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

Abstract

In this paper local bivariate C 1 spline quasi-interpolants on a criss-cross triangulation of bounded rectangular domains are considered and a computational procedure for their construction is proposed. Numerical and graphical tests are provided.

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

“…Here we propose an example of approximation of the function f with singularities, by considering the bivariate Schoenberg-Marsden operator [3,8,10] (9) where…”

“…However some B-splines near the boundary of Ω have supports not completely contained in Ω. In [3,8,10] a local basis for S 1 2 (T mn ) is given, with all supports included in Ω.…”

“…Considering all pairs of adjacent triangles of T mn , together with the given C ℓ smoothness, ℓ = −1, 0, 1 across their common edge, we are able to count the constrained B-coefficients and therefore to detect the number of degrees of freedom, obtaining the space dimension (3).…”

NURBS on Criss-cross Triangulations and Applications

“…In particular, since we know that there exist quasi-interpolating operators exact on the space P 2 (see e.g [4, Sect. 2.4], [7,9,19]), then the optimal approximation order is achieved for sufficiently smooth functions, i.e. if ρ ∈ C 3 (Ω 0 ) there exists a constant C > 0 such that…”

“…[18]), surface reconstruction (see e.g. [1,19,20,21,22]). Here we want to give a further contribution to the researches on this topic.…”