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.

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In this paper we generate and study new cubature formulas based on spline quasi-interpolants defined as linear combinations of C 1 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 results illustrate the methods.

Please cite this article in press as: Dagnino, C., et al. Curve network interpolation by C 1 quadratic B-spline surfaces. Comput. Aided Geom. Des. (2015), http://dx. Highlights• 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. AbstractIn 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.