Paola Lamberti

Shape-preserving C 2 functional interpolation via parametric cubics

The paper proposes a method for the construction of a shape preserving C2 function interpolating a given set of data. The constructed interpolant is a parametric cubic curve. The shape of the curve can be easily controlled via tension parameters which have an immediate geometric interpretation. The approximation order is investigated and numerical examples are presented.

Numerical integration of 2‐D integrals based on local bivariate C 1 quasi‐interpolating splines

In this paper cubature formulas based on bivariate C1 local polynomial splines with a four directional mesh [4] are generated and studied. Some numerical results with comparison with other methods are given. Moreover the method proposed is applied to the numerical evaluation of 2‐D singular integrals defined in the Hadamard finite part sense. Computational features, convergence properties and error bounds are proved.

Numerical integration over polygons using an eight-node quadrilateral spline finite element

In this paper, a cubature formula over polygons is proposed and analysed. It is based on an eight-node quadrilateral spline finite element [C.-J. Li, R.-H. Wang, A new 8-node quadrilateral spline finite element, J. Comp. Appl. Math. 195 (2006) 54-65] and is exact for quadratic polynomials on arbitrary convex quadrangulations and for cubic polynomials on rectangular partitions. The convergence of sequences of the above cubatures is proved for continuous integrand functions and error bounds are derived. Some numerical examples are given, by comparisons with other known cubatures.

Tensioned Quasi-Interpolation Via Geometric Continuity

The paper proposes a method for the construction of C2 quasi-interpolating functions with tension properties. The constructed quasi-interpolant is a parametric cubic curve and its shape can be easily controlled via tension parameters which have an immediate geometric interpretation. Numerical examples are presented.

On the approximation power of bivariate quadratic C splines

Abstract In this paper we investigate the approximation power of local bivariate quadratic C1 quasi-interpolating (q-i) spline operators with a four-directional mesh. In particular, we show that they can approximate a real function and its partial derivatives up to an optimal order and we derive local and global upper bounds both for the errors and for the spline partial derivatives, in the case the spline is more differentiable than the function. Then such general results are applied to prove new properties of two interesting q-i spline operators, proposed and partially studied in Chui and Wang (Sci. Sinica XXVII (1984) 1129–1142).

B-spline bases for unequally smooth quadratic spline spaces on non-uniform criss-cross triangulations

In this paper, we investigate bivariate quadratic spline spaces on non-uniform criss-cross triangulations of a bounded domain with unequal smoothness across inner grid lines. We provide the dimension of the above spaces and we construct their local bases. Moreover, we propose a computational procedure to get such bases. Finally we introduce spline spaces with unequal smoothness also across oblique mesh segments.

Curve network interpolation by C1 quadratic B-spline surfaces

In this paper we investigate the problem of interpolating a B-spline curve network, in order to create a surface satisfying such a constraint and defined by blending functions spanning the space of bivariate C 1 quadratic splines on criss-cross triangulations. We prove the existence and uniqueness of the surface, providing a constructive algorithm for its generation. We also present numerical and graphical results and comparisons with other methods. Interpolation of a B-spline curve network by a surface based on C 1 quadratic B-splines on criss-cross triangulations.Proof of the existence and uniqueness of the surface and constructive algorithm for its generation.Numerical and graphical results and comparisons with other spline methods.

Near-best C 2 quartic spline quasi-interpolants on type-6 tetrahedral partitions of bounded domains

In this paper, we present new quasi-interpolating spline schemes defined on three-dimensional bounded domains, based on trivariate

On the construction of local quadratic spline quasi-interpolants on bounded rectangular domains

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