A survey of curve and surface methods in CAGD
Computer Aided Geometric Design
Triangular Berstein-Be´zier patches
Computer Aided Geometric Design
An introduction to splines for use in computer graphics & geometric modeling
An introduction to splines for use in computer graphics & geometric modeling
On the numerical condition of polynomials in Berstein form
Computer Aided Geometric Design
Algorithms for polynomials in Bernstein form
Computer Aided Geometric Design
Curves and surfaces in computer aided geometric design
Curves and surfaces in computer aided geometric design
Mathematical elements for computer graphics (2nd ed.)
Mathematical elements for computer graphics (2nd ed.)
The numerical problem of using Be´zier curves and surfaces in the power basis
Computer Aided Geometric Design
Mathematical methods in computer aided geometric design
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
Arbitrarily high degree elevation of Be´zier representations
Computer Aided Geometric Design
Generalizing rational degree elevation
Computer Aided Geometric Design
Legendre-Bernstein basis transformations
Journal of Computational and Applied Mathematics - Special issue/Dedicated to Prof. Larry L. Schumaker on the occasion of his 60th birthday
On the smooth convergence of subdivision and degree elevation for Bézier curves
Computer Aided Geometric Design - Pierre Bézier
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
Journal of Computational and Applied Mathematics
Application of Legendre--Bernstein basis transformations to degree elevation and degree reduction
Computer Aided Geometric Design
Comparison of interval methods for plotting algebraic curves
Computer Aided Geometric Design
Distance for degree raising and reduction of triangular Bézier surfaces
Journal of Computational and Applied Mathematics
Rates of convergence of control polygons
Computer Aided Geometric Design
Application of Chebyshev II-Bernstein basis transformations to degree reduction of Bézier curves
Journal of Computational and Applied Mathematics
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The polynomials determined in the Bernstein (Bezier) basis enjoy considerable popularity in computer-aided design (CAD) applications. The common situation in these applications is, that polynomials given in the basis of degree n have to be represented in the basis of higher degree. The corresponding transformation algorithms are called algorithms for degree elevation of Bernstein polynomial representations. These algorithms are only then of practical importance if they do not require the ill-conditioned conversion between the Bernstein and the power basis. We discuss all the algorithms of this kind known in the literature and compare them to the new ones we establish. Some among the latter are better conditioned and not more expensive than the currently used ones. All these algorithms can be applied componentwise to vector-valued polynomial Bezier representations of curves or surfaces.