This paper is concerned with the description of an algorithm for generating the B-nets of box splines and an algorithm based on subdivision of these B-nets for graphically displaying spline surfaces on a three-or four-directional mesh. The combination of these two algorithms is shown to compare favorably over the other existing algorithms for this purpose. 0 1 x1. Introduction It is well known ...

In this brief note, we evaluate certain quartic and octic Gauss sums with the use of theorems on fourth and eighth power difference sets. We recall that a subset H of a finite (additive) abelian group G is said to be a difference set of G [5, p. 64] if for some fixed natural number A, every nonzero element of G can be written as a difference of two elements of/fin exactly A ways. Throughout the...

A new approximation method for conic section by quartic Bézier curves is proposed. This method is based on the quartic Bézier approximation of circular arcs. We give the upper bound of Hausdorff distance between the conic section and the quartic Bézier curve, and also show that the approximation order is eight. And we prove that our approximation method has a smaller upper bound than previous q...

In this paper we first revisit a classical problem of computing variational splines. We propose to compute local variational splines in the sense that they are interpolatory splines which minimize the energy norm over a subinterval. We shall show that the error between local and global variational spline interpolants decays exponentially over a fixed subinterval as the support of the local vari...

This paper is concerned with the spline interpolation of functions with a boundary layer component. It is shown that polynomial formulas of spline interpolation for such functions lead to significant errors. We proposed nonpolynomial spline interpolation formulas, fitted to a boundary layer component. Nonsmooth and smooth on whole interval interpolants are constructed. The accuracy of construct...

Abstract Given gridded cell-average data of a smooth multivariate function, we present constructive explicit procedure for generating high-order global approximation the function. One contribution is derivation approximations to point-values function directly from data. The second development univariate B-spline-based quasi-interpolation operators using Multivariate spline are obtained by tenso...

Here presented is the interrelationship between Eulerian polynomials, Eulerian fractions and Euler-Frobenius polynomials, Euler-Frobenius fractions, Bsplines, respectively. The properties of Eulerian polynomials and Eulerian fractions and their applications in B-spline interpolation and evaluation of Riemann zeta function values at odd integers are given. The relation between Eulerian numbers a...

Simple geometric proofs are given for the total positivity of the B-spline collocation matrix and the variation diminishing property of the B-spline representation of a spline.

In this paper, we propose a method to deal with numerical integral by using two kinds of C quasi-interpolation operators on the bivariate spline space, and also discuss the convergence properties and error estimates. Moreover, the proposed method is applied to the numerical evaluation of 2-D singular integrals. Numerical experiments will be carried out and the results will be compared with some...

X n Given a sequence of points { i}i=l on a regular quadric S: X T A X = 0 C E d, d >1 3, we study the problem of constructing a G I rational quadratic spline curve lying on 5' that interpolates { X ~ } ~ j . It is shown that a necessary condition for the existence of a nontrivial interpolant is ( X ~ A X 2 ) ( X T i A X i + I ) > 0, i = 1 , 2 , . . . , n 1. Also considered is a Hermite interpo...