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.