Abstract Subdivision algorithm is an efficient way to reconstruct curves and surfaces for discrete data points which can reconstruct feature and edge contour for edge extraction. By introducing local pushback operation, a brand-new interproximate subdivision framework is established which bridges the gap between interpolating schemes and approximating ones. This subdivision framework not only contains most existing schemes, but also includes some new schemes. Then, a class of nonstationary interproximate subdivision schemes are proposed. Properties of the schemes such as continuity and convexity are further discussed. With the help of the framework, limit curves can freely interpolate given points and approximate the other ones if data points have been divided into interpolating points and approximating ones by certain rules. Numerical examples show that the proposed approach can faithfully interpolate feature data points and obtain better visual effects than the ones obtained via other known schemes.
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