Degree reduction of Be´zier curves
Computer-Aided Design
On the stability of transformations between power and Bernstein polynomial forms
Computer Aided Geometric Design
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
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
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Journal of Computational and Applied Mathematics
Best one-sided approximation of polynomials under L1 norm
Journal of Computational and Applied Mathematics - Selected papers of the international symposium on applied mathematics, August 2000, Dalian, China
Application of Legendre--Bernstein basis transformations to degree elevation and degree reduction
Computer Aided Geometric Design
Optimal multi-degree reduction of Bézier curves with constraints of endpoints continuity
Computer Aided Geometric Design
Using Jacobi polynomials for degree reduction of Bézier curves withCk-constraints
Computer Aided Geometric Design
Computer Aided Geometric Design
Matrix representation for multi-degree reduction of Bézier curves
Computer Aided Geometric Design
Optimal multi-degree reduction of Bézier curves with G2-continuity
Computer Aided Geometric Design
On the degree elevation of Bernstein polynomial representation
Journal of Computational and Applied Mathematics
Multi-degree reduction of Bézier curves with constraints, using dual Bernstein basis polynomials
Computer Aided Geometric Design
Approximating tensor product Bézier surfaces with tangent plane continuity
Journal of Computational and Applied Mathematics
Multi-degree reduction of Bézier curves using reparameterization
Computer-Aided Design
Explicit G2-constrained degree reduction of Bézier curves by quadratic optimization
Journal of Computational and Applied Mathematics
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A polynomial curve on [0,1] can be expressed in terms of Bernstein polynomials and Chebyshev polynomials of the second kind. We derive the transformation matrices that map the Bernstein and Chebyshev coefficients into each other, and examine the stability of this linear map. In the p=1 and ~ norms, the condition number of the Chebyshev-Bernstein transformation matrix grows at a significantly slower rate with n than in the power-Bernstein case, and the rate is very close (somewhat faster) to the Legendre-Bernstein case. Using the transformation matrices, we present a method for the best multi-degree reduction with respect to the t-t^2-weighted square norm for the unconstrained case, which is further developed to provide a good approximation to the best multi-degree reduction with constraints of endpoints continuity of orders r,s (r,s=0). This method has a quadratic complexity, and may be ill-conditioned when it is applied to the curves of high degree. We estimate the posterior L"1-error bounds for degree reduction.