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1.
In this work, we give an algorithm for constructing a normalized B-spline basis over a Worsey-Piper split of a bounded domain
of ℝ3. These B-splines are all positive, have local support and form a partition of unity. Therefore, they can be used for constructing
local approximants and for many other applications in CAGD. We also introduce the Worsey-Piper B-spline representation of
C
1 quadratic polynomials or splines in terms of their polar forms. Then, we use this B-representation for constructing several
quasi-interpolants which have an optimal approximation order. 相似文献
2.
Let be the uniform triangulation generated by the usual three directional mesh of the plane and let H
1 be the regular hexagon formed by the six triangles of surrounding the origin. We study the space of piecewise polynomial functions in C
k
(R
2) with support H
1 having a sufficiently high degree n, which are invariant with respect to the group of symmetries of H
1 and whose sum of integer translates is constant. Such splines are called H
1-splines. We first compute the dimension of this space in function of n and k. Then we prove the existence of a unique H
1-spline of minimal degree for any fixed k0. Finally, we describe an algorithm computing the Bernstein–Bézier coefficients of this spline. 相似文献
3.
In this paper we generate and study new cubature formulas based on spline quasi-interpolants in the space of quadratic Powell-Sabin splines on nonuniform triangulations of a polygonal domain in ?2. By using a specific refinement of a generic triangulation, optimal convergence orders are obtained for some of these rules. Numerical tests are presented for illustrating the theoretical results. 相似文献
4.
In this paper, we propose an interesting method for approximating the solution of a two dimensional second kind equation with a smooth kernel using a bivariate quadratic spline quasi-interpolant (abbr. QI) defined on a uniform criss-cross triangulation of a bounded rectangle. We study the approximation errors of this method together with its Sloan’s iterated version and we illustrate the theoretical results by some numerical examples. 相似文献
5.
In [7], Lyche and Schumaker have described a method for fitting functions of class C 1 on the sphere which is based on tensor products of quadratic polynomial splines and trigonometric splines of order three associated with uniform knots. In this paper, we present a multiresolution method leading to C 2-functions on the sphere, using tensor products of polynomial and trigonometric splines of odd order with arbitrary simple knot sequences. We determine the decomposition and reconstruction matrices corresponding to the polynomial and trigonometric spline spaces. We describe the general tensor product decomposition and reconstruction algorithms in matrix form which are convenient for the compression of surfaces. We give the different steps of the computer implementation of these algorithms and, finally, we present a test example. 相似文献
6.
Driss Sbibih Abdelhafid Serghini Ahmed Tijini 《Mediterranean Journal of Mathematics》2013,10(3):1273-1292
In this paper, we construct a quadratic composite finite element of class C 1 and quartic composite finite element of class C 2 on a new triangulation τ 10 which is obtained by splitting each triangle of a given triangulation τ into ten smaller subtriangles. These new elements can be used for constructing spline spaces with local basis that can be applied for solving some Hermite interpolation problems with optimal approximation order. 相似文献
7.
In a recent paper (Allouch, in press) [5] on one dimensional integral equations of the second kind, we have introduced new collocation methods. These methods are based on an interpolatory projection at Gauss points onto a space of discontinuous piecewise polynomials of degree r which are inspired by Kulkarni’s methods (Kulkarni, 2003) [10], and have been shown to give a 4r+4 convergence for suitable smooth kernels. In this paper, these methods are extended to multi-dimensional second kind equations and are shown to have a convergence of order 2r+4. The size of the systems of equations that must be solved in implementing these methods remains the same as for Kulkarni’s methods. A two-grid iteration convergent method for solving the system of equations based on these new methods is also defined. 相似文献
8.
9.
Let be the uniform triangulation generated by the usual three-directional mesh of the plane and let 1 be the unit square consisting of two triangles of . We study the space of piecewise polynomial functions in C
k
(R
2) with support 1 having a sufficiently high degree n, which are symmetrical with respect to the first diagonal of 1. Such splines are called 1-splines. We first compute the dimension of this space in function of n and k. Then, for any fixed k0, we prove the existence of 1-splines of class C
k
and minimal degree. These splines are not unique. Finally, we describe an algorithm computing the Bernstein–Bézier coefficients of these splines, and we give an example. 相似文献
10.