无振荡均匀三次B样条插值法

An Oscillation Free Uniform Cubic B Spline Interpolation

三次Ｂ样条因其控形能力强，具有变差减少性和ｃ２连续性，故在自由曲线和曲面设计中获得广泛的应用．但若将其用于插值，则常导致出现不希望的拐点和振荡．无振荡均匀Ｂ样条插值法通过在需要控制曲线切线或曲面参数曲线的切线的地方增加辅助控制点，就可以达到良好的消除振荡的效果，且保留了均匀三次Ｂ样条的全部优点。

Cubic B splines are widely used in free form curve and surface design because of their good ability of shape control, variety diminution and c 2 class continuity. However, applying these techniques to interpolation will quite often lead to undesirable inflection points and oscillations. By means of increasing auxiliary control points according to the characteristics of a given data set, oscillation free uniform cubic B spline interplant can get a good result of avoiding oscillation, whilst all the advantages of uniform cubic B spline can be conserved. It will be quite easy and natural to insert a straight line segment into a curve or a plane patch into a curved surface.