Multi-degree reduction of Bézier curves using reparameterization

Authors:
Xiao-Diao Chen;Weiyin Ma;Jean-Claude Paul
Affiliations:
Hangzhou Dianzi University, Hangzhou, 310037, PR China and Department of MEEM, City University of Hong Kong, Hong Kong, China;Department of MEEM, City University of Hong Kong, Hong Kong, China;School of Software, Tsinghua University, Beijing 100084, PR China and INRIA, France
Venue:
Computer-Aided Design
Year:
2011

Citing 25
Cited 3

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
Approximate conversion of rational splines

Computer Aided Geometric Design
Degree reduction of Be´zier curves

Selected papers of the international symposium on Free-form curves and free-form surfaces
Geometric Hermite interpolation

Computer Aided Geometric Design
Geometric Hermite interpolation with maximal order and smoothness

Computer Aided Geometric Design
The geometry of optimal degree reduction of Be´zier curves

Computer Aided Geometric Design
Degree reduction of B-spline curves

Computer Aided Geometric Design
Curves and surfaces for CAGD: a practical guide

Curves and surfaces for CAGD: a practical guide
Bezier and B-Spline Techniques

Bezier and B-Spline Techniques
A unified approach for degree reduction of polynomials in the Bernstein basis part I: real polynomials

Journal of Computational and Applied Mathematics
Application of Legendre--Bernstein basis transformations to degree elevation and degree reduction

Computer Aided Geometric Design
Distance for degree raising and reduction of triangular Bézier surfaces

Journal of Computational and Applied Mathematics
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
Constrained polynomial degree reduction in the L2-norm equals best weighted Euclidean approximation of Bézier coefficients

Computer Aided Geometric Design
Degree reduction of disk Bézier curves

Computer Aided Geometric Design
Approximation of circular arcs and offset curves by Bézier curves of high degree

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
A note on constrained degree reduction of polynomials in Bernstein-Bézier form over simplex domain

Journal of Computational and Applied Mathematics
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

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
Optimal multi-degree reduction of Bézier curves with geometric constraints

Computer-Aided Design

Quantified Score

Hi-index	0.00

Visualization

Abstract

L"2-norms are often used in the multi-degree reduction problem of Bezier curves or surfaces. Conventional methods on curve cases are to minimize @!"0^1@?A(t)-C(t)@?^2dt, where C(t) and A(t) are the given curve and the approximation curve, respectively. A much better solution is to minimize @!"0^1@?A(@f(t))-C(t)@?^2dt, where A(@f(t)) is the closest point to point C(t), that produces a similar effect as that of the Hausdorff distance. This paper uses a piecewise linear function L(t) instead of t to approximate the function @f(t) for a constrained multi-degree reduction of Bezier curves. Numerical examples show that this new reparameterization-based method has a much better approximation effect under Hausdorff distance than those of previous methods.