Chaikin algorithm and its generalization

One of the methods for obtaining the curve and the surface of complex shape in the engineering geometry, computer graphics, including area of computer vision - multi-view geometry, multi-view stereo reconstruction is Chaikin algorithm, suggested in 1974. Unfortunately, the algorithm works with broken lines so at each step we get a continuous, but not a smooth curve or surface. The current article (paper, work) aims to generalize known in engineering geometry Chaikin algorithm for modeling of curves and surfaces of arbitrary smoothness class. We have proved that Chaikin's algorithm is a special case of the wavelet recovery of B-spline curve, or B-spline surface smoothness of class C
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. Using a filterbank constructed on the basis of B-splines of arbitrary order for Spline wavelets, we suggested a generalization of the Chaikin algorithm for modeling of curves and surfaces of arbitrary smoothness class. The generalized Chaikin algorithm proposed is a set of theoretical tools for computer-aided design, computer vision systems.