The Spline Approximation of Tensor Product Offset Surface

In the system of geometric modeling,we generally use rational parametric curves and surfaces with low degree to approximate offset curves and surfaces.In this paper,we consider the spline approximation of tensor product offset surfaces.The spline surface and the original surface are combined to generate a new rational surface by adding the weights.This approximating offset surface interpolates some sample nodes on the offset surface.The degree of the approximating surface can't exceed the original surface,and it is C2-continue.The number of control points and approximation error depend on the choosing of interpolatory points,and we can get the best approximation by adjusting the weights.