We derive a natural extension of Boehm's free-form y-spline, the G* interpolating y-spline. Primarily, the conditions under which singularities in the spline formulation occur are investigated. Also, the effect that these singularities have on the interpolant are studied. Comparisons are made to the behavior of the interpolating v-spline.

Linear interpolation has been adapted in many signal and image processing applications due to its simple implementation and low computational cost. In standard linear interpolation the kernel is the second order B-spline   2 β t . In this work we show that the interpolation error can be remarkably diminished by using the time-shifted B-spline   2 β t Δ as an interpolation kernel. We verify ...

We generalize the univariate divided difference to a multivariate setting by considering linear combinations of point evaluations that annihilate the null space of certain differential operators. The relationship between such a linear functional and polynomial interpolation resembles that between the divided difference and Lagrange interpolation. Applying the functional to the shifted multivari...

This paper describes the use of cubic splines for interpolating monotonic data sets. Interpolating cubic splines are popular for fitting data because they use low-order polynomials and have C2 continuity, a property that permits them to satisfy a desirable smoothness constraint. Unfortunately, that same constraint often violates another desirable property: monotonicity. The goal of this work is...

Application of geometric transformation to images requires an interpolation step. When applied to image rotation, the presently most e cient GPU implementation for the cubic spline image interpolation still cost about 10 times as much as linear interpolation. This implementation involves two steps: a pre lter step performs a two-pass forward-backward recursive lter, then a cubic polynomial inte...