In this paper a method for interpolating planar data points by cubic G splines is presented. A spline is composed of polynomial segments that interpolate two data points, tangent directions and curvatures at these points. Necessary and sufficient, purely geometric conditions for the existence of such a polynomial interpolant are derived. The obtained results are extended to the case when the de...

This paper studies the merits of using knot interval notation for B-spline curves, and presents formulae in terms of knot intervals for common B-spline operations such as knot insertion, differentiation, and degree elevation. Using knot interval notation, the paper introduces MD-splines, which are B-spline-like curves that are comprised of polynomial segments of various degrees (MD stands for “...

A cubic spline regression model was used to fit the experimental open-circuit potential ~OCP! curves of two intercalation electrodes of a lithium-ion battery. All the details of an OCP curve were accurately predicted by the resulting model. The number of regression intervals used to fit an OCP curve was determined in a way such that in each regression interval the OCP exhibits a profile predict...

In this paper,wedesign differentiable, two-dimensional, piecewise polynomial cubic prewavelets of particularly small compact support. They are given in closed form, and provide stable, orthogonal decompositions of L(R). In particular, the splines we use in our prewavelet constructions give rise to stable bases of spline spaces that contain all cubic polynomials, whereas the more familiar box sp...

We study the number of Laurent polynomials in a sum of square magnitudesof a nonnegative Laurent polynomial associated with bivariate box splines on the three-and the four-direction meshes. In addition, we study the same problem associated withtrivariate box splines. The number of Laurent polynomials in a sum of squares magnitudeof a nonnegative Laurent polynomial determines the...

Walking pattern synthesis is carried out using a spline-based parametric optimization technique. Generalized coordinates are approximated by spline functions of class C3 fitted at knots uniformly distributed along the motion time. This high-order differentiability eliminates jerky variations of actuating torques. Through connecting conditions, spline polynomial coefficients are determined as a ...

We construct approximate confidence intervals for a nonparametric regression function. The construction uses polynomial splines with free knot locations. The number of knots is determined by the GCV criteria. The estimates of knot locations and coefficients are obtained through a nonlinear least square solution that corresponds to the maximum likelihood estimate. Confidence intervals are then c...

We explore a class of polynomial tensor-product spline surfaces on 3-6 polyhedra, whose vertices have valence n = 3 or n = 6. This restriction makes it possible to exclusively use rational linear transition maps between the pieces: transitions between the bi-cubic tensor-product spline pieces are either C1 or they are G1 (tangent continuous) based on one single rational linear reparameterizatio...

This essay reviews those basic facts about (univariate) B-splines that are of interest in CAGD. The intent is to give a self-contained and complete development of the material in as simple and direct a way as possible. For this reason, the B-splines are defined via the recurrence relations, thus avoiding the discussion of divided differences which the traditional definition of a B-spline as a d...