Real Root Solving for Bivariate Quadratic Equation System Based on Classification Method

In order to improve accuracy and topological stability in calculating the intersection of planar quadratic curves,we present a real-root solving method for bivariate quadratic equation systems,which is based on the classification of the quadratic curves.Each equation is first classified to several types of quadratic curves in the x-y plane according to its coefficients.Then transform the equation system into a quartic equation via the parametric equation of an arbitrary quadratic curve.Solve the quartic equation,and finally obtain the roots of the bivariate quadratic equation system.The experiments illustrate that our method can improve the accuracy,compared with the method of Wu.