Local progressive-iterative approximation format for blending curves and patches

Just by adjusting the control points iteratively, progressive-iterative approximation presents an intuitive and straightforward way to fit data points. It generates a curve or patch sequence with finer and finer precision, and the limit of the sequence interpolates the data points. The progressive-iterative approximation brings more flexibility for shape controlling in data fitting. In this paper, we design a local progressive-iterative approximation format, and show that the local format is convergent for the blending curve with normalized totally positive basis, and the bi-cubic B-spline patch, which is the most commonly used patch in geometric design. Moreover, a special adjustment manner is designed to make the local progressive-iterative approximation format is convergent for a generic blending patch with normalized totally positive basis. The local progressive-iterative approximation format adjusts only a part of the control points of a blending curve or patch, and the limit curve or patch interpolates the corresponding data points. Based on the local format, data points can be fit adaptively. (C) 2010 Elsevier B.V. All rights reserved.