(2n−1)-point binary approximating scheme

We present a family of (2n-1)-point binary approximating subdivision schemes with free parameters for describing curves. Almost all existing odd-point binary symmetric approximating schemes belong to this family of schemes. Moreover, some of well-known even point approximating schemes are special cases of our scheme. Furthermore, it has been shown that odd-point schemes are better than even-point schemes in the sense of error bounds between kth level control polygon and limit curve of the schemes.