NURBS on Criss-cross Triangulations and Applications

Abstract

In this paper we consider and analyse NURBS based on bivariate quadratic B-splines on criss-cross triangulations of the parametric domain Ω0 = [0, 1] × [0, 1], presenting their main properties, showing their performances to exactly construct quadric surfaces and reporting some applications related to the modeling of objects. Moreover, we propose applications to the numerical solution of partial differential equations, with mixed boundary conditions on a given physical domain Ω, by using three different spline methods to set the prescribed Dirichlet boundary conditions.

On spline quasi-interpolation through dimensions

“…In particular, [62,79] deal with the construction and study of new quasi-interpolating operators, in [12,48,59] generalized spline quasi-interpolants are proposed, in [1,20,[49][50][51]53] new integration formulas based on spline quasi-interpolants are constructed, in [15,54,61,63,64,80,81,84] and [4,11] quasi-interpolants are used for the numerical approximation of the solution of differential and integral equations, respectively. Furthermore, in [7,16,17,23,52,65,66] quasi-interpolants are used in different areas of science and engineering: imaging, Computer Aided Geometric Design, industry, etc. Finally, in [19], we find some other interesting references to papers on the above topics.…”

Trivariate near-best blending spline quasi-interpolation operators

“…Some applications of QIOs concern for example the computation of multivariate integrals, the solution of differential and integral equations (see e.g. [12,13,15,16,17]).…”