Explicit formula relating the Jacobi, Hahn and Bernstein polynomials
SIAM Journal on Mathematical Analysis
Discrete Be´zier curves and surfaces
Mathematical methods in computer aided geometric design II
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
Discrete Bernstein bases and Hahn polynomials
SPOA VII Proceedings of the seventh Spanish symposium on Orthogonal polynomials and applications
The geometry of optimal degree reduction of Be´zier curves
Computer Aided Geometric Design
Convergent inversion approximations for polynomials in Bernstein form
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
Using Jacobi polynomials for degree reduction of Bézier curves withCk-constraints
Computer Aided Geometric Design
A unified matrix representation for degree reduction of Bézier curves
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
Dual generalized Bernstein basis
Journal of Approximation Theory
Optimal multi-degree reduction of Bézier curves with G2-continuity
Computer Aided Geometric Design
Application of Chebyshev II-Bernstein basis transformations to degree reduction of Bézier curves
Journal of Computational and Applied Mathematics
Constrained multi-degree reduction of triangular Bézier surfaces using dual Bernstein polynomials
Journal of Computational and Applied Mathematics
Sample-based polynomial approximation of rational Bézier curves
Journal of Computational and Applied Mathematics
Multi-degree reduction of Bézier curves using reparameterization
Computer-Aided Design
Polynomial approximation of rational Bézier curves with constraints
Numerical Algorithms
Using weighted norms to find nearest polynomials satisfying linear constraints
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Linear methods for G1, G2, and G 3-Multi-degree reduction of Bézier curves
Computer-Aided Design
Journal of Computational and Applied Mathematics
Explicit G2-constrained degree reduction of Bézier curves by quadratic optimization
Journal of Computational and Applied Mathematics
An explicit method for G3 merging of two Bézier curves
Journal of Computational and Applied Mathematics
Construction of dual B-spline functions
Journal of Computational and Applied Mathematics
Optimal multi-degree reduction of Bézier curves with geometric constraints
Computer-Aided Design
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We present a novel approach to the problem of multi-degree reduction of Bezier curves with constraints, using the dual constrained Bernstein basis polynomials, associated with the Jacobi scalar product. We give properties of these polynomials, including the explicit orthogonal representations, and the degree elevation formula. We show that the coefficients of the latter formula can be expressed in terms of dual discrete Bernstein polynomials. This result plays a crucial role in the presented algorithm for multi-degree reduction of Bezier curves with constraints. If the input and output curves are of degree n and m, respectively, the complexity of the method is O(nm), which seems to be significantly less than complexity of most known algorithms. Examples are given, showing the effectiveness of the algorithm.