Approximate Bézier curves by cubic LN curves

Huang, Wei-Xian; Jin, Cong-Jian; Wang, Guojin

doi:10.1016/j.amc.2011.08.032

Cited by 3 publications

(1 citation statement)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Some studies on data fitting using rational Be´zier functions, to determine the best conic approximation of a given curve which is based on Hausdorff distance function [7], approximate rational Be´zier curves by Be´zier curves through the concept of C ðu;vÞ -continuity [1] and as iteration method for approximation of rational Be´zier curves by adjusting control points gradually using the scheme of weighted progressive iteration approximations through a global L perror [9]. Recently, a few researchers such as Huang et al [6] whose derived offset by using cubic Be´zier for approximating degree n Be´zier with comparing three methods, Hausdorff distance, shifting control and approximation based on L 2 norm in order to find the better approximation. While Yang et al [21] focused on curves on surfaces which present a parabola approximation method based on the cubic rational Be´zier surfaces.…”

Section: Introductionmentioning

confidence: 99%

Data fitting by G1 rational cubic Bézier curves using harmony search

Mohamed

Majid

Piah

2015

Egyptian Informatics Journal

View full text Add to dashboard Cite

A metaheuristic algorithm, called Harmony Search (HS) is implemented for data fitting by rational cubic Be´zier curves. HS is a derivative-free real parameter optimization algorithm, and draws an inspiration from the musical improvisation process of searching for a perfect state of harmony. HS is suitable for multivariate non-linear optimization problem. It is mainly achieved by data fitting using rational cubic Be´zier curves with G 1 continuity for every joint of segments of the whole data sets. This approach has significant contributions in making the technique automated. HS is used to optimize positions of middle points and values of the shape parameters. Test outline images and comparative experimental analysis are presented to show effectiveness and robustness of the proposed method. Statistical testing between HS and two other different metaheuristic algorithms is used in the analysis on several outline images. All of the algorithms improvised a near optimal solution but the result that is obtained by the HS is better than the results of the other two algorithms.Ó 2015 Production and hosting by Elsevier B.V. on behalf

show abstract