Inverse B-spline interpolation |

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
Interpolation error of the
third-order B-spline interpolant (dashed line) compared to that of
the lower smoothness spline interpolant (solid line).
Figure 23. | |
---|---|

specspl4mom4
Discrete interpolation responses
of third-order B-spline and lower smoothness spline interpolants
(left) and their discrete spectra (right) for .
Figure 24. | |
---|---|

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.

Inverse B-spline interpolation |

2014-02-15