Properly posed sets of nodes for multivariate lagrange interpolation in Cs

In this paper, we apply techniques from the theory of ideals and varieties in algebraic geometry to study the geometric structure of a properly posed set of nodes (or PPSN, for short) for multivariate Lagrange interpolation along an algebraic hypersurface. We provide a hyperplane-superposition process to construct the PPSN for interpolation along an algebraic hypersurface, and as a result, we offer a clear understanding of the geometric structure of the PPSN for multivariate Lagrange interpolation in C-s.