Approximating rational triangular Bézier surfaces by polynomial triangular Bézier surfaces |
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Authors: | Hui-Xia Xu Guo-Jin Wang |
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Affiliation: | 1. Department of Mathematics, Zhejiang University, Hangzhou 310027, Zhejiang, People’s Republic of China;2. Institute of Mathematics, Zhejiang Wanli University, Ningbo 315100, Zhejiang, People’s Republic of China |
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Abstract: | An attractive method for approximating rational triangular Bézier surfaces by polynomial triangular Bézier surfaces is introduced. The main result is that the arbitrary given order derived vectors of a polynomial triangular surface converge uniformly to those of the approximated rational triangular Bézier surface as the elevated degree tends to infinity. The polynomial triangular surface is constructed as follows. Firstly, we elevate the degree of the approximated rational triangular Bézier surface, then a polynomial triangular Bézier surface is produced, which has the same order and new control points of the degree-elevated rational surface. The approximation method has theoretical significance and application value: it solves two shortcomings-fussy expression and uninsured convergence of the approximation-of Hybrid algorithms for rational polynomial curves and surfaces approximation. |
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Keywords: | Rational triangular Bé zier surface Polynomial triangular Bé zier surface Hybrid algorithm Degree-elevation Approximation |
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