A precise tie between a univariate spline’s knots and its zeros abundance and dissemination is formulated. As an application, a conjecture formulated by De Concini and Procesi is shown to be true in the special univariate, unimodular case. As a supplement, the same conjecture is shown, through computing a counterexample, to be false when unimodularity hypothesis is dropped.

In this paper the sampled signal reconstruction problem is formulated and solved as the sampled-data H smoothing problem, in which an analog reconstruction error is minimized. Both infinite (non-causal reconstructors) and finite (reconstructors with relaxed causality) preview cases are considered. The optimal reconstructors are in the form of the cascade of a discrete-time smoother and a genera...

An algorithmic approach to degree reduction of interval B-spline curve is presented in this paper. The curves that are useful in geometric modeling should have a relatively smooth shape and should be intuitively connected with the path of the sequence of control points. One family of curves satisfying this requirement is represented by the B-spline curves. The four fixed Kharitonov's polynomial...

In this paper we consider spline function of general degree m which has the same area as the function does in each partition of the sub-intervals. The existence and uniqueness in general of spline functions also been studied and obtained the result. : In this paper we consider spline function of general degree, i.e.,of degree m, m=2,3,.... We first give definitions and notations. We take 0 =x 0...

In many practical applications, piecewise polynomial surfaces need to be connected by using different smoothness degrees and, in the literature, tensor product spline surfaces of such a kind have been widely investigated. Several problems can arise with tensor product surfaces, for example this choice may cause oscillations far from the shape to be built. Therefore, in some cases spline surface...

Recently in [7). a new multivariate B-spline scheme based on blending functions and control vertices was developed . This surface scheme allows CIo-1-continuous piecewise polynomial surfaces of degree k over arbitrary triangulations to be modelled . Actually, piecewise polynomial surfaces over a refined triangulation are produced given an arbitrary triangulation . The scheme exhibits both affin...

This paper presents cubic spline interpolation based trajectory planning method which is aiming to achieve smooth biped robot walking trajectory. We first characterize the bipedal walking cycle and point out some major issues that need to be addressed to plan a continuous swing leg trajectory by using the concept of cubic polynomial and cubic spline interpolation. By applying these interpolatio...

A new multivariate B-spline scheme based on blending functions and control ver-tices has recently been developed by Dahmen, Micchelli, and Seidel 4]. This surface scheme allows to model piecewise polynomial surfaces of degree k over arbitrary triangulations, such that the resulting surfaces are C k?1-continuous everywhere. The scheme exhibits both aane invariance and the convex hull property, a...

In this paper fuzzy piecewise cubic interpolation is constructed for fuzzy data based on B-spline basis functions. We add two new additional conditions which guarantee uniqueness of fuzzy B-spline interpolation.Other conditions are imposed on the interpolation data to guarantee that the interpolation function to be a well-defined fuzzy function. Finally some examples are given to illustrate the...