An iterative algorithm for polynomial approximation of rational triangular Bezier surfaces

作者：Hu, Qianqian^*

来源：Applied Mathematics and Computation, 2013, 219(17): 9308-9316.

DOI：10.1016/j.amc.2013.03.053

• Rational triangular Bezier surfaces
• Polynomial approximation
• Weighted progressive iteration
• Triangular Bernstein basis
• Gauss Legendre quadrature rule

This paper presents the weighted progressive iteration approximation (WPIA) property for the triangular Bernstein basis over a triangle domain with uniform parameters, which is extended from the PIA property for triangular Bernstein basis proposed by Chen and Wang in [J. Chen, G. J. Wang, Progressive-iterative approximation for triangular Bezier surfaces, Computer-Aided Design 43(2011) 889-895]. We also provide how to choose an optimal value of the weight to own the fastest convergence rate for triangular Bernstein basis. Furthermore, anew and efficient iterative method is proposed for polynomial approximation of rational triangular Bezier surfaces. The algorithm is reiterated until a halting condition about approximation error is satisfied. And the approximation error in L-p-norm (p = 1, 2, infinity) is calculated by the symmetric Gauss Legendre quadrature rule for composite numerical integration over a triangular surface. Finally, several numerical examples are presented to validate the effectiveness of this method.

• 出版日期2013-5-1
• 单位浙江工商大学