Abstract: Rounding and filleting sharp edges are fulfilled with the enveloping algorithm presented by KS function and interior radius vector sweeping. The basic idea is to decompose the smoothing process into two steps. At first, the local non-convex areas are sequentially smoothed. Then the remaining local convex areas together with the preprocessed local non-convex areas are smoothed as a whole. Some typical examples are given to illustrate the advantages of the new method in some applications.