PROGRESSIVE ITERATIVE APPROXIMATION FOR BEZIER CURVES WITH SHAPE PARAMETERS
SHAOTAO LUO
School of Mathematics and Finance, Hunan University of Humanities, Science and Technology, Loudi 417000, P.R. China.
ZIXUAN TANG
School of Mathematics and Finance, Hunan University of Humanities, Science and Technology, Loudi 417000, P.R. China.
CHENGZHI LIU *
School of Mathematics and Finance, Hunan University of Humanities, Science and Technology, Loudi 417000, P.R. China.
*Author to whom correspondence should be addressed.
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.