限制在光滑参数曲线上的С~1曲面插值

给出了一种限制在光滑参数曲线上的C1曲面插值方法.首先通过曲线参数化,建立从曲线到实参数轴的一个一一映射,将限制在曲线上的曲面插值问题转化为实参数轴上的一元插值问题,然后采用范数极小的方法给出参数轴上的一元C1插值函数,再将此插值函数映射到原曲线上即得到限制在参数曲线上的插值函数.理论推导和图形实例显示表明该方法具有逼近效果好的优点.

C~1 surface interpolation restricted to smooth parametric curve

An approach to resolve the problem of C~1 surface interpolation restricted to a smooth parametric curve was given.Through curve parametrizing,an one-to-one map from the curve onto real parametric axis was set up and the problem of surface interpolation restricted to curve was transformed to one-dimensional interpolation on the real parametric axis.Then,an one-dimensional C~1 interpolation function was given by using the method of minimum norm.Finally,the required interpolating function restricted to the parametric curve could be obtained by mapping the one-dimensional function onto the original parametric curve.Theoretical deduction and graphical illustration showed that such an approach was effective to produce good approximation result.