Summary: ``Surfaces generated from bivariate tensor parametric splines are particularly interesting in geometrical modeling in the field of reverse engineering. Precisely in this paper we focus on a particular class of bivariate tensor splines defined by means of an integral operator and of two shape parameters. \par ``The main goal of the present work is to show and prove some geometrical properties of this class of bivariate splines, denoted by $\lambda$-$\tau$ VDIS, really important in the surface reconstruction.''