Progressive iterative approximation and bases with the fastest convergence rates
Computer Aided Geometric Design
Interpolation by geometric algorithm
Computer-Aided Design
Point-tangent/point-normal B-spline curve interpolation by geometric algorithms
Computer-Aided Design
Volumetric parameterization and trivariate B-spline fitting using harmonic functions
Computer Aided Geometric Design
Loop subdivision surface based progressive interpolation
Journal of Computer Science and Technology
Totally positive bases and progressive iteration approximation
Computers & Mathematics with Applications
Progressive interpolation using loop subdivision surfaces
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
The convergence of the geometric interpolation algorithm
Computer-Aided Design
Technical Section: An extended iterative format for the progressive-iteration approximation
Computers and Graphics
On the progressive iteration approximation property and alternative iterations
Computer Aided Geometric Design
Technical note: Progressive iteration approximation and the geometric algorithm
Computer-Aided Design
Adaptive data fitting by the progressive-iterative approximation
Computer Aided Geometric Design
Computer Aided Geometric Design
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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.