【摘要】 讨论了构造可调整C2 连续的四次B啨ｚｉｅｒ插值曲线问题 .用四次B啨ｚｉｅｒ曲线构造Ｃ2 连续的插值曲线可提供额外的自由度 ,用于控制曲线的形状 .新方法构造辅助曲线用于描述B啨ｚｉｅｒ曲线的形状 .自由度由极小化样条曲线和辅助曲线的一阶导矢差的平方的积分确定 .讨论了C2 连续的四次B啨ｚｉｅｒ曲线需满足的连续性方程 .新方法的优点是曲线须满足的连续性方程是严格三对角占优势的、曲线的不连续点在给定的数据点处、曲线是局部可调整的 .此外 ,新方法具有保凸性 .最后以具体实例对新方法和现有三、四次样条函数方法做了比较 .更多还原

【Abstract】 The problem of constructing an adjustable C 2 quartic Bézier curve to interpolate a set of given data points is discussed. Constructing C 2 interpolation curve by quartic Bézier curve offers additional freedom degrees those can be used to adjust the shape of the curve. On each sub-interval, the quartic Bézier curve segment has one freedom degree that is used to adjust the shape of the segment. It is proven that for any freedom degrees, there is a C 2 quartic Bézier curve to interpolate the given data points. To make the quartic Bézier curve have the desired shape, the new method constructs an additional curve to describe the shape of the quartic Bézier curve. The freedom degrees are determined by minimizing the integral of the squared difference of the first derivatives of the Bézier curve and additional curve. If there are local irregularities on the portions of the quartic Bézier curve, the irregular portions could be locally removed by adjusting the corresponding freedom degrees and redefining the corresponding slope vectors at the data points. The continuity equations for constructing C 2 quartic Bézier curve are discussed. The properties of the new method are that (1) the equations that the quartic Bézier curve has to satisfy for being C 2 continuous are strictly row diagonally dominant; (2) the discontinuous points of the curve are at the given data points; (3) the curve is locally adjustable; (4) if the given data points are convex, the constructed quartic Bézier curve is convex. The comparison of the new method with cubic and quartic spline methods is included.更多还原