In this paper, we derive an explicit formula for the bivariate Lagrange basis polynomials of a general set checkerboard nodes. This generalizes existing results at Padua nodes, Chebyshev Morrow-Patterson and Geronimus We also construct subspace spanned by linearly independent vanishing that vanish nodes prove uniqueness in quotient space defined as with certain degree over polynomials.

We show that the intertwining of sequences of good Lagrange interpolation points for approximating entire functions is still a good sequence of interpolation points. We give examples of such sequences.

This note shows that a wide class of algebraically motivated constructions for Lagrange interpolation polynomials always yields a tensor product interpolation space as long as the nodes form a tensor product grid or a lower subset thereof.