The NURBS book
Approximation with Active B-Spline Curves and Surfaces
PG '02 Proceedings of the 10th Pacific Conference on Computer Graphics and Applications
Fitting B-spline curves to point clouds by curvature-based squared distance minimization
ACM Transactions on Graphics (TOG)
Progressive iterative approximation and bases with the fastest convergence rates
Computer Aided Geometric Design
Interpolation by geometric algorithm
Computer-Aided Design
B-spline curve fitting based on adaptive curve refinement using dominant points
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
Adaptive knot placement in B-spline curve approximation
Computer-Aided 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
The convergence of the geometric interpolation algorithm
Computer-Aided Design
Progressive interpolation using loop subdivision surfaces
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
B-spline surface fitting based on adaptive knot placement using dominant columns
Computer-Aided Design
B-spline surface fitting by iterative geometric interpolation/approximation algorithms
Computer-Aided Design
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Progressive-iteration approximation (PIA) is a new data fitting technique developed recently for blending curves and surfaces. Taking the given data points as the initial control points, PIA constructs a series of fitting curves (surfaces) by adjusting the control points iteratively, while the limit curve (surface) interpolates the data points. More importantly, progressive-iteration approximation has the local property, that is, the limit curve (surface) can interpolate a subset of data points by just adjusting a part of corresponding control points, and remaining others unchanged. However, the current PIA format requires that the number of the control points equals that of the data points, thus making the PIA technique inappropriate to fitting large scale data points. To overcome this drawback, in this paper, we develop an extended PIA (EPIA) format, which allows that the number of the control points is less than that of the given data points. Moreover, since the main computations of EPIA are independent, they can be performed in parallel efficiently, with storage requirement O(n), where n is the number of the control points. Therefore, due to its local property and parallel computing capability, the EPIA technique has great potential in large scale data fitting. Specifically, by the EPIA format, we develop an incremental data fitting algorithm in this paper. In addition, some examples are demonstrated in this paper, all implemented by the parallel computing toolbox of Matlab, and run on a PC with a four-core CPU.