This paper presents a new fast and local method of 3D surface reconstruction for scattered data. The algorithm makes use of quasiinterpolants to compute the control points from a coarse to fine hierarchy to generate a sequence of bicubic B-spline functions whose sum approaches to the desired interpolation function. Quasi-interpolants gives a procedure for deriving local spline approximation met...

This paper deals with the topic of numerical integration on scattered data in Rd , d ≤ 10, by a class of spline functions, called Lobachevsky splines. Precisely, we propose new integration formulas based on Lobachevsky spline interpolants, which take advantage of being expressible in the multivariate setting as a product of univariate integrals. Theoretically, Lobachevsky spline integration for...

In this paper we generate and study new cubature formulas based on spline quasi-interpolants defined as linear combinations of C bivariate quadratic B-splines on a rectangular domain Ω, endowed with a non-uniform criss-cross triangulation, with discrete linear functionals as coefficients. Such B-splines have their supports contained in Ω and there is no data point outside this domain. Numerical...

In this paper we address the problem of constructing quasi-interpolants in the space of quadratic Powell-Sabin splines on nonuniform triangulations. Quasi-interpolants of optimal approximation order are proposed and numerical tests are presented.