基于有理二次Bézier曲线段的G^2连续闭曲线插值

Interpolating G^2 continuous closed curve with rational conics.

本文给出了两段相邻的有理二次 Bézier曲线 G2 连续的条件 ,提出了通过调整权因子而不是调整控制顶点来修改二次有理 Bézier曲线的形状的方法 ,从而实现了两相邻曲线间的 G2 连续拼接 ;实现了两分离二次有理 Bézier曲线间的 G2 连续过渡 .最后还给出了在仅仅增加或改变一个控制顶点的情况下 ,利用二次 Bézier曲线插值平面凸多边形的顶点 ,构成 G2

The weights of rational Bézier curves other than the control points are adjusted to make the adjacent curve segments meet with \%G\%\+2 continuity. The approach is then used to construct a \%G\%\+2 blending curve between two given separate rational quadric Bézier curves and a global \%G\%\+2 continuous closed curve to interpolate a 2D point set. The results demonstrate the effectiveness of the proposed algorithm.