Properly posed set of nodes for bivariate Lagrange interpolation

In this paper, in order to make a further research on the problem of properly posed set of nodes for bivariate Lagrange interpolation along an algebraic curve which was posed in [1], [2] and [3], we introduce the concept of weak Grobner basis and give a new method of constructing properly posed set of nodes for bivariate Lagrange interpolation along an algebraic curve, which generalizes the main result in [2].