带有给定切线多边形的C^2和C^3 Bzier闭样条曲线

C^2 and C^3 Continuous Bézier Spline Curve with Given Tangent Polygon

讨论与给定切线多边形相切的分段四次和五次 Bézier曲线 ,所构造的曲线是 C2 和 C3连续的 ,且对切线多边形是保形的 .曲线上的所有 Bézier曲线段的控制顶点由切线多边形的顶点直接计算产生 .最后实例表明 ,本文的方法是有效的 .

This paper proposes an approach of constructing planar piecewise Bézier curve of 4th or 5th degree with all edges tangent to a given control polygon and the curve segments are joined together with C 2 and C 3 continuity. The segmented Bézier curves are all shape preserving to their tangent polygon. Finally, a few numerical examples illustrate that the method given in this paper is effective for CAGD.