Approximating rational triangular Bezier surfaces by polynomial triangular Bezier surfaces

摘要

An attractive method for approximating rational triangular Bezier surfaces by polynomial triangular Bezier 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 Bezier 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 Bezier surface, then a polynomial triangular Bezier 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.