There are thousands of articles published on variants of splines, including least squares cubic splines. One of the first least squares articles was de Boor and Rice [1], and a comprehensive explanatory textbook is Dierckx [2]. Unfortunately, every example in the literature and on the web of a least squares cubic spline makes use of B-splines. While B-splines have a certain elegance, they are s...

A-splines are implicit real algebraic curves in Bernstein-B ezier (BB) form that are smooth. We develop a spectrum of physical A-spline curve models using various energy formulations based on the theory of elasticity. Our bending and stretching energy formulations yield interactive physically based modeling with A-splines while preserving the advantages of free-form modeling of complex shapes. ...

We give some empirical comparisons between two nonparametric regression methods based on regularization: the elastic or thin-plate splines, and plastic splines based on total variation penalties. 1. Nonparametric regression with elastic and plastic splines We seek f to fit the dependence of response points zi ∈ R on two-dimensional covariates (xi, yi) living in the domain Ω. To this end, we emp...

The convergences of three L1 spline methods for scattered data interpolation and fitting using bivariate spline spaces are studied in this paper. That is, L1 interpolatory splines, splines of least absolute deviation, andL1 smoothing splines are shown to converge to the given data function under some conditions and hence, the surfaces from these three methods will resemble the given data values...

Splines can be constructed by convolving the indicator function of a cell whose shifts tessellate Rn. This paper presents simple, geometric criteria that imply that, for regular shift-invariant tessellations, only a small subset of such spline families yield nested spaces: primarily the well-known tensor-product and box splines. Among the many nonrefinable constructions are hex-splines and thei...

In this paper we prove that there exists a unique positive symmetrical univariate B-spline with minimal support. It is obtained as linear combination of a minimal number of successive classical B-splines with multiple knots in the space, S d , of cardinal polynomial splines of class C and degree d. Next, we show that the approximation order in the space generated by the integer translates of th...

Bivariate quadratic simplicial B-splines defined by their corresponding set of knots derived from a (suboptimal) constrained Delaunay triangulation of the domain are employed to obtain a Cl-smooth surface. The generation of triangle vertices is adjusted to the area1 distribution of the data in the domain. We emphasize here that the vertices of the triangles initially define the knots of the B-s...

Time series associated with single-molecule experiments and/or simulations contain a wealth of multiscale information about complex biomolecular systems. We demonstrate how a collection of Penalized-splines (P-splines) can be useful in quantitatively summarizing such data. In this work, functions estimated using P-splines are associated with stochastic differential equations (SDEs). It is shown...