Weighted \(G^0\)- and \(G^1\)-Degree Reduction of Disk Bezier Curves
DOI:
https://doi.org/10.26713/jims.v8i1.351Abstract
A Bezier curve in the plane whose control points are disks is called a disk Bezier curve. In this paper we introduce a novel approach to find weighted degree reduction of disk Bezier curve with \(G^0\)- and \(G^1\) continuity at the boundary. Numerical examples are provided to demonstrate the efficiency and simplicity of the proposed method. Moreover some figures are provided to illustrate the comparisons with other methods.Downloads
References
F. Chen and W. Yang, Degree reduction of disk Bézier curves, Computer Aided Geometric Design 21 (2004), 263–280.
K. Höllig and J. Hörner, Approximation and modeling with B-splines, SIAM Titles in Applied Mathematics 132 (2013).
Q. Hu and G.Wang, Multi-degree reduction of disk Bézier curves in (L_2) norm, Journal of information and Computational Science 7 (5) (2010), 1045–1057.
P. Jiang and J. Tan, Degree reduction of disk Said-ball curves, Journal of Computational System 1 (3) (2005), 389–398.
Q. Lin, J. Rokne, Disk Bézier curves, Computer Aided Geometric Design 15 (1998), 721–737.
N.M. Patrikalakis, Robustness issues in geometric and solid modeling, Computer-Aided Design 32 (2000), 629–689.
A. Rababah, Taylor theorem for planer curves, Proceedings of the American Mathematical Society 119 (3) (1993), 803–810.
A. Rababah, Distances with rational triangular Bézier surfaces, Applied Mathematics and Computation 160 (2005), 379–386.
A. Rababah, High accuracy Hermite approximation for space curves in (mathbb{R}^d), Journal of Mathematical Analysis and Applications 325 (2007), 920–931.
A. Rababah and S. Mann, Linear Methods for (G_1)-, (G_2)-, and (G_3)-multi-degree reduction of Bézier curves, Computer-Aided Design 45 (2013), 405–414.
A. Rababah and Y. Hamza, Multi-degree reduction of disk Bézier curves with (G_0)- and (G_1)-continuity, Journal of Inequalities and Applications 2015 (2015), 307.
A. Rababah and S. Ibrahim, Weighted (G_1)-multi-degree reduction of Bézier curves, International Journal of Advanced Computer Science and Applications 7 (2) (2016), 540–545.
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