PROGRESSIVE ITERATIVE APPROXIMATION FOR BEZIER CURVES WITH SHAPE PARAMETERS

Main Article Content

SHAOTAO LUO
ZIXUAN TANG
CHENGZHI LIU

Abstract

In this paper, we exploit the progressive iterative approximation (PIA) and the weighted progressive iterative approximation (WPIA) for Bezier curve with shape parameters. By introducing a shape parameter, we can adjust the shape of curve as well as the convergence rate of PIA and WPIA. By choosing a appropriate shape parameter, the PIA and WPIA have the fastest convergence rate. Numerical examples also show that the optimal shape parameter make the iterative method converge faster than the PIA and WPIA for the classic Bezier curves.

Keywords:
-Bezier curve, shape parameter, progressive iterative approximation, spectral radius.

Article Details

How to Cite
LUO, S., TANG, Z., & LIU, C. (2020). PROGRESSIVE ITERATIVE APPROXIMATION FOR BEZIER CURVES WITH SHAPE PARAMETERS. Asian Journal of Mathematics and Computer Research, 27(2), 42-48. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/5239
Section
Original Research Article

References

Lin H, Maekawa T, Deng C. Survey on geometric iterative methods and their applications.

Computer-Aided Design. 2018;95:40-51.

Lin H, Bao H,Wang G. Totally positive bases and progressive iterative approximation. Comput.

Math. Appl. 2005;50:575-586.

Lu L. Weighted progressive iterative approximation and convergence analysis. Comput. Aided Geom. Design. 2010;2:129-137.

Carnicer J, Delgado J, Pena J. Richardson method and totally nonnegative linear systems.

Linear Algebra Appl. 2010;11:2010-2017.

Carnicer J, Delgado J. On the progressive iterative approximation property and alternative iterations. Comput. Aided Geom. Design. 2011;28:523-526.

Deng S, Wang G. Numerical analysis of the progressive iterative approximation method.

Comput. Aided Design and Graphics. 2012;7:879-884.

Liu C, Han X, Li J. The Chebyshev accelerating method for progressive iterative approximation. Commun. Inf. Syst. 2017;17:25-43.

Zhang L, Tan J, Ge X, Guo Z. Generalized B-splines geometric iterative tting method with mutually dierent weights. Journal of Comput. & Appl. Math.. 2018;329:331-343.

Liu C, Han X, Li J. Progressive-iterative approximation by extension of cubic uniform B-spline curves. Journal of Computer-Aided Design & Computer Graphics. 2006;11:269-274.

Wu X. Bezier curve with shape parameter. Journal of Image and Graphics. 2019;31:899-910. Farouki R. The Bernstein polynomial basis: A centennial retrospective. Computer Aided

Geometric Design. 2012;29:379-419.

Yan L, Han X. The extended cubic uniform B-spline curve based on totally positive basis.

Journal of Graphics. 2016;37:329-336.