The features of single and double arc approximating

and combines the merits of two kinds of fitting are discussed. By the algorithm of approximating curve in optimizing three-point arc and mixing single and double arc in permission tolerance

smooth link of whole approximating arc with inflexion points and extreme value points is attained. The nature of segmental points of parameter equation is discussed to ensure the reliability of judging segmental points. The arc lengthening method in extreme value points of curvature is used to further decrease segments of arc approximating. Symmetrical algorithm for symmetrical graph is used to increase symmetry of the graph

thus the program runs more rapidly. The nodes are solved by programming in matlab software to provide reference for processing complex curve in numerical control and CAD system.