A survey of curve and surface methods in CAGD
Computer Aided Geometric Design
Approximate conversion of spline curves
Computer Aided Geometric Design - Special issue: Topics in CAGD
Degree reduction of Be´zier curves
Computer-Aided Design
Chebyshev economization for parametric surfaces
Computer Aided Geometric Design
The numerical problem of using Be´zier curves and surfaces in the power basis
Computer Aided Geometric Design
Optimal approximate conversion of spline surfaces
Computer Aided Geometric Design
Mathematical methods in computer aided geometric design
Spline conversion for trimmed rational Be´zier- and B-spline surfaces
Computer-Aided Design - Special Issue: Be´zier Techniques
On the stability of transformations between power and Bernstein polynomial forms
Computer Aided Geometric Design
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Degree reduction of Be´zier curves
Selected papers of the international symposium on Free-form curves and free-form surfaces
The geometry of optimal degree reduction of Be´zier curves
Computer Aided Geometric Design
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
The Mathematical Basis of the UNISURF CAD System
The Mathematical Basis of the UNISURF CAD System
Degree Reduction of Bézier Surfaces
Proceedings of the 5th IMA Conference on the Mathematics of Surfaces
Application of Chebyshev II-Bernstein basis transformations to degree reduction of Bézier curves
Journal of Computational and Applied Mathematics
Approximating tensor product Bézier surfaces with tangent plane continuity
Journal of Computational and Applied Mathematics
Multi-degree reduction of triangular Bézier surfaces with boundary constraints
Computer-Aided Design
On the degree elevation of Bernstein polynomial representation
Journal of Computational and Applied Mathematics
Multi-degree reduction of Bézier curves using reparameterization
Computer-Aided Design
The Bernstein polynomial basis: A centennial retrospective
Computer Aided Geometric Design
Explicit G2-constrained degree reduction of Bézier curves by quadratic optimization
Journal of Computational and Applied Mathematics
| Hi-index | 7.30 |
The polynomials determined in the Bernstein (Bézier) basis enjoy considerable popularity and the algorithms for reducing their degree are of practical importance in computer aided design applications. On the other hand, the conversion between the Bernstein and the power basis is ill conditioned, thus only the degree reduction algorithms which may be carried out without using this conversion are of practical value. Our unified approach enables us to describe all the algorithms of this kind known in the literature, to construct a number of new ones, which are better conditioned and cheaper than some of the currently used ones, and to study the errors of all of them in a simple homogeneous way.All these algorithms can be applied componentwise to a vector-valued polynomial representing a Bézier curve. Consider the values of the derivatives, whose orders vary successively from 1 to a given number i or k at the start and end point, respectively, of this curve. The current algorithms allow us to preserve these points and values for i equal to k, the new ones do that also without the latter constraint.