Regular node configurations of quadratic curves for bivariate graded Lagrange interpolation are mainly investigated in this paper. By using Bezout theorem, a new constructive method of Quadratic-Superposition Process is presented in constructing three different kinds of regular node configurations via quadratic curves for bivariate graded Lagrange interpolation, i.e., circle, ellipse and hyperbola node configurations. Two examples characterizing irregular node configurations of a hyperbola and a parabola are included. An example of application is finally given, which illustrates in 3D that the constructed bivariate graded interpolating polynomial passes through the prescribed nine points to interpolate the bivariate real-valued function. The main conclusions of the previous study on this aspect are generalized by this method, which is also very meaningful.

regularnodeconfiguration, quadratic curve, bivariate graded Lagrange interpolation, Bezout theorem.