A geometric non-linear interpolatory subdivision scheme via approximation scheme

In this article, we proposed a non-linear interpolatory scheme based on an approximating scheme. A key step in our subdivision scheme is that we introduce a tangent polygon of the given initial polygon, then we obtain an interpolation scheme by applying corner cutting with poly-line to this tangent polygon. Numerical examples show that our approach combines the advantages of approximating subdivision schemes with the precise control of interpolatory schemes, and can avoid the potential pitfalls and unacceptable cases appeared in the traditional interpolatory subdivision scheme. The proposed scheme is convexity-preserving, the introduced free parameters are effective to the shape adjustment of the limit curve, and the limit curve is G¹ smooth.