切的分段四次C-Bézier曲线和四次C-B样条闭曲线和开曲线;所构造的C-Bézier曲线是C1连续的,且对切线多边形是保形的;四次C-B样条闭曲线和开曲线是C3连续的,且对切线多边形也是保形的;所构造曲线段的控制点由切线多边形的顶点直接计算产生。最后以实例表明,本文的方法是有效的。

Quartic C-curves, including quartic C-Bézier curves and quartic C-B spline curves, are yielded by the basis { sin t, cos t,t^2,t, 1 } . They have a lot of good properties which Bézier curves and B spline curves possess. This paper presents an approach of constructing planar piecewise quartic C-Bézier curves and quartic C-B spline curves with all edges tangent to a given control polygon. The C-Bézier curve segments are joined together with C^1 continuity and the quartic C-B spline closed curves and open curves are Ca continuous. All curves are shape preserving to their tangent polygons. All control points of the curve segments can be calculated simply by the vertices of the given tangent polygon. Finally some numerical examples illustrate that the method given in this paper is effective.