Thin plate splines for transfinite interpolation at concentric circles
We propose a new method for constructing a polyspline on annuli, i.e. a C 2 surface on ℝ2 \ {0}, which is piecewise biharmonic on annuli centered at 0 and interpolates smooth data at all interface circles. A unique surface is obtained by imposing Beppo Levi conditions on the innermost and outermost...
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2013-06-01
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| Series: | Mathematical Modelling and Analysis |
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| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/4125 |
| Summary: | We propose a new method for constructing a polyspline on annuli, i.e. a C 2 surface on ℝ2 \ {0}, which is piecewise biharmonic on annuli centered at 0 and interpolates smooth data at all interface circles. A unique surface is obtained by imposing Beppo Levi conditions on the innermost and outermost annuli, and one additional restriction at 0: either prescribing an extra data value, or asking that the surface is non-singular. We show that the resulting Beppo Levi polysplines on annuli are in fact thin plate splines, i.e. they minimize Duchon's bending energy.
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| ISSN: | 1392-6292 1648-3510 |