形状可调的C^2拟三次Bézier样条曲线

Shape adjustable C^2 continuous quasi-cubic Bézier spline curve

文章基于一类带2个形状参数的拟三次Bézier曲线,讨论了两相邻拟三次Bézier曲线间的光滑拼接条件,构造了C2连续的样条曲线,该样条曲线可以是开的,也可以是闭的。组合曲线段的控制顶点由所给控制多边形的顶点直接计算产生,通过改变形状参数的取值,可以局部调整样条曲线接近其控制多边形的程度。

Based on the method of quasi-cubic Bézier curve with two shape parameters, the smooth splicing conditions between two adjacent quasi-cubic Bézier curves are discussed. A class of C2 continuous spline curves is constructed. The curve can be open or closed. The control vertices of the combined curve segment are computed directly by the vertices of the given control polygon. By changing the value of the shape parameters, the spline curve can be locally adjusted to the extent of its control polygon.