NURBS on Criss-cross Triangulations and Applications

In this paper we consider and analyse NURBS based on bivariate quadratic B-splines on criss-cross triangulations of the parametric domain $Omega_0 = [0, 1] imes [0, 1]$, 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 , by using three different spline methods to set the prescribed Dirichlet boundary conditions.