Using Jacobi polynomials for degree reduction of Bézier curves with \(C^k\)-constraints

DOI10.1016/S0167-8396(03)00082-7zbMath1069.65504OpenAlexW2087284445MaRDI QIDQ2388523

Young Joon Ahn

Publication date: 14 September 2005

Published in: Computer Aided Geometric Design (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-8396(03)00082-7

zbMATH Keywords

degree reductionChebyshev polynomialJacobi polynomial\(C^{k}\)-continuity\(L_{\infty}\)-norm

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (15)

Constrained multi-degree reduction with respect to Jacobi norms ⋮ Application of degree reduction of polynomial Bézier curves to rational case ⋮ Constrained polynomial degree reduction in the \(L_2\)-norm equals best weighted Euclidean approximation of Bézier coefficients ⋮ Approximating tensor product Bézier surfaces with tangent plane continuity ⋮ Optimal multi-degree reduction of Bézier curves with \(G^1\)-continuity ⋮ Bézier form of dual bivariate Bernstein polynomials ⋮ Polynomial approximation of rational Bézier curves with constraints ⋮ Multi-degree reduction of Bézier curves with constraints, using dual Bernstein basis polynomials ⋮ Rational Bézier curves approximated by Bernstein-Jacobi hybrid polynomial curves ⋮ Explicit algorithms for multiwise merging of Bézier curves ⋮ A quadratic programming method for optimal degree reduction of Bézier curves with \(G^{1}\)-continuity ⋮ Degree reduction of composite Bézier curves ⋮ Application of Chebyshev II-Bernstein basis transformations to degree reduction of Bézier curves ⋮ Constrained degree reduction of polynomials in Bernstein-Bézier form over simplex domain ⋮ Optimal multi-degree reduction of Bézier curves with \(G^2\)-continuity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The geometry of optimal degree reduction of Bézier curves
• Chebyshev economization for parametric surfaces
• Approximation by constrained parametric polynomials
• Good degree reduction of Bézier curves using Jacobi polynomials
• Degree reduction of Bézier curves by uniform approximation with endpoint interpolation
• GEOMETRIC CONIC SPLINE APPROXIMATION IN CAGD
• Degree reduction of Bézier curves
• Degree reduction of Bézier curves

This page was built for publication: Using Jacobi polynomials for degree reduction of Bézier curves with \(C^k\)-constraints