Totally positive bases for shape preserving curve design and optimality of B-splines
Computer Aided Geometric Design
Advanced surface fitting techniques
Computer Aided Geometric Design
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
Dual evolution of planar parametric spline curves and T-spline level sets
Computer-Aided Design
Loop subdivision surface based progressive interpolation
Journal of Computer Science and Technology
Totally positive bases and progressive iteration approximation
Computers & Mathematics with Applications
Sample-based polynomial approximation of rational Bézier curves
Journal of Computational and Applied Mathematics
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
Weighted progressive interpolation of Loop subdivision surfaces
Computer-Aided Design
Polynomial approximation of rational Bézier curves with constraints
Numerical Algorithms
B-spline surface fitting by iterative geometric interpolation/approximation algorithms
Computer-Aided Design
Adaptive data fitting by the progressive-iterative approximation
Computer Aided Geometric Design
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We present a new and efficient method for weighted progressive iteration approximations of data points by using normalized totally positive bases. Compared to the usual progressive iteration approximation, our method has a faster convergence rate for any normalized totally positive basis, which is achieved by choosing an optimal value for the weight. For weighted progressive iteration approximations, we prove that the normalized B-basis of a space provides the fastest convergence rate among all normalized totally positive bases of the space. These results are also valid for tensor product surfaces.