Large scale least squares scattered data fitting
Applied Numerical Mathematics
Interpolation by geometric algorithm
Computer-Aided Design
Point-tangent/point-normal B-spline curve interpolation by geometric algorithms
Computer-Aided Design
Loop subdivision surface based progressive interpolation
Journal of Computer Science and Technology
Incenter subdivision scheme for curve interpolation
Computer Aided Geometric Design
Totally positive bases and progressive iteration approximation
Computers & Mathematics with Applications
Weighted progressive iteration approximation and convergence analysis
Computer Aided Geometric Design
Local progressive-iterative approximation format for blending curves and patches
Computer Aided Geometric Design
Technical Section: An extended iterative format for the progressive-iteration approximation
Computers and Graphics
Weighted progressive interpolation of Loop subdivision surfaces
Computer-Aided Design
B-spline surface fitting by iterative geometric interpolation/approximation algorithms
Computer-Aided Design
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The progressive and iterative approximation (PIA) method is an efficient and intuitive method for data fitting. However, in the classical PIA method, the number of the control points is equal to that of the data points. It is not feasible when the number of data points is very large. In this paper, we develop a new progressive and iterative approximation for least square fitting (LSPIA). LSPIA constructs a series of fitting curves (surfaces) by adjusting the control points iteratively, and the limit curve (surface) is the least square fitting result to the given data points. In each iteration, the difference vector for each control point is a weighted sum of some difference vectors between the data points and their corresponding points on the fitting curve (surface). Moreover, we present a simple method to compute the practical weight whose corresponding convergence rate is comparable to that of the theoretical best weight. The advantages of LSPIA are two-fold. First, with LSPIA, a very large data set can be fitted efficiently and robustly. Second, in the incremental data fitting procedure with LSPIA, a new round of iterations can be started from the fitting result of the last round of iterations, thus saving great amount of computation. Lots of empirical examples illustrated in this paper show the efficiency and effectiveness of LSPIA.