UE-Brzier （unified and extended Brzier） basis is the unified form of Brzier-like bases, including polynomial Brzier basis, trigonometric polynomial and hyperbolic polynomial Brzier basis. Similar to the original Brz...UE-Brzier （unified and extended Brzier） basis is the unified form of Brzier-like bases, including polynomial Brzier basis, trigonometric polynomial and hyperbolic polynomial Brzier basis. Similar to the original Brzier-like bases, UE-Brzier basis func-tions are not orthogonal. In this paper, a group of orthogonal basis is constructed based on UE-Brzier basis. The transformation matrices between UE-Brzier basis and the proposed orthogonal basis are also solved.展开更多
The explicit expression of the G3 basis function is presented in this paper. It is derived by constructing the conversion matrix between G3 basis function and Brzier representation. After the matrix decomposition, equ...The explicit expression of the G3 basis function is presented in this paper. It is derived by constructing the conversion matrix between G3 basis function and Brzier representation. After the matrix decomposition, equations for constructing G3 splines can be presented independently of geometric shape parameters＇ values. It makes the equation＇s solving easier. It is also known that the general form of the G3spline basis function is given in the first time. Its geometric construction method is presented.展开更多
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
基金Supported by National Science Foundation of China(No.60904070,61272032)the Natural Science Foundation of Zhejiang Province(No.LY12F02002,Y1111101)
文摘UE-Brzier （unified and extended Brzier） basis is the unified form of Brzier-like bases, including polynomial Brzier basis, trigonometric polynomial and hyperbolic polynomial Brzier basis. Similar to the original Brzier-like bases, UE-Brzier basis func-tions are not orthogonal. In this paper, a group of orthogonal basis is constructed based on UE-Brzier basis. The transformation matrices between UE-Brzier basis and the proposed orthogonal basis are also solved.
基金Supported by National Natural Science Foundation of China(Grants 61100129)Open Program of Key Laboratory of Intelligent Information Processing,Institute of Computing Technology,Chinese Academy of Sciences(IIP2014-7)
文摘The explicit expression of the G3 basis function is presented in this paper. It is derived by constructing the conversion matrix between G3 basis function and Brzier representation. After the matrix decomposition, equations for constructing G3 splines can be presented independently of geometric shape parameters＇ values. It makes the equation＇s solving easier. It is also known that the general form of the G3spline basis function is given in the first time. Its geometric construction method is presented.
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.
