Curve network interpolation by C1 quadratic B-spline surfaces

•Interpolation of a B-spline curve network by a surface based on C1C1 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.

In 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 C1C1 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.