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![]() | Inverse B-spline interpolation | ![]() |
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It is not too difficult to construct a convolutional basis with better
interpolation properties than those of B-splines, for example by
sacrificing their smoothness. The following piece-wise cubic function
has a lower smoothness than in equation (13)
but slightly better interpolation behavior:
Figures 23 and 24 compare the test
interpolation errors and discrete responses of methods based on the
B-spline function and the lower smoothness function
. The latter method has a slight but visible performance
advantage and a slightly wider discrete spectrum.
spl4mom4
Figure 23. Interpolation error of the third-order B-spline interpolant (dashed line) compared to that of the lower smoothness spline interpolant (solid line). |
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specspl4mom4
Figure 24. Discrete interpolation responses of third-order B-spline and lower smoothness spline interpolants (left) and their discrete spectra (right) for ![]() |
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Blu et al. (1998) have developed a general approach for constructing non-smooth piece-wise functions with optimal interpolation properties. However, the gain in accuracy is often negligible in practice. In the rest of this paper, I use the classic B-spline method.
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![]() | Inverse B-spline interpolation | ![]() |
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