In order to reduce the calculation complexity and improve the processing efficiency of pen-cutting process,an arc approximating method is proposed to detect the pen-cutting regions in the NC machining of freeform surfaces.In this algorithm,an improved quadtree algorithm is presented to subdivide and approximate the freefrom surface.Then,arc approximation is performed to approximately calculate the curvature radius for the purpose of quickly judging the local interference,reducing the calculation complexity and improving the search efficiency.Finally,a binary-tree method is used to exactly detect the boundary points and to determine the boundary of pen-cutting regions.Case results indicate that the proposed algorithm is effective because it can fast and accurately search the local interference regions,with a time cost reducing from the traditional 85.047s of the point-by-point searching to 33.734s.