Probabilistic and analytic formulas for the periodic splines interpolating with multiple nodes

Geodesic Interpolating Splines

We propose a simple and eecient method to interpolate landmark matching by a non-ambiguous mapping (a diieomorphism). This method is based on spline interpolation, and on recent techniques developed for the estimation of ows of diieomorphisms. Experimental results show interpolations of remarkable quality. Moreover, the method provides a Riemannian distance on sets of landmarks (with xed car-di...

On Mixed Interpolating-Smoothing Splines and the ν-Spline

Generating dimension formulas for multivariate splines

Dimensions of spaces of multivariate splines remain unknown in general. A computational method to obtain explicit formulas for the dimension of spline spaces on simplicial partitions is described. The method is based on Hilbert series and Hilbert polynomials. It is applied to conjecture the dimension formulas for splines on the Alfeld split of a simplex and on several other partitions. AMS clas...

Commutator Properties for Periodic Splines

Commutator properties are established for periodic smoothest splines (on uniform meshes) operated on by certain pseudo-diierential operators. The commutation involves the operations of multiplication by a smooth function, and application of the operator of orthogonal projection onto a spline space; or the orthogonal projection is replaced by a discrete version of orthogonal projection obtained ...

Smooth, Easy to Computer Interpolating Splines

We present a system of interpolating splines with first and approximate second order geometric continuity. The curves are easily computed in linear time by solving a system of linear equations without the need to resort to any kind of successive approximation scheme. Emphasis is placed on the need to find aesthetically pleasing curves in a wide range of circumstances; favorable results are obta...