| The Dimensions of Spline Spaces on Quasi-Rectangular Meshes |
| Received:October 19, 2006 Revised:January 19, 2007 |
| Key Words:
bivariate spline smoothing cofactor-conformality method dimension formula quasi-rectangular mesh T-mesh L-mesh.
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| Fund Project:the National Natural Science Foundation of China (Nos.60533060; 10726067); the Natural Science Foundation for Doctoral Career of Liaoning Province (No.20061060); the Science Foundation of Dalian University of Technology (No.SFDUT07001). |
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| Abstract: |
| A quasi-rectangular mesh (denoted by $\Delta_{QR}$) is basically a rectangular mesh ($\Delta_{R}$) that allows local modifications, including T-mesh ($\Delta_{T}$) and L-mesh ($\Delta_{L}$). In this paper, the dimensions of the bivariate spline spaces $S_k^\mu(\Delta_{QR})$ 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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2008.04.001 |
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