Degree reduction of Be´zier curves
Computer-Aided Design
Chebyshev economization for parametric surfaces
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
Computer Aided Geometric Design - Special issue dedicated to Paul de Faget de Casteljau
Least squares approximation of Bézier coefficients provides best degree reduction in the L2-norm
Journal of Approximation Theory
Degree reduction of B-spline curves
Computer Aided Geometric Design
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
Construction of orthogonal bases for polynomials in Bernstein form on triangular and simplex domains
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
A note on the paper in CAGD (2004, 21 (2), 181-191)
Computer Aided Geometric Design
Optimal multi-degree reduction of Bézier curves with G2-continuity
Computer Aided Geometric Design
Multi-degree reduction of triangular Bézier surfaces with boundary constraints
Computer-Aided Design
A note on constrained degree reduction of polynomials in Bernstein-Bézier form over simplex domain
Journal of Computational and Applied Mathematics
Constrained multi-degree reduction of triangular Bézier surfaces using dual Bernstein polynomials
Journal of Computational and Applied Mathematics
Multi-degree reduction of Bézier curves using reparameterization
Computer-Aided Design
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In this paper we show that the orthogonal complement of a subspace in the polynomial space of degree n over d-dimensional simplex domain with respect to the L"2-inner product and the weighted Euclidean inner product of BB (Bezier-Bernstein) coefficients are equal. Using it we also prove that the best constrained degree reduction of polynomials over the simplex domain in BB form equals the best approximation of weighted Euclidean norm of coefficients of given polynomial in BB form from the coefficients of polynomials of lower degree in BB form.