The T-meshes are local modification of rectangular meshes which allow T-junctions. The splines over T-meshes are involved in many fields, such as finite element methods, CAGD etc. The dimension of a spline space is a ...The T-meshes are local modification of rectangular meshes which allow T-junctions. The splines over T-meshes are involved in many fields, such as finite element methods, CAGD etc. The dimension of a spline space is a basic problem for the theories and applications of splines. However, the problem of determining the dimension of a spline space is difficult since it heavily depends on the geometric properties of the partition. In many cases, the dimension is unstable. In this paper, we study the instability in the dimensions of spline spaces over T-meshes by using the smoothing cofactor-conformality method. The modified dimension formulas of spline spaces over T-meshes with T-cycles are also presented. Moreover, some examples are given to illustrate the instability in the dimensions of the spline spaces over some special meshes.展开更多
This paper studies on the dimensions of spline spaces over some given T-meshes.Using the smoothing cofactor-conformality method,we study the instability in the dimensions of the spline spaces over T-meshes with 2-nest...This paper studies on the dimensions of spline spaces over some given T-meshes.Using the smoothing cofactor-conformality method,we study the instability in the dimensions of the spline spaces over T-meshes with 2-nested and 3-nested T-cycles.We define a singularity factor of each simple T-cycle,the instability and the structure’s degeneration are associated with the singularity factors.In order to get a stable dimension formula over T-mesh with a N-nested T-cycle,a constraint on the T-mesh is introduced.Finally,a possible degeneration for a case of parallel T-cycles is illustrated.展开更多
A quasi-rectangular mesh (denoted by △QR) is basically a rectangular mesh (△R) that allows local modifications, including T-mesh (△T) and L-mesh (△L). In this paper, the dimensions of the bivariate spline spaces S...A quasi-rectangular mesh (denoted by △QR) is basically a rectangular mesh (△R) that allows local modifications, including T-mesh (△T) and L-mesh (△L). In this paper, the dimensions of the bivariate spline spaces Skμ(△QR) are discussed by using the Smoothing Cofactor-Conformality method. The dimension formulae are obtained with some constraints depending on the order of the smoothness, the degree of the spline functions and the structure of the mesh as well.展开更多
基金Acknowledgments. This work is partly supported by the National Natural Science Foundation of China （Nos. 11290143, Ul135003, 11471066, 11271060, 11301052）, Fundamental Research of Civil Aircraft （No. MJ-F-2012-04）, and the Fundamental Research Funds for the Central Universities （Nos. DUT13LK07, DUT13LK45, DUT14YQ111）.
文摘The T-meshes are local modification of rectangular meshes which allow T-junctions. The splines over T-meshes are involved in many fields, such as finite element methods, CAGD etc. The dimension of a spline space is a basic problem for the theories and applications of splines. However, the problem of determining the dimension of a spline space is difficult since it heavily depends on the geometric properties of the partition. In many cases, the dimension is unstable. In this paper, we study the instability in the dimensions of spline spaces over T-meshes by using the smoothing cofactor-conformality method. The modified dimension formulas of spline spaces over T-meshes with T-cycles are also presented. Moreover, some examples are given to illustrate the instability in the dimensions of the spline spaces over some special meshes.
基金This work is supported by the National Natural Science Foundation of China(Nos.11471066,11572081,11290143,11601064)Fundamental Research of Civil Aircraft(No.MJ-F-2012-04)the Fundamental Research Funds for the Central Universities(DUT15LK44).
文摘This paper studies on the dimensions of spline spaces over some given T-meshes.Using the smoothing cofactor-conformality method,we study the instability in the dimensions of the spline spaces over T-meshes with 2-nested and 3-nested T-cycles.We define a singularity factor of each simple T-cycle,the instability and the structure’s degeneration are associated with the singularity factors.In order to get a stable dimension formula over T-mesh with a N-nested T-cycle,a constraint on the T-mesh is introduced.Finally,a possible degeneration for a case of parallel T-cycles is illustrated.
基金the National Natural Science Foundation of China (Nos.60533060 10726067)+1 种基金the Natural Science Foundation for Doctoral Career of Liaoning Province (No.20061060)the Science Foundation of Dalian University of Technology (No.SFDUT07001)
文摘A quasi-rectangular mesh (denoted by △QR) is basically a rectangular mesh (△R) that allows local modifications, including T-mesh (△T) and L-mesh (△L). In this paper, the dimensions of the bivariate spline spaces Skμ(△QR) are discussed by using the Smoothing Cofactor-Conformality method. The dimension formulae are obtained with some constraints depending on the order of the smoothness, the degree of the spline functions and the structure of the mesh as well.
