用四次Bézier曲线构造C~2连续的插值曲线

【作者】 张彩明； 刘捷； 汪嘉业；

【机构】 山东大学计算机科学与技术学院；

【摘要】 本文讨论了构造C~2连续的四次Bézier插值曲线问题。把四次样条曲线降为C~2连续可提供额外的自由度,用于控制曲线的形状。自由度由极小化插值曲线和辅助曲线的一阶导数差的平方的积分确定。讨论了C~2连续的四次Bézier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三对角占优势的,曲线的不连续点在给定的数据点处,具有额外的自由度调整曲线的形状。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】 This paper discusses the problem of constructing C~2 quartic spline curve interpolation.Decreasing the continuity of the quartic spline to C~2 offers additional freedom degrees those can be used to adjust the shape of the curve.The freedom degrees are determined by minimizing the integral of the squared difference of the first derivative of the interpolation curve and additional curve.The continuity equations for constructing C~2 quartic spline curve is discussed.The advantages of the new method is that 1) the equations that the curve has to satisfy is stricdy row diagonally dominant;2) the discontinuous points of the curve are at the given data points;3) it offers additional freedom degrees to adjust the shape of me curve.The comparison of me new method with cubic and quartic spline methods is included.更多还原