Abstract: The different levels of Loop subdivision surfaces could be used as the geometrical models for different procedures of the NC machining.Using the existing algorithms which did not consider the crease or the border,we may receive different results other than what we expect.Firstly,a method is presented to compute the limit offset positions for the sharp points.Secondly,the Gauss-Jacobi iterative formulas to compute the offset positions of the initial control points based on the limit offset positions are provided.At last,the astringency of the iterative formulas is proved.The results illustrate the feasibility of the methods.