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...

as a generalization of the triple i method, the universal triple imethod is investigated from the viewpoints of both fuzzy reasoningand fuzzy controller. the universal triple i principle is putforward, which improves the previous triple i principle. then,unified form of universal triple i method is established based onthe (0,1)-implication or r-implication. moreover, the reversibilityproperty o...

We describe an algorithm for constructing a Lagrange interpolation pair based on C cubic splines defined on tetrahedral partitions. In particular, given a set of points V ∈ IR, we construct a set P containing V and a spline space S 3 (△) based on a tetrahedral partition △ whose set of vertices include V such that interpolation at the points of P is well-defined and unique. Earlier results are e...

The problem of interpolation of discrete set of data on the interval [a, b] representing the function f is investigated. A family of C splines with one free generating function is introduced in order to solve this problem. Cubic C splines belong to this family. The required conditions which must satisfy the generating function in order to obtain explicit interpolants are presented and examples ...

We explore the construction of parametric surfaces which interpolate prescribed 3D scattered data using spaces of parametric splines defined on a 2D triangulation. The method is based on minimizing cettain natura1 energy expressions. Several examples involving filling hoies and crowning surfaces are presented, and the role of the triangulation as a Parameter is explored. The problem of creating...

The first published result in fuzzy rule interpolation was the α-cut based fuzzy rule interpolation, termed as KH fuzzy rule interpolation, originally devoted for complexity reduction. Some deficiencies of this method was presented later, such as subnormal conclusion for certain configuration of the involved fuzzy sets. However, since that several conceptually different fuzzy rule interpolation...

The construction of range restricted univariate and bivariate interpolants to gridded data is considered. We apply Gregory’s rational cubic C splines as well as related rational quintic C splines. Assume that the lower and upper obstacles are compatible with the data set. Then the tension parameters occurring in the mentioned spline classes can be always determined in such a way that range rest...

PSD allows you to move the creature to any pose and resculpt the skin surface in that pose. The sculpted alteration is smoothly (rather than linearly) interpolated as the creature moves to and away from that particular pose. Because the edits can occur at any pose, the underlying interpolation problem is one of scattered interpolation, as opposed to interpolation schemes such as splines that as...

We present a Hermite interpolation problem via splines of odd-degree which, to the best knowledge of the authors, has not been considered in the literature on interpolation via odd-degree splines. In this new interpolation problem, we conjecture that the interpolation error is bounded in the supremum norm independently of the locations of the knots. Given an integer k ≥ 3, our spline interpolan...

This paper proposes a new image resizing method based on splines, which is constructed by the Thieletype continued fractions and the Newton interpolation. Like most interpolation techniques proposed in the past, this paper focuses on determining pixel values using the relationship between neighboring points. The interpolation is carried out by choosing the osculatory interpolants in every subin...