Using Jacobi polynomials for degree reduction of Bézier curves withCk-constraints

Authors:
Young Joon Ahn
Affiliations:
Department of Mathematics Education, Chosun University, Gwangju, 501-449, South Korea
Venue:
Computer Aided Geometric Design
Year:
2003

Citing 5
Cited 9

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
The geometry of optimal degree reduction of Be´zier curves

Computer Aided Geometric Design

Constrained polynomial degree reduction in the L2-norm equals best weighted Euclidean approximation of Bézier coefficients

Computer Aided Geometric Design
Optimal multi-degree reduction of Bézier curves with G2-continuity

Computer Aided Geometric Design
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
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
Constrained approximation of rational Bézier curves based on a matrix expression of its end points continuity condition

Computer-Aided Design
Multi-degree reduction of Bézier curves using reparameterization

Computer-Aided Design
Polynomial approximation of rational Bézier curves with constraints

Numerical Algorithms

Quantified Score

Hi-index	0.00

Visualization

Abstract

We propose the constrained Jacobi polynomial as an error function of good degree reduction of Bézier curve with Ck-constraints at the boundaries, k = 2, 3. The result is a natural extension of the method proposed by Kim and Ahn (2000). The best Ck-constrained degree reduction in L∞-norm, k 0, cannot be obtained in explicit form and requires higher computational complexity such as Remes algorithm. The method of Ck-constrained degree reduction using the constrained Jacobi polynomials is represented in explicit form, and its L∞-norm error is obtainable using Newton method and is slightly larger than that of the best Ck-constrained degree reduction. We also present the subdivision scheme for the Ck-constrained degree reduction within given tolerance. As an illustration, our method is applied to Ck-constrained degree reduction of planar Bézier curve, and compare its result to that of the best Ck-constrained degree reduction.