Transformations between Bivariate Polynomial Bases

It is well known, that any interpolating polynomial p (x, y) on the vector space Pn,m of two-variable polynomials with degree less than n in terms of x and less than m in terms of y, has various representations that depends on the basis of Pn,m that we select i.e. monomial, Newton and Lagrange basis e.t.c.. The aim of this short note is twofold : a) to present transformations between the coordinates of the polynomial p (x, y) in the aforementioned basis and b) to present transformations between these bases