A kind of mixed tensor product negative Bemstein-B6zier basis function is presented in this paper. Some important prop- erties of this kind of basis function are discussed and mixed tensor product negative Bemstein-B6...A kind of mixed tensor product negative Bemstein-B6zier basis function is presented in this paper. Some important prop- erties of this kind of basis function are discussed and mixed tensor product negative Bemstein-B6zier is defined based on it. The ba- sic properties of the such surface are discussed. Via de Casteljan algorithm, the evaluation algorithm and subdivision algorithm for mixed tensor product negative Bernstein-B6zier surfaces are derived as extensions of the algorithms of B6zier curves and negative Bernstein curves.展开更多
As an important type of polynomial approximation, approximation of functions by Bernstein operators is an important topic in approximation theory and computational theory. This paper gives global and pointwise estimat...As an important type of polynomial approximation, approximation of functions by Bernstein operators is an important topic in approximation theory and computational theory. This paper gives global and pointwise estimates for weighted approximation of functions with singularities by Bernstein operators. The main results are the Jackson＇s estimates of functions f∈ （Wwλ）2 andre Cw, which extends the result of （Della Vecchia et al., 2004）.展开更多
A new algorithm is presented that generates developable Bézier surfaces through a Bézier curve called a directrix. The algorithm is based on differential geometry theory on necessary and sufficient condition...A new algorithm is presented that generates developable Bézier surfaces through a Bézier curve called a directrix. The algorithm is based on differential geometry theory on necessary and sufficient conditions for a surface which is developable, and on degree evaluation formula for parameter curves and linear independence for Bernstein basis. No nonlinear characteristic equations have to be solved. Moreover the vertex for a cone and the edge of regression for a tangent surface can be obtained easily. Aumann’s algorithm for developable surfaces is a special case of this paper.展开更多
文摘A kind of mixed tensor product negative Bemstein-B6zier basis function is presented in this paper. Some important prop- erties of this kind of basis function are discussed and mixed tensor product negative Bemstein-B6zier is defined based on it. The ba- sic properties of the such surface are discussed. Via de Casteljan algorithm, the evaluation algorithm and subdivision algorithm for mixed tensor product negative Bernstein-B6zier surfaces are derived as extensions of the algorithms of B6zier curves and negative Bernstein curves.
文摘As an important type of polynomial approximation, approximation of functions by Bernstein operators is an important topic in approximation theory and computational theory. This paper gives global and pointwise estimates for weighted approximation of functions with singularities by Bernstein operators. The main results are the Jackson＇s estimates of functions f∈ （Wwλ）2 andre Cw, which extends the result of （Della Vecchia et al., 2004）.
基金Project supported by the National Basic Research Program (973) of China (No. 2004CB719400), the National Natural Science Founda-tion of China (Nos. 60373033 and 60333010) and the National Natural Science Foundation for Innovative Research Groups (No. 60021201), China
文摘A new algorithm is presented that generates developable Bézier surfaces through a Bézier curve called a directrix. The algorithm is based on differential geometry theory on necessary and sufficient conditions for a surface which is developable, and on degree evaluation formula for parameter curves and linear independence for Bernstein basis. No nonlinear characteristic equations have to be solved. Moreover the vertex for a cone and the edge of regression for a tangent surface can be obtained easily. Aumann’s algorithm for developable surfaces is a special case of this paper.
