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
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
Basis conversion among Bézier, Tchebyshev and Legendre
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 triangular Bézier surfaces with corners continuity in the norm L2
Journal of Computational and Applied Mathematics
Constrained degree reduction of polynomials in Bernstein-Bézier form over simplex domain
Journal of Computational and Applied Mathematics
Application of Chebyshev II-Bernstein basis transformations to degree reduction of Bézier curves
Journal of Computational and Applied Mathematics
Constrained multi-degree reduction of Bézier surfaces using Jacobi polynomials
Computer Aided Geometric Design
Multi-degree reduction of Bézier curves with constraints, using dual Bernstein basis polynomials
Computer Aided Geometric Design
Matrix representation for multi-degree reduction of Bézier curves
Computer Aided Geometric Design
Multi-degree reduction of triangular Bézier surfaces with boundary constraints
Computer-Aided Design
Explicit G2-constrained degree reduction of Bézier curves by quadratic optimization
Journal of Computational and Applied Mathematics
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Given a Bézier curve of degree n, the problem of optimal multi-degree reduction (degree reduction of more than one degree) by a Bézier curve of degree m (m n - 1) with constraints of endpoints continuity is investigated. With respect to L2 norm, this paper presents one approximate method (MDR by L2) that gives an explicit solution to deal with it. The method has good properties of endpoints interpolation: continuity of any r, s (r, s ≥ 0) orders can be preserved at two endpoints respectively. The method in the paper performs multi-degree reduction at one time and does not need the stepwise computing. When applied to the multi-degree reduction with endpoints continuity of any orders, the MDR by L2 obtains the best least squares approximation. Comparison with another method of multi-degree reduction (MDR by L∞), which achieves the nearly best uniform approximation with respect to L∞ norm, is also given. The approximate effect of the MDR by L2 is better than that of the MDR by L∞. Explicit approximate error analysis of the multi-degree reduction methods is presented.