| Bivariate Splines and Golden Section Based on Theory of Elasticity |
| Received:April 02, 2009 Revised:October 14, 2009 |
| Key Words:
multivariate spline smoothing cofactor conformality condition bending of thin plate golden section.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.60533060; 60373093; 10726068), the Natural Science Foundation of Hebei Province (Grant Nos.A2009000735; A2010000908), Research Project of Hebei Educational Committee (Grant No.2009448) and Shanghai Key Laboratory for Contemporary Applied Mathamtics (Grant No.09FG067). |
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| Abstract: |
| Splines are important in both mathematics and mechanics. We investigate the relationships between bivariate splines and mechanics in this paper. The mechanical meanings of some univariate splines were viewed based on the analysis of bending beams. For the 2D case, the relationships between a class of quintic bivariate splines with smoothness 3 and bending of thin plates are presented constructively. Furthermore, the variational property of bivariate splines and golden section in splines are also discussed. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2011.01.001 |
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