The h-B´ezier curve is a generalized model of B´ezier curve based on the sense of h-calculus.In order to enhance the modeling ability of Said-Ball curve and improve the speed of recursive valuation of h-B´ezier curve,this paper proposes the h-Said-Ball basis function of arbitrary order and constructs the h-Said-Ball curve.By analyzing the transformation relationship between the recursive valuation algorithm of Said-Ball curve and B´ezier curve,combining the recursive valuation algorithm of h-B´ezier curve and the construction method of h-Bernstein basis function,the expressions of arbitrary times of h-Said-Ball basis function are obtained.The h-Said-Ball basis has excellent properties such as non-negativity,unit decomposition,and endpoint interpolation,and there is an explicit transformation matrix between it and the h-Bernstein basis.Further,the h-Said-Ball curve is defined and its basic properties are analyzed,and the recursive valuation algorithm and envelope representation are derived.h-Said-Ball curve is half the computational effort of the h-B´ezier curve.With the help of the corner cutting algorithms from the h-Said-Ball curve to the h-B´ezier curve,it is shown that the h-Said-Ball basis is a fully positive basis,and thus the h-Said-Ball curve has variational reduction and convexity preservation.Numerical examples show the modeling advantages and flexibility of the h-Said-Ball curve over the Said-Ball curve.
维普
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