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Approximating rational triangular Bézier surfaces by polynomial triangular Bézier surfaces

✍ Scribed by Hui-Xia Xu; Guo-Jin Wang

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
510 KB
Volume
228
Category
Article
ISSN
0377-0427

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✦ Synopsis

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 degreeelevated 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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