Convexity of rational curves and total positivity
Journal of Computational and Applied Mathematics
A shape preserving representation with an evaluation algorithm of linear complexity
Computer Aided Geometric Design
Progressive iterative approximation and bases with the fastest convergence rates
Computer Aided Geometric Design
Iterative refinement for Neville elimination
International Journal of Computer Mathematics - RECENT ADVANCES IN COMPUTATIONAL AND APPLIED MATHEMATICS IN SCIENCE AND ENGINEERING
Loop subdivision surface based progressive interpolation
Journal of Computer Science and Technology
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
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
Technical note: Progressive iteration approximation and the geometric algorithm
Computer-Aided Design
A comparison of different progressive iteration approximation methods
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
Adaptive data fitting by the progressive-iterative approximation
Computer Aided Geometric Design
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In this paper, we study the progressive iteration approximation property of a curve (tensor product surface) generated by blending a given data point set and a set of basis functions. The curve (tensor product surface) has the progressive iteration approximation property as long as the basis is totally positive and the corresponding collocation matrix is nonsingular. Thus, the B-spline and NURBS curve (surface) have the progressive iteration approximation property, and Bezier curve (surface) also has the property if the corresponding collocation matrix is nonsingular.